The History of Multiple-Subwoofer Optimization

Introduction

This article discusses how multiple subwoofer optimization came about, and provides links to a number of articles that trace the early development of the subject.

Bruno Korst-Fagundes Masters Thesis

The earliest known effective attempt to simultaneously fix frequency response errors at multiple listening positions can be found in the 1995 Master's thesis of Bruno Korst-Fagundes, and his paper with Xie and Snelgrove. He assumed multiple speakers with a mono source signal and didn't specifically mention subwoofers, but his concept applies equally well to subs. He split the mono signal into separate EQ for each speaker and found that if the number of speakers is equal to the number of listening positions at which their frequency response is measured, it's possible in theory to get perfectly flat response of the combined speaker outputs at multiple listening positions simultaneously. His approach works by solving a set of simultaneous linear equations at each frequency, based on measurements from each speaker to each listening position. The solution to each system of equations at a given frequency yields the required gain and phase of each sub's DSP filter at that frequency. A high-order finite-impulse-response (FIR) filter having the calculated gain and phase response at each frequency is then designed for each speaker. This approach requires special-purpose FIR filter hardware and has some practical problems related to the need for impractically high filter gains at some frequencies. The practical need to limit these gains places a limit on how flat the combined subwoofer responses can be in practice.

JBL BassQ

JBL used a variation of the approach originated by Korst-Fagundes on a product called the BassQ, which is no longer made. Its theory of operation is described in U.S. Patent 8355510.

Sound Field Management (SFM) and Other Work by Harman

Harman also has a patented system called Sound Field Management (SFM). Its theory of operation from an engineering perspective is described in the article "Low-Frequency Optimization Using Multiple Subwoofers" by Todd Welti and Allan Devantier. This article was originally published in the Journal of the Audio Engineering Society (JAES) in May of 2006. Information about SFM from a consumer perspective can be found in the article by Floyd Toole on the Audioholics site titled "The Birth of Sound Field Management", which is part of a longer article called "History of Multi-Sub & Sound Field Management (SFM) for Small Room Acoustics". SFM works by minimizing a metric called the mean spatial variance (MSV). The goal of SFM is to first minimize the variation with listening position of the combined sub frequency responses (the MSV) without regard to the flatness of the response. A single separate PEQ, gain and delay per subwoofer are adjusted to minimize the MSV. After this step, EQ that's common to all subs is performed to flatten response. Finally, integration with the mains is performed in a third step. SFM is described in U.S. Patents 7526093, 8705755 and 8280076. This work did not depend on the use of room simulation.

In addition to his work on SFM, Harman's Todd Welti has contributed a number of studies of multiple subwoofers in rooms, analyzing subwoofer positions, room dimensions and seating arrangements and how they all interact. Those studies make use of room simulation, and are not related to Harman's SFM technology. Instead, they assume identical subs with identical signals applied to them, with varying subwoofer and seating placement arrangements. There is an interesting YouTube interview with Todd Welti, in which he summarizes the results of these studies.

Earl Geddes Approach

Discussion of the Geddes approach in the DIY community seems to have begun in a thread at diyaudio.com that began in December of 2008, more than two years after Welti and Devantier published their JAES article on Sound Field Management. Todd Welti was involved in discussions in that thread under the moniker "cap'n todd". Geddes' approach is intended to be used with DSP devices having simple infinite-impulse-response (IIR) filters, such as PEQ and shelving filters. An approach that uses low-cost DSP hardware makes a lot of practical sense. Despite discussion in that thread spanning more than fifteen years, he's never described specifics of how he computes the per-sub filter parameter values.

The Double Bass Array (DBA) and Controlled Acoustic Bass System (CABS)

The origin of the term "Double Bass Array" is difficult to track down, but it appears to be a paper (only available in German) by Anselm Goertz, Markus Wolff and Lutz Naumann from the German company Klein and Hummel. A number of posters on audio forums from Germany have noted that DBAs are popular in that country. Early influence of the paper by Goertz, Wolff and Naumann may explain this regional popularity.

This paper is very short at just two pages, but there is a lengthy PhD thesis by Adrian Celestinos (PDF here), published in 2007, on a very closely-related system that he calls Controlled Acoustic Bass System (CABS). The intent of the CABS is the same as that of the DBA: to launch a plane wave from the front wall via an array of subwoofers, then subsequently absorb it actively at the back wall using an identical array of subs, in opposite polarity to those at the front, and delayed by an amount corresponding to the depth dimension of the room.

To simplify the discussion of the DