Exploring Linear Phase Speakers, Part I

I’m getting closer to experimenting with comparisons between earspeakers and real speakers. Since earspeakers (any headphones, really) are usually rather symmetric, I decided to physically change my desktop speaker setup to make it more symmetric, too. In the process, I also decided to retune my LXdesktop using the new tools added in Acourate V3 and V4: speaker linearization using a sinc pulse and the new acouStep tuning algorithm, which virtually eliminates pre-ringing in the tuned speaker response.

From my experience with the last tuning of LXdesktop, I realized that it’s much easier to tune speaker drivers by modeling them as components of a linear-phase crossover rather than a traditional minimum-phase crossover. Mathematically, modeling the drivers as minimum-phase crossover bands and then linearizing the phase afterward (as described in the Grimm Audio paper on the LS1 speaker) is equivalent to using linear-phase crossovers in the first place. In practice, however, speaker drivers that behave like linear-phase filters are much easier to time-align. Plus, the sinc-pulse linearization tool introduced in Acourate V3 makes it very straightforward to bring drivers to linear-phase crossover behavior.

The Idealized Speaker Model

Let’s state the goal first. Ideally, we want the entire speaker to behave as a linear-phase band-pass filter. Why “linear-phase”? Because linear phase guarantees constant group delay. That means that if the speaker plays a short wideband impulse, such as a click, all of its component frequencies reach the ear simultaneously. In other words, a linear-phase speaker preserves the waveform of transients in its direct sound (within its passband, of course), ensuring natural reproduction.

And why “band-pass”? Because the speaker is physically limited in the range of frequencies that it can reproduce. Even a big, high-quality speaker can’t cover the entire range from 0 Hz to infinity. First, this is not needed, because the range of human hearing is limited. Second, there are physical limits on how low and how high acoustic transducers can go. Going too low or too high requires too much energy and can easily overload the drivers. Thus, any speaker covers a limited frequency range, which technically makes it a band-pass filter.

Note that within the flat part of the passband, far away from the band edges, a minimum-phase filter also produces a similarly linear result. The defining property of a minimum-phase system is that its phase response is uniquely determined by its amplitude response (the two are related via the Hilbert transform), and so is its group delay. Where the frequency response is flat, a minimum-phase filter produces a flat (zero) phase response and a constant group delay. However, it introduces phase shifts as soon as the frequency response bends, and a band-pass filter, by definition, bends at both ends.

As a theoretical foundation for our experiment, we can use the open-access AES paper “Modeling and Delay-Equalizing Loudspeaker Responses” by A. Mäkivirta, J. Liski, and V. Välimäki, written as part of a collaboration between Genelec and the Acoustics Lab of Aalto University in Finland. The paper takes exactly this approach: it starts by modeling a speaker as an ideal band-pass filter.

This is fairly straightforward for a single-driver loudspeaker. In practice, however, most speakers use multiple drivers. Rare exceptions are speakers with a single full-range driver, and full-range electrostatic and magnetic planar speakers. All of my speakers are multi-driver, which means that their ideal counterpart, the band-pass filter, is in turn split into overlapping band-pass components. The splitting is done by crossovers. In my LXdesktop speakers, the crossovers are implemented in DSP, so they can have any desired behavior. Mäkivirta’s paper discusses the classic case of minimum-phase crossovers and describes the challenges of time-aligning them. One important property of minimum-phase crossovers is that, in a speaker with more than one crossover, they must be chained using a special topology:

This is because the phase shift created by the woofer-mid crossover must be applied to both the midrange and the tweeter drivers; otherwise, the parts of this composite crossover will not sum to a flat frequency response. Note that since the cutoff of the woofer-mid high-pass filter lies far below the tweeter’s band, this filter has no effect on the amplitude of the tweeter signal; it only affects its phase.

Linear-phase crossover filters do not have this issue because their effect on the phase is strictly linear: they only produce a pure time delay. As long as all the filters share the same delay (that is, their impulse responses are centered at the same sample position), they can be arranged in a simpler way:

The basic idea behind driver tuning stays the same, though. We do not consider the crossover filters and the speaker drivers separately. Instead, we try to coerce each speaker driver into becoming an ideal crossover component by developing a correction filter for it, based on the transfer function of the corresponding part of the ideal crossover.

Because of the extra complexity of minimum-phase crossovers, I use linear-phase crossovers in my project. In this case, each driver is coerced into its crossover component behavior using Acourate’s sinc-pulse linearization. This process takes two inputs: the actual response of the driver measured close to it, including the effects of diffraction at the baffle edges (note that a true near-field measurement, with the microphone right at the cone, would exclude them), and the desired crossover impulse response. The output is a filter that brings the driver as close as possible to the desired behavior.

The Catch at the Low End

There is one important caveat that Mäkivirta’s paper explains. Since neither the whole speaker nor its lowest-frequency component (in my case, the subwoofer) goes down to 0 Hz, there is a roll-off at low frequencies. For a subwoofer, or any large driver, the roll-off frequency can be quite low; let’s use 15 Hz as an example. The caveat is that if we represent this roll-off as a linear-phase filter, the filter has massive pre-ringing. If we represent it as a minimum-phase filter instead, group delay is inevitable because, as I noted earlier, in a minimum-phase system amplitude changes are unambiguously coupled with phase changes.

Let’s look at both alternatives. Below is the frequency response of a 4th-order Butterworth high-pass filter at 15 Hz:

And this is the RMS view of the impulse response (IR) of its linear-phase version:

We can see pre-ringing that lasts about 300 ms. Although its energy is concentrated around the cutoff frequency, where hearing is not very sensitive, with a capable subwoofer it is likely audible on bass-heavy transients, sounding like “breathing.” So, it is much more natural to use a minimum-phase filter for the high-pass part (after all, speaker drivers naturally tend to be minimum-phase devices). By definition, minimum-phase filters have no pre-ringing; however, the minimum-phase 4th-order Butterworth high-pass filter has a significant group delay, which reaches about 22 ms at 20 Hz:

Psychoacoustic research has shown that the human ear is relatively insensitive to the late arrival of low frequencies relative to the initial wavefront, especially with music and in typical rooms, where reverberation time at the low end can be quite long. For references, see another paper from the same Genelec–Aalto University collaboration, “Audibility of loudspeaker group-delay characteristics”, and Section 9.6.5 of the 4th edition of F. Toole’s “Sound Reproduction” book. The listening tests described in the paper found that group delay can exceed 10 ms below 200 Hz without the difference being audible, whereas in the 300 Hz–1 kHz range, differences became audible above just 1–2 ms.

Going back to the linear-phase high-pass filter: its 300 ms of pre-ringing far exceeds the span of pre-masking (backward masking) in human hearing, which, according to the studies reviewed in the same paper, is only about 5–20 ms. That explains why this pre-ringing is audible.

Practical Tradeoff: A Mixed-Phase Filter

Based on this, it is fine to keep the minimum-phase 4th-order Butterworth roll-off at low frequencies. This means that even our idealized, theoretical model of the speaker is not completely linear-phase. Instead, it is mixed-phase: it has minimum-phase behavior at the low end and linear-phase behavior above it. Mäkivirta’s paper comes to a similar conclusion: it is simply not practical to coerce the speaker into linear-phase behavior at low frequencies.

Here are the characteristics of our idealized speaker model. The frequency response is tapered at both the low and high ends:

The group delay is flat everywhere except at the low end, where it is determined by the Butterworth high-pass filter:

(Note that since this is a linear-phase filter for a 48 kHz sampling rate, centered at sample position 32,768, the group delay baseline is about 682 ms.) And this is the step response:

From this distance, it might look like a minimum-phase response. However, if we zoom into the onset, we can see some minimal pre-ringing from the linear-phase low-pass filter:

Its duration is well under a millisecond (a few periods of the cutoff frequency), and it is thus covered by the pre-masking mechanisms of human hearing.

Examining Linear-Phase Studio Monitors

As described in the Grimm Audio paper on the design of the LS1 speaker, its designers chose a minimum-phase LR4 crossover and then corrected its phase by applying an anti-causal all-pass filter (the sum of an LR4 crossover is a 2nd-order all-pass with a Q of 0.7, and its inverse is a non-causal filter, which is implemented as an FIR with added delay). Let’s see what other makers of linear-phase studio monitors do. I measured the behavior of two professional studio monitors: the Genelec 8331A and the Dutch & Dutch 8c.

The anti-causal all-pass filter introduces extra latency: from 4 ms to 30 ms, depending on the frequency of the crossover being compensated. Since this may be critical in live monitoring scenarios, manufacturers usually keep the natural minimum-phase behavior available, calling it the “low latency” mode.

Also note that this type of correction is only practical with DSP because it involves non-causal (look-ahead) filters, which can only be realized by adding delay. As a consequence, although both of these studio monitors accept a traditional analog input, it is there only for legacy compatibility. Their native input is digital, so the analog signal first goes through analog-to-digital conversion. Because of that, both monitors have a baseline latency of 3.2 ms, even in the “low latency” mode.

Genelec 8331A

This is a small desktop-size monitor with a bandwidth of 45 Hz to 37 kHz. The low end is extended by means of a port. Two notable design features of this speaker are the coaxial mid-tweeter driver and the two “racetrack”-shaped woofers at the top and bottom of the front panel, hidden under a cover.

This is the smallest speaker in Genelec’s “The Ones” series. The next model up (8341A) uses the same mid-tweeter driver, while the two larger models (8351B and 8361A) use a slightly bigger one. As the speakers get bigger, so do their woofers. This makes the largest model in the series look a bit unusual, earning it the nickname “Cyclops.” Even this big guy only extends down to 30 Hz, so covering the full audio range requires a subwoofer or the specially designed W371A, a stand with an integrated woofer. See the full specs here.

One caveat with these speakers is that to get full access to their features, including the ability to switch between the “low latency” and “linear phase” modes, the user needs to buy a proprietary “Loudspeaker Manager User Kit” (GLM), which alone costs as much as a mid-priced speaker:

To characterize the linear-phase correction filter, I measured the speaker in the same physical setup in the “low latency” and “linear phase” modes. Then I could simply divide the obtained transfer functions (complex division in the frequency domain, that is, deconvolution of the impulse responses) to derive the correction filter. Below are the phase and group delay differences between the two modes of the 8331A (the frequency response stays the same):

(Note that the group delay is contaminated by room interaction.) We can see that, similar to the Grimm Audio LS1 approach, the “linear phase” mode adds an anti-causal all-pass filter that corrects the phase deviation caused by the minimum-phase crossover. Genelec does not reveal which type of crossover the speaker uses. The manual only specifies the crossover frequencies: 500 Hz for woofer/midrange and 3 kHz for midrange/tweeter (both of the latter are part of the same coaxial driver). The all-pass filter applies up to 540° of phase rotation, so the crossover might be a combination of an LR4 (360° of phase rotation) and an LR2 (180°). I modeled an LR4 + LR2 crossover pair at the 8331A’s crossover frequencies. Here is the phase of the compensating all-pass filter for this model, overlaid with the actual filter of the 8331A:

The slope of the phase is very similar, but the details differ. This might be because Genelec uses different crossover types, and also because they employ a cleverly engineered approach with windowed IIR filters instead of a straightforward inverse FIR filter. Their design aims to achieve the lowest possible latency, even in the “linear phase” mode. According to the manual, this mode adds only 6.9 – 3.2 = 3.7 ms of extra latency. The RMS view of the all-pass filter’s impulse response shows that the pre-ringing is at -60 dB at approximately -3.7 ms relative to the peak:

This means that the extra delay is due to the filter itself. In particular, there is no evidence of delay caused by FFT buffering, which would be inevitable if the designers used a classic FIR filter applied via frequency-domain processing.

The choice of crossover frequencies also helped keep the filter short. However, I think that the 500 Hz woofer crossover frequency was actually dictated in large part by the physical arrangement. Since the woofers sit behind the front baffle, which acts as a waveguide for the coaxial driver (see this paper on the design of “The Ones”), they radiate mostly upward and downward, not toward the listener. Thus, the designers had to keep the woofers in the frequency region where their radiation stays omnidirectional.

We also need to confirm that the low end of the speaker stays minimum-phase in the “linear phase” mode. Indeed, it does. Since my group delay graph is contaminated by room interaction, here is a clean group delay graph of the 8331A in this mode from Genelec’s site:

The group delay starts to increase below 200 Hz, reaching 30 ms at 50 Hz, which is totally acceptable according to the research cited above.

Dutch & Dutch 8c

This is a big, full-bandwidth speaker (20 Hz to 20 kHz). Full-bandwidth output is achieved by integrating two rear-firing 8-inch subwoofer drivers in a sealed enclosure. They are designed to couple with the front wall (the wall behind the speakers), so the speaker should be installed close to it, about 20–80 cm away. This is an unusual recommendation because, normally, placing a speaker near a wall causes speaker-boundary interference response (SBIR) problems at low-mid frequencies. However, the clever design of this speaker mitigates this issue in two ways. First, the midrange woofer sits in its own sub-enclosure with acoustically resistive slots on both sides of the cabinet. The slots let out the delayed and attenuated rear radiation of the driver, which cancels the front radiation toward the back. This makes the woofer’s radiation pattern a cardioid over its entire working range (100 Hz and up). See the measurements in Erin’s Audio Corner for full details. Second, since the subwoofers themselves are so close to the wall, the first SBIR notch falls well above their 100 Hz cutoff, in the region covered by the cardioid midrange. Note that SBIR caused by large surfaces in front of the speaker (the floor!) is still present.

The acoustic design of this speaker is great, and so are its electronics. It features an Ethernet connection, which allows accessing its DSP controls from a smartphone app and manipulating the correction filters directly from Room EQ Wizard. Switching between the “low latency” and “linear phase” modes is done from the app. Let’s examine how the speaker’s response differs between the modes. As with the Genelec, the frequency response stays the same; only the phase, and consequently the group delay, changes:

(The ripple on the group delay graph is exactly the floor reflection I mentioned earlier.) Compared to Genelec’s all-pass filter, there is more phase rotation here: roughly two full turns. Unlike Genelec, Dutch & Dutch does not conceal the details of its crossover. The official documentation specifies that there are two LR4 crossovers: one between the tweeter and the woofer at 1250 Hz, and another between the woofer and the subwoofers at 100 Hz.

Just to confirm, I modeled the same configuration of minimum-phase crossovers and derived the compensating all-pass filter. It matches the measured all-pass filter of the 8c:

Due to the much lower crossover frequency, the all-pass filter’s impulse response is necessarily longer. Dutch & Dutch specifies that it adds 30 ms of delay (33.2 ms total versus 3.2 ms in the “low latency” mode). Interestingly, the RMS view of the filter’s impulse response suggests that it could probably be windowed to 8.5 ms:

(This graph overlays the measured response of the speaker’s all-pass filter, in green, with the theoretical one, in purple, which looks much cleaner.)

The designers may have chosen 30 ms either to achieve better frequency resolution of the filter, or simply because this is the granularity of their DSP processing (Martijn Mensink, the designer of the speaker, discusses the system’s latency here).

Preliminary Conclusions

Representing a loudspeaker as a mixed-phase band-pass filter makes it possible to achieve flat group delay over almost its entire working range, except for the bass region, where the ear is insensitive to group delay deviations.

Modern professional DSP-based studio monitors offer a tradeoff between the low latency of minimum-phase behavior and the better sonic precision of linear-phase behavior. Since linear-phase behavior inevitably introduces extra latency, it cannot be the default and must be enabled manually in the control software.

For LXdesktop, though, I don’t need to support a low-latency mode, so I can start with linear-phase crossovers, which make driver time alignment easier, especially without access to an anechoic chamber.

Earspeakers Calibration and Acoustic Measurements

The next step in my ongoing study of the phantom center and diffuse sound colorations on stereo speakers (see Part I, Part II) will be about the “ideal” conditions for reproducing the phantom center that can be created in a normal, non-anechoic room by means of earspeakers. These listening devices are also known in research circles as “free-field” or “extraaural” headphones. Their main difference from regular headphones is that they create much less occlusion of the ears. This design factor allows them to be used in situations where we need to compare sound from headphones with external sounds directly. With earspeakers this is possible because the listener does not have to take them off in order to be able to hear the external sound practically unaffected by the headphones (although, as we will see, this is not entirely true).

And this property of earspeakers is really unique. Even open-back circumaural headphones of lightweight construction, for example electrostatic headphones, do attenuate high frequencies severely (for example, see the paper “Comparing the effect of different open headphone models on the perception of a real sound source…”) and also affect sound localization of external sources (see the paper “The Influence of Headphones on the Localization of External Loudspeaker Sources”).

I read about a study in which the researchers actually tried to compensate for the headphone-induced attenuation by applying a reverse filter to the speaker signals. I tried that myself with the Sennheiser HD800. However, I was not satisfied with the result for two reasons:

1. Applying significant high-frequency amplification (an inverse filter for the occlusion from the headphones) to the sound from speakers evokes stronger room reflections and the overall result does not sound fully natural.

2. Since having headphones on the head also affects other components of the HRTF such as ILD and ITD, external sounds filtered by open-back headphones still are not perceived the same as without them, even with the spectrum being compensated. In particular, this affects the phantom center because it relies on the symmetry of the stereo pair.

So, having your ears unoccluded while experimenting with the phantom center is actually a good idea. The problem is that all models of acoustic headphones that leave your ears unoccluded do look really strange, if not completely weird (see this open-access paper for photos). There are only a couple of commercial models, namely: AKG K1000 (discontinued), Sony PFR-V1 (discontinued), MySphere 3.2 (still in production; however, is rather expensive). These are very niche products, and the discontinued models are hard to find for a reasonable price.

However, AR/VR researchers do love earspeakers because of their property to allow hearing both natural and synthesized acoustic reality at the same time, creating “augmented reality.” And researchers come up with various designs and ideas for substitutes. One interesting example is a modification of AKG K702 headphones with custom earpads that are cut out in front and in the back (see “DIY Modifications for Acoustically Transparent Headphones”). I don’t have the K702, but I do have the K701 which is really the same model, just without the detachable cable. So along with the K1000 and the PFR-V1 I will try these as well.

I emphasized “acoustic headphones” in the paragraph above because another well-known way of having ears unoccluded is to use bone conducting headphones. I considered them initially, but then rejected them for a number of reasons:

1. I don’t know how to calibrate them properly, as bone conduction works differently from acoustic transmission.

2. They usually use wireless (Bluetooth) connection which adds a lot of latency.

3. According to this research, “BC [bone conducting] earphone can’t provide enough interaural level difference (ILD)” and thus can affect perception of phantom sources, too.

But what about all these wireless earbuds with the “transparency” feature? Sure, they have lots of microphones inside and outside, and a DSP. In theory, they could implement an acoustic pass-through that is indistinguishable from wearing no earbuds at all. However, the question is why anyone would need that (apart from VR researchers). The goal of engineers working on wireless earbuds is to ensure that the user does not get hit by a car while listening to their favorite podcast, and that the user can communicate with a flight attendant while having airplane engine noise in the background—that’s it. For these scenarios, earbuds don’t actually need to replicate the true transfer function of an unoccluded ear. In fact, the DSP may artificially boost up certain frequency bands in order to improve the external voice clarity, which is the opposite of what I need for my research.

We see that achieving high-fidelity acoustic transparency is non-trivial. So the goal of the exploration described here is to measure the key aspects of earspeakers in order to ensure that I’m aware of their shortcomings. Also, since I bought the K1000 and PFR-V1 second-hand, they are a bit old (it’s practically impossible to buy them in new condition because they have been discontinued) and thus may have some aging-related problems. Another task is to check how the “transparentized” K701 compares to real earspeakers.

This is what I measured for all three headphones:

• electrical impedance;
• usable frequency range;
• distortion;
• cross-talk;
• acoustical transparency.

Also, since I tried using miniDSP EARS (or is it HEARS?—that’s what is written on the label that I see on my device) for some of the measurements, there are some notes about this peculiar acoustic tool.

Electrical Impedance

This measurement is needed to ensure that the drivers are matched. For this, I used QuantAsylum QA490 unit. My AKG K701 shows good alignment:

However, in the PFR-V1 due to its age the left coil shows lower impedance than the right one:

Thankfully, the difference in the impedance seems to be constant across the frequency range which means we can compensate for that by increasing voltage (volume level) into the right speaker. I have found that I need to add +2 dB to the right channel.

The AKG K1000 is more interesting because it uses a 4-pin XLR plug. I don’t have an adapter from it to a TRS. I first tried to use QuantAsylum QA460 (a speaker amplifier), however I found that the nominal impedance of the K1000 is 120 Ohm, and that’s too high for the default value of the current sensing resistor in the QA460—0.01 Ohm. QuantAsylum’s Matt recommends that the resistor value should be 100 times less than the load.

I did not want to resolder the resistor just for this measurement, so instead of the QA460 I used Dayton Audio DATSv3. It worked fine and has shown that the K1000 also has an imbalance between its speakers. Unlike the PFR-V1, the imbalance of the K1000 is not uniform and is mostly pronounced at mid to low frequencies:

Sorry, DATS uses a bit less readable palette. So, for the K1000 I ended up adding a low shelf filter at 2.36 kHz, Q 0.8, gain +2 dB, and a peak at 3.3 kHz, Q 5.5, gain +3 dB. All this alignment was checked acoustically on miniDSP EARS and Neumann KU-100.

Note that although I read in many places that AKG K1000 are “hard to drive”, and sometimes people have to connect them to speaker amplifiers, I did not have any issues with driving them. I used two headphone amplifiers: the SMSL SP200 with “high gain” setting driven from the XLR input, and Monoprice Monolith (THX AAA 788) driven from its digital input. Neither of the amplifiers had any problems driving the K1000 to 100 dB SPL and even higher. That’s the level which is enough for my needs since that’s 100 dB near your ears, not at a speaker one meter away.

Usable Frequency Response

Since earspeakers operate in a free-field condition—they do not create a pressure chamber on the listener’s ear—all constraints of loudspeaker drivers apply to them. Due to the small surface area of the driver, they can’t be efficient at low frequencies. Typically, small (3"–4") loudspeaker drivers that must produce bass are designed to have wider excursion so that they can push and pull air more efficiently. However, it’s hard to design a miniature headphone driver this way.

In an attempt to overcome this limitation, Sony PVR-V1 has a “bass duct” which is intended to be placed near the ear canal entrance:

This creates challenges for measurement because artificial pinnae are simplified and are made of silicone thus their retention force is much lighter that of a real ear. So I tried measuring them both on the miniDSP EARS and the Neumann KU-100. The results are actually consistent and show severe bass limitation:

Note that for this measurement I used the miniDSP EARS with “raw” calibration file. I did not intend to produce a measurement comparable with data from other rigs, I just wanted to figure out where they start to roll off low frequencies. The result looks similar to free-field measurements performed long ago by Rin Choi, modulo the peak between 4–5 kHz which comes from EARS. Basically, the PFR-V1 earspeakers are only usable down to 650 Hz (-6 dB from the midrange) as trying to compensate for bass loss via equalization will just drive up distortion in the driver.

The driver of the AKG K1000 is much better, and its bass starts to roll off only below 90 Hz. Although Hans Zimmer would not endorse use of these headphones for listening to his music, this range is probably enough for classical music.

This is also obtained on EARS with “raw” calibration. Note that apart from the lack of standardized calibration, both miniDSP EARS and Neumann KU-100 are perfectly adequate for measuring earspeakers because their operation does not depend on replicating the true impedances of a human ear canal.

The AKG K701 with cut out earpads loses its sealing completely and thus starts to roll off the bass early:

For comparison, this is the FR of the left speaker for all three earspeakers:

All in all, I think the K1000 is the most adequate earphone in terms of the usable frequency bandwidth.

SPL Calibration of miniDSP EARS

Yet another myth I had read, apart from the K1000 being hard to drive, is that the miniDSP EARS is impossible to calibrate for loudness. This is how I performed their SPL calibration. I found that the silicone ears can be easily removed, opening access to the microphone capsule:

The diameter of its wrapping grommet matches the size of the Beyerdynamic MM-1 microphone so I used its adapter for coupling the acoustic calibrator:

I found that the capsules are well-matched. However, the sensitivity factor specified in the calibration files is wrong which makes the SPL level reported by REW to be off by about 20 dB. I have switched the EARS to 0 dB gain and edited the calibration file to specify correct sensitivity factor: 2.7 instead of 0.1 dB.

One interesting thing that I did not know before is that on Windows at least, REW monitors the software microphone gain and adjusts the reported SPL number accordingly. This is a good thing because it allows the user to adjust the gain so that the sound captured by the EARS at high SPL does not get clipped in the digital domain.

Distortion

I was mostly interested in whether my earphones have any significant distortion that can affect loudness perception. By “significant” I mean “higher than the room noise level.” Since earphones offer no isolation from the room noise, this criterion works well. I ensured that the room noise was 42 dB or below (C weighted) while I was measuring.

When measuring using the KU-100, the distortion products for all three headphones were below the noise floor in the mid-to-high frequency range. I couldn’t measure bass distortion adequately due to higher level of ambient noise in this region. Since with the open design the drivers have to work hard, I would expect that they distort. However, it is known that our hearing system is much less sensitive to low-frequency distortions, and they also do not play an important role in my experiments, so that’s not a problem.

However, with the miniDSP EARS there were peaks of the 2nd harmonic between 4–5 kHz. It was suspicious to me that this happens the same way for all three headphone models. I also tried placing Genelec 8331A speaker close to EARS and measuring it, and it has shown the same peak. So I think what happens here is that the construction of the silicone pinnae of EARS creates a resonance in that region and that overloads the microphone even when the resulting peak is at modest 100 dB SPL. That means, EARS are not suitable for measuring headphone distortion.

Cross-talk

That’s a practically interesting measurement. Since earphones are “open” designs, there is cross-talk by definition. Will this create a coloration of the phantom center? I measured it on the KU-100 in order to create a realistic head shadowing condition.

What I have found is that the level of cross-talk is actually quite low. If we consider the cross-talk from my speaker setup and hypothetically reduce it by what can usually be achieved with application of Cross-Talk Cancellation (CTC) in a non-anechoic room, the cross-talk from earspeakers is still below that level.

By the way, while exploring this, I have discovered a nice feature of REW that I did not know about for all these years of using it. On the SPL and phase graph it’s possible to select a frequency range by dragging the mouse cursor with Shift key pressed, and this shows min, max and average SPL for that region. So calculating the average cross-talk level consists of two steps:

1. Take the difference in dB (A / B) between the contra-lateral and ipsi-lateral transfer functions (“Trace Arithmetic” in REW). Since there are HRTF-induced notches and peaks all over the frequency range, applying 1/3-octave smoothing makes sense.

2. On the calculated SPL graph, select with Shift the frequency range of interest (I usually use 100–14000 Hz to avoid areas where SNR is lower) and read the average SPL.

If we look this way on the SPL graph of the difference between the ipsi- and contra-lateral sound for my desktop speakers (measured on the KU-100), it shows the effect of the head shadowing (the more shadowing—the better). The average level of shadowing is about 11 dB, and it is slanted towards high frequencies:

Below is a table comparing the average shadowing among earspeakers:

Earspeaker	Avg. shadowing, dB
AKG K1000	19
AKG K701 DIY Transp.	48
Sony PFR-V1	36.5

If we consider the PFR-V1, their shadowing is 25 dB better than on external speakers. Considering that CTC algorithms for loudspeakers can at best remove about 20 dB of cross-talk, Sony already performs better.

The AKG K1000 is the worst performer, probably due to large size of speakers and completely open design. On the graph below we can see that at 3 kHz its shadowing drops and matches the shadowing from speakers:

(The numbers on the legend correspond to the 3 kHz point).

So, probably it is a good idea to apply CTC to the K1000. It appears especially effective because traditional nearfield CTC requires head tracking since the head is constantly moving relative to the speakers. However, since the K1000 always moves together with the head, the CTC filter remains constant.

However, so far I did not succeed with creating a CTC filter for the K1000. I tried using a method based on actual HRTF measurement. That’s because the proximity of the earspeaker to the head makes the transfer function of ipsi-lateral crosstalk highly dependent on the parameters of the head.

Also, unlike the louspeaker situation, the wavefront which reaches the opposite ear is not planar—it is spherical. Because of that, when measuring the actual transfer function at the opposite ear of the KU-100 I can see a lot of group delay deviations, and the resulting impulse response does not even have any distinctive peak—it looks more similar to ripples on a sea surface. Because of that, achieving correct time alignment is insurmountably challenging. I will try harder next time.

Acoustical Transparency

This is an important consideration since I plan to switch between playback in earspeakers and loudspeakers (that’s the whole point of using earspeakers in the first place!). As I mentioned in the beginning, even open-back headphones create significant alterations to the frequency response of external sources, as well as to their ITD and ILD. Earspeakers are a bit more transparent but not entirely.

A paper by C.  Porschmann “How Wearing Headgear Affects Measured Head-Related Transfer Functions” measured how wearing the AKG K1000 affects the HRTF of the KU-100. I also measured my earphones on the KU-100, using Genelec 8331A as an external sound source:

I compared the measurements from the paper with mine (using the SOFA files they have provided) and discovered that although the IRs for bare KU-100 look quite similar to my measurements—modulo the effect of a different distance from the speaker to the head—the measurements with AKG K1000 on the head look significantly different. The peaks and notches simply do not match. I started exploring this discrepancy and realized that the acoustical shadowing that the K1000 creates is highly dependent on the angle at which they are opened.

I think this leads to the important realization that measuring these occlusion transfer functions must always be done for the current setup and can’t be considered as “generic.” I suppose, the external speaker directivity also may heavily influence the result, thus occlusion transfer functions measured with a Genelec speaker will also differ from those measured using an LXmini. Because of that, let’s consider the compensating transfer functions for these three headphones just as a guideline.

Besides the data from the paper on headgear, another paper which had introduced the idea of the “transparent” K701 (“DIY Modifications…”) also has measurements of them and the K1000 on the KU-100. However, these measurements are from certain directions: front, back, and top only. Note that these two papers calculate the transparency in an opposite way. The headgear paper divides “reference” (bare head) HRTF by the HRTF of the head with the gear on, while the K701 paper carries the division the other way around. In my view, since we need to compensate for the occlusion by applying a reverse filter to the external speaker, we need to follow the headgear paper approach.

Below are occlusion graphs for each earspeaker, for frontal (0°), side (42°), and rear (138°) directions. For side directions, this is for the ipsilateral ear only. Also, for compatibility with the graphs from papers, my graphs are time windowed for 3 ms and 1/3 octave smoothing applied.

We can see that Sony PFR-V1 is the most unoccluding earspeaker, with AKG K1000 coming next, and the “DIY Transparent” K701 modification is actually not so transparent for rear sources.

Conclusions

Unfortunately, none of the earspeakers is an ideal one. Here is their comparison on the acoustic parameters:

Earspeaker	LF cutoff, Hz	Shadowing, dB	Transparency
AKG K1000	~60	19	Fair
AKG K701 DIY Tr.	~300	48	Poor
Sony PFR-V1	~700	36.5	Good

Thus, for simulating anechoic listening on speakers, it makes sense to use the Sony PFR-V1 as much as possible, by limiting the sound sample choice according to the headphone bandwidth. One caveat here is that by cutting out this frequency range we sufficiently limit the bandwidth below 1.5 kHz where the auditory system uses ITD for sound source localization.

The AKG K1000 can be used for wider selection of samples and does not have any issues providing ITD cues; however, we need to take care about reducing its cross-talk, and compensating for partial loss of transparency when comparing its output with external loudspeakers.

Spectral Correction of Phantom Audio Sources, Part II

Stereo Setup with LXdesktop

Now let’s experiment with real speakers in a real room. For this experiment, I re-arranged my LXdesktop setup into a more conventional placement and orientation. Because my desktop setup sits close to the walls, I positioned the speakers to minimize strong reflections in the first 15 ms. The best configuration delayed the first strong reflection to 12 m, resulting in a 42° speaker angle and 74 cm listening distance. Below are ETC graphs for the left and the right speaker:

Next, I loaded the original LXmini filters into a convolution plugin hosted by Reaper. I used a physical center speaker—a Genelec 8331A—to find the right room curve, first equalizing it for a flat response. Then, starting from the “Harman target curve” that I’ve got from ASR I slightly adjusted the high frequencies roll-off in order to compensate for the near field speaker location. The resulting “nearfield Harman” target curve looks like this:

I then used this curve to equalize both LXdesktop speakers using simple IIR filters generated by REW. I used microphone oriented towards the ceiling in order to avoid coincidental high frequencies bump for the center speaker:

(This photo is from early experiments, the LXdesktop speakers are in their original “wide” setup). After experimenting with the Genelec, I realized that it sounds a bit different from LXdesktop likely due to difference in the radiation pattern. So I built a third LXdesktop speaker just to avoid this difference. The resulting test setup is below:

This is how all three speakers are tuned with respect to the target curve (with 15 cycles of Frequency-Domain Window (FDW) applied):

As you can see they are set up to measure as close as possible to each other.

Notes on Loudness Equalization Approaches

A phantom center and a discrete center equalized to the same linear frequency response do not sound the same. We are interested in matching their perceived sounding, not the frequency response of their linear model as measured by an omnidirectional microphone. If I try to equalize the centers based on the conventional frequency response measurement using anthropometric KU-100 or even binaural microphones, the perceived sound will still not match exactly. After all, non-linear effects, the radiation pattern, and the resulting room reflections of the sound from the speakers play very important role in the final perception of the sound image, and they are not the same between a physical center produced by a single speaker and the phantom center produced by a pair of speakers. Even more distinctive would be the sound for the diffuse field scenario.

We can try to approach the equalization in a controlled way from subjective perspective. The method proposed by D. Griesinger for headphone equalization and implemented by his Sonic Focus app can be employed for matching the perceived sound of speakers. It’s actually even more straightforward for them. Griesinger’s idea is that a human can listen to short 1/3 octave filtered bursts of pink noise and compare their loudness. For the purpose of headphones tuning, the human compares loudness between the current band and the reference band (500 Hz) which results in building an equal loudness contour—a subjective EQ. Others and I have tried this approach (see this MSc thesis by T. Kinnunen). It requires significant effort and yields inconsistent results.

With speakers, however, we don't need to build a loudness contour. We can simply switch rapidly between the reference and target speakers to compare the loudness of each 1/3-octave band directly—I will refer to this later as “modified Griesinger's method.” The results of this tuning are consistent, however it still requires time and effort to go over every 1/3 octave band and meticulously tune the equalizer for it. In addition, one needs to go back and forth multiple times because the bands of human hearing do not necessarily match this fixed 1/3 octave quantization and tuning one band may affect the perception of loudness for adjacent bands. However, I like the overall idea with using perceived loudness as the metric because it takes into account many factors such as non-linearity of speakers and the effects of the room and of the comb filtering.

Can we measure loudness objectively, similar to frequency response? Of course, we can to some extent because loudness is a very important metric for hearing safety, and acousticians do work hard on making the measurement process as automatic and repeatable as possible. One of the methods which is an international standard is the Moore-Glasberg model (ISO 532-2) which can be applied to tones, broadband noises, and complex sounds with emphasized spectral components. The method simulates the highly non-linear, level-dependent compression of the cochlea. There is an implementation of this method within MATLAB’s Acoustic Toolbox—the acousticLoudness function. As you can see from examples, for ISO 532-2 it is possible to obtain a nice graph of loudness per frequency, which looks similar to the frequency response, but in fact is a psychoacoustic measurement. The paper by V. Gunnarsson which I referred to in the first part of this post also employs ISO 532-2 loudness model for assessing the discrepancy between phantom and physical sound sources.

There is a catch: loudness is measured in sones, which can not be directly converted into the decibel values needed for equalization. There are only “rules of thumb,” for example “a 10 dB increase in physical energy roughly doubles the perceived loudness.” But that depends on the frequency range that we are working with and possibly the room conditions. In addition, as I mentioned, the loudness model is non-linear by itself (in order to simulate human hearing correctly). Thus, the character of the sound largely affects the resulting loudness perception.

Gunnarsson sidesteps the issue of translating sones into decibels for equalization by not actually using the loudness model to calculate the correction filters. Instead, he calculates the filters using the composite summed power spectra of both ear signals. Please refer to his paper for more details on this approach.

I decided that instead of using a proxy measurement for loudness, we can automate loudness matching. In some sense, this is similar to performing manual loudness matching by ear as in the modified Griesinger’s method. But instead of doing this manually, we solve a minimization problem for the difference between two loudness curves by applying equalization and adjusting the gain of its bands until we reach the desired tolerance. Basically this is still “matching by ear” but performed by a computer.

There is another hurdle. The ISO 532-2 model expects a measurement microphone with a flat transfer function and internally applies its own pinna gain. But we are using a KU-100 dummy head to correctly capture stereo cross-talk, meaning our measurement is already pre-emphasized by the KU-100's physical pinnae. Since the loudness model is non-linear and mimics the effects of masking and cochlear compression, the presence of double pinna filtering will affect the result in a non-obvious way. Because the loudness model is non-linear, this double pinna filtering corrupts the result. Unlike a purely Linear Time-Invariant (LTI) system, we cannot assume the pinna filter will cancel itself out when we subtract the two curves.

That means, before feeding any readings from KU-100 into MATLAB’s acousticLoudness, first we need to remove the pinna filtering. Thankfully, there is an easy approach to this called free-field equalization (FF-EQ). We basically measure the transfer function of KU-100 for the frontal sound source, smoothen it, and use it as a calibration function. That means, the output from a physical center will be seen a flat line—well, not entirely flat because we do not intend to remove the frontal notch fully, as this will inevitably introduce coloration and skew the results from the loudness model. After applying FF-EQ, the outputs from all other directions around KU-100 will be relative to the frontal source.

I used Claude Code to help me to write the automated loudness matching MATLAB script. Claude wrote a function loudnessmatch which takes as parameters:

• the SPL level of the “reference” FF-EQd binaural recording (because perceived loudness depends on it, recall equal-loudness contours);
• the reference recording itself (for example, the recording from a physical center speaker);
• the recording of the source system that we need to equalize to the reference.

And then the function uses a 29 band 1/3 octave IIR equalizer (similar to what Griesinger’s DGSonicFocus app employs), and carefully minimizes the difference in calculated loudness between the reference and EQ’d source recordings. The function outputs both the values of the equalizer bands and the impulse response of the filter.

Anechoic Simulation of Loudness Matching

Before jumping forward to measure and adjust loudness between physical speakers I decided to run a quick test on the same Ambisonics simulation of KU-100. It was interesting to compare the difference between impulse responses (linear model) with the equalization needed to match loudness (non-linear human hearing model).

This is what we have for the physical vs. phantom center:

And this is for the “diffuse field” (actually, two rear speakers):

I used 80 dB SPL as the source loudness. In theory, when playing audio at a sufficiently different level (e.g., 65 dB SPL or 95 dB SPL), the target loudness matching curve would change (again, see the equal-loudness contours). Thus, the loudness matching approach is sort of an optimization compared to purely linear matching.

As we can see, for the physical vs. phantom center loudness matching has the midrange peak attenuated by about 2 dB and also represents a more regularized curve. For the “diffuse field,” loudness matching also smoothens the dip and makes it slightly less pronounced. Also, the region between 6–10 kHz is amplified instead of being attenuated as frequency response measurement suggests. I guess, this has something to do with equal loudness contours. Anyway, it’s interesting to figure out how does its prediction compare with what I can hear.

Physical Center vs. Phantom Center on Speakers

Matching the frequency response of stereo speakers to a center speaker does not make the phantom center sound like a physical center. To confirm this, I matched their SPL levels by using a measurement microphone while playing correlated signal from the stereo pair.

Then I started playing various mono recordings of acoustic instruments (from Alan Parsons’ “Sound Check” CD) and pink noise, and noticed obvious differences in the sounding of the physical and the phantom center:

• the phantom center sounds wider;

• it gets automatically “anchored” to the center speaker even when in fact the center is muted (I had to check myself a couple of times at first—I was sure that I forgot to mute the center);

• if I close my eyes, the phantom center might be perceived as elevated, depending on the sound being reproduced;

• the tonality is indeed different, which is especially obvious for the pink noise signal. The interesting thing is that the phantom center sounds “softer” and more pleasant to my ears. Maybe that’s why a lot of music producers still prefer it to the physical center. Going a bit ahead, this is caused by differences in IACC, I will explore that in subsequent posts.

So, yes, the “phantom image problem” is real and even with speakers that have narrow, directed radiation pattern the sound from the opposite speaker creates comb filtering. However, even the single, physical center is not immune to the comb filtering problem because the sound from it reflects from nearby surfaces and from the listener’s torso! This can be easily confirmed by stepping towards and away from the speaker. One may argue that this comb filtering is “natural”, however it is not helping me to “unhear” it!

Linear Model

First, let’s now compare the result from the anechoic simulation of KU-100 from the first part of the post with a measurement on a KU-100 in my room:

Below is the comparison between them, the KU-100 room measurement is averaged for the left and the right ear, and I have applied Psychoacoustic smoothing in REW to the result. I also included the Linkwitz EQ curve:

We can see in a room the segment of 300–3000 Hz matches the Linkwitz EQ curve closer than of the anechoic measurement using an ideal point source. Obviously, the room has its influence on the bass region making sources at different locations to produce different sound pressure, so that region is uneven. The high frequency bump is also observed in the room, and the Linkwitz EQ is missing it.

I also measured the same setup using in-ear microphones, and derived the compensation the same way. The result is close to the KU-100 measurement despite the fact that KU-100 is just a head without torso:

What about stereo phantom source to physical center compensation in a real room? For a reference, I used graphs from the paper by B. Shirley et al. “The Effect of Stereo Crosstalk on Intelligibility…” which Toole cites in his book (and also re-uses their graph for illustrating the “phantom image problem” in a non-anechoic room). The graph below compares the following curves: compensation needed for KU-100 and for me in a real room, and Shirley’s result (recall that graphs in my posts are all “EQ graphs,” thus where the original transfer function has a dip, on my graph you see the inversion of it—a hump):

We can see that in my room the location of the cross-talk interference dip is at a different frequency range, only partially overlapping with the Shirley’s result, and it is also wider.

Loudness Model (Non-Linear)

Now a more interesting and practical comparison in terms of perceived loudness. I used an excerpt of 5 seconds of pink noise recorded from each of the sources using KU-100 with SPL of 80 dB in front of the head. The noise was then “free field equalized” (FF-EQ) using the compensation curve obtained during the anechoic experiment. After my loudness matching script has produced the compensation EQ, I loaded it into the Reaper and repeated the recording and measurement in order to ensure that the EQ indeed compensates modelled loudness. It all worked out quite smooth! Below is the graph comparing loudness alignment needed for the phantom center vs. physical center of the anechoic simulation, real KU-100 in my room, and also the linear measurement of KU-100 in my room:

We can see that EQ by loudness is more gentle. It’s interesting to note that loudness matching for the anechoic simulation looks more similar to simple linear matching from room measurements of KU-100.

And then, since my head is a bit different from KU-100, I used DGSonicFocus to check the loudness of each band between the phantom and physical center as perceived by my ears. I have noted some slight differences and applied some compensation:

The differences are quite minor, so I ust conclude that the ISO 532-2 model works really well in this case.

Listening Impressions

Of course, after this meticulous matching of the phantom center it’s interesting to compare how does it sound. Since we only considered the perceived loudness aspect and attempted to fix the spectral coloration, there are still other factors that can contribute to perceived sonic differences.

Comparing full stereo recordings is pointless here; a single physical center cannot convey the intended width and depth of the mix. So I only checked mono dry recordings of vocals and instruments from that Alan Parsons’ test CD.

The most striking difference is of course in the perceived width. A phantom center sound source is always perceived as wider than a physical speaker. For some instruments, especially playing in the lower frequency range this creates much more pleasant feeling of envelopment by its sound. However, for physically smaller instruments like flute or tambourine this widening sounds artificial and make the sound image more blurred. A mono recording of a snare drum completely lost its dry character when played over stereo speakers. I suppose, such sharp transients interact more actively with the room than sounds of more stationary character.

Another difference that is easy to spot is the image stability. In my near field setup moving the head laterally completely changes the location of a phantom center source, while the physical center unsurprisingly remains stable.

A more subtle difference is that dry instruments played via physical center speaker sound a bit “punchier”, with more “in your face” sound. I guess, whether it’s good or not depends on whether one wants “realism” vs. “relaxation.”

As a side note, I think, these differences make it clear why music producers (as opposed to movie dialogue and FX producers) all express greatly varying opinions on the use of the physical center in modern multichannel and object-based recordings. On one hand, it improves the clarity and the “presence” of the rendered source, but on the other hand it could be too much “real” to the point of being disturbing and unpleasant. That’s why it becomes an art in itself how to support the discrete source with phantom source, or how to play with the “sound width” parameter in object-based representation in order to achieve the desired character of the reproduced source.

Finally, the loudness-based equalization almost completely fixed the problem of phantom center elevation. Even with eyes closed—to avoid visual anchoring of the sound to the center speaker—both physical and the phantom center sources are perceived at the same height. With the only exception of the pink noise signal! This is a true acid test for source similarity. Not only the tonality difference due to comb filtering could still be heard, but the perceived height was also not matching, with phantom center sounding elevated compared to physical center. We probably have reached the limit of what can be achieved with a phantom source.

Diffuse Field Simulation on Stereo Speakers

The reference source was the same pair of stereo speakers but facing the back of KU-100 (I have turned it around). The test signal was decorrelated pink noise, at the same output level. Matching loudness in this case required building a more divergent EQ curve. We could see that from the anechoic simulation example, and in the actual room the result is almost the same. Let’s compare the EQ curve obtained in the room with the anechoic curve and the diffuse field compensation curve proposed by Gunnarsson:

We can see that the curve from Gunnarsson’s paper is indeed diffuse field because it lacks the head interference dip.

Making any direct comparisons between the “real” source and its rendering via stereo speakers for this case is quite hard in my setup. However, I relied on Griesinger’s original method of creating an equal loudness curve. I created one for physical behind the head location of speakers (staying with my back turned to them) playing uncorrelated (between left and right) noise bands, as a “reference,” and then turned facing them, and corrected the algorithmically produced curve to yield a similar loudness contour. Here is my final curve:

I suppose, diffuse field (in my case, it’s not even a proper diffuse field since it’s not all around me) is perceived a bit differently from point sources, and because of that the loudness model does not exactly match my personal perception.

Then I tried several tracks that feature off-stage, behind the back, and very diffuse sources:

• left/right imaging test (Track 10 from “Chesky Records Jazz Sampler & Audiophile Test Compact Disc, Vol. 1”);
• tom-tom drum naturally panned around (Track 28 “Natural stereo imaging” from “Chesky Records Jazz Sampler & Audiophile Test Compact Disc, Vol. 3”);
• music instruments performed all around the microphone (Track 47 “Generic Image and Resolution Test” from “Chesky Records Jazz Sampler & Audiophile Test Compact Disc, Vol. 2”);
• F16 and Tornado jets flying by overhead (Track 88 from the “Sound Check” CD by Alan Parsons and Stephen Court);
• Track 1 from “Ambient 1: Music For Airports” by Brian Eno;
• the recording of rain featured at the very end of the movie “Memoria” (2021).

The employed diffuse field compensation noticeably improves presentation of “off-stage” sources and makes overall sound more enveloping. I have combined it with the phantom source EQ by putting the diffuse sound compensation into the side channel of the Mid-Side equalizer. It might sound a bit unusual because the Side channel by definition emphasizes anti-correlated rather than uncorrelated signals. However, commercial music producers typically avoid having strongly anti-correlated signals because they: a) sound really weird, and b) disappear completely when the stereo track gets downmixed into mono. Thus, typically the side channel contains just hard panned left and right channel sources (with the right channel being inverted) and also weakly anti-correlated sources, that is—the ambience.

The thought about hard panned sources had brought me to one realization which required a bit more experimentation.

The Effect of Mid-Side EQ on Hard-Panned Sources, and Up/Downmix Alternative

In commercial stereo recordings it is not unusual to encounter “engineered” (as opposed to “live recorded”) music where the producer panned some instrument to one channel exclusively (also known as “hard panning”). These kinds of mixes were used actively in the early days of stereo, for example on such tracks as:

• “Anna (Go to Him)” by Beatles from one of their first albums (1963);
• “The Time Has Come By” by The Chambers Brothers (1967);
• “Space Oddity” by David Bowie (1969).

But even stereo albums from more mature recording era could use hard-panned instruments, at least in some elements, for example in Madonna’s “American Life” song (same titled album from 2003) we can hear a synth and a guitar hard-panned to left and right channels, respectively, during some moments of the song.

What happens to such hard-panned sources when we employ our Mid-Side EQ for phantom center and diffuse sound compensation? If we just used to compensation for the phantom center, the answer would be trivial—hard-panned source will get reduced amount of the phantom center compensation because it’s applied to the half of the signal—the part from the Mid component, while the Side component is left untouched. But if we also put our diffuse field compensation EQ into the Side channel, then the result becomes less predictable. Linear-phase EQ only affects signal amplitude, but applying different EQs to two instances of the signal and then summing them back introduces severe spatial bleeding and frequency-dependent panning shifts. For instance, this is what happens to hard-panned signals with our spectral correcting EQ (the effect is symmetric for left and right channels):

We can see that application of this EQ introduces “bleeding” and coloration. The situation around the region between 4–5 kHz—this is where the side channel EQ has a deep wide notch—is especially dire. Not good! Can this be fixed? One approach is to abandon diffuse field compensation and use phantom center compensation exclusively, and also reduce the swings of EQ as much as possible balancing phantom center “correctness” vs. the effect on hard-panned sources.

Another approach is to use more sophisticated tool for stereo signal decomposition which actually understands the correlation between signals and perform what is called “Primary-Ambient Extraction” (PAE). In other words, use a modern multichannel upmixer (as opposed to older matrix-based upmixers). PAE algorithms typically utilize time-frequency masking (analyzing the Short-Time Fourier Transform). This allows the algorithm to dynamically route correlated energy to the center and uncorrelated energy to the sides on a per-frequency-bin basis. However, as we saw from my experiments on using upmixers to improve headpone rendering, these algorithms can add artefacts for complex dynamic signals (especially noise-like).

In order to check the differences between the Mid-Side and this approach, I fired up HALO Upmixer and configured it for 5.0 upmixing with hard-panned center extraction and producing an “exact” upmix which can be then precisely downmixed back into stereo with a ITU-R BS.775-compliant downmixer, for example, Nugen’s own HALO Downmixer.

In this processing chain we apply the phantom center compensation to the extracted center channel, and the diffuse field compensation to the side left and side right channels, and then we do a downmix back into stereo:

I’ll call this Up-Downmix EQ, or “U/D EQ” for short. It works better in terms of reducing coloration of hard-panned sources. For comparison:

We can see that the amount of coloration to hard-panned sources and their “bleeding” has been reduced significantly, however it was not eliminated entirely—why? Here is why:

• The PAE-based upmixer does not just route source left channel into the left channel of 5.0 upmix (if we think about it, even a matrix based upmixer would put the source L channel both into the L and C channels because it would make C as L+R). Instead, a PAE upmixer spreads it among all three frontal channels (L, C, and R) with phase relationships that cause them to cancel completely in the right channel of the downmix. This is with the assumption that the intermediate 5.0 representation was not tampered with.

• However, since our purpose is actually to apply EQ to some of those 5.0 channels, we disrupt this balance, and as a result, in the downmix the components from L, R, and C do not cancel themselves perfectly in the right channel of the downmix.

Note that HALO Upmixer’s behavior with hard-panned sources depends dramatically on whether the opposite channel contains true digital silence (literal zeroes) or acoustic silence (e.g., a -120 dB copy of the primary channel). In the digital silence case, HALO Upmixer puts the signal (say, from the left channel) into left front, center, and left rear channels, effectively creating the same problem for hard-panned sources as Mid-Side EQ. However, if the opposite channel actually has a copy of the primary channel, although reduced as much that it will never be heard via an electro-acoustic system, the algorithm detects correlation, and spreads the signal in the frontal pane, as I had described in previous paragraphs. We can see this difference by looking at HALO’s own visualization of the acoustic field:

As for the “bleed” that the equalization of the intermediate 5.0 representation creates—it’s really negligible. In order to confirm that, I measured using KU-100 a “clean” hard-panned channel and compared it with the result of Up/Downmixing processing. The results are very close:

This is likely the best we can do to leave hard-panned sources untouched while providing spectral compensation for both the phantom center and diffuse field. I have compared whether this upmix/downmix equalization approach with my initial Mid-Side EQ approach, and I think it sounds a bit “fuller” considering sides on tracks with lots of ambience, for example, the rain recording mentioned earlier. My hypothesis here is that since side sources are less colored by the frontal source signature, they are indeed perceived as coming from sides, while with M/S EQ they are more colored with the diffuse curve and their location becomes more ambiguous.

Another benefit of the upmix/downmix approach is that it allows more flexibility for controlling the resulting sound field as HALO Upmixer in particular allows changing the angles of rear speakers—this effectively balances the energy between virtual front and back, and also includes psychoacoustic shelving filter for the rear channels which helps to adjust conveniently the perceived height of off-stage sources. For sure, to some extent we can emulate that in the Mid/Side EQ by adjusting gain and shelving of the side component, but this can bring in its own issues.

For now, as I see it, we have reached the limit of how phantom center reproduction can be compensated purely by spectral correction without eliminating the physical sources of the divergence: the comb filtering and the fact that the speakers are located on sides of the listener instead of in front. It would be interesting to check what happens if we try to fix the root of the problem by employing true binaural rendering.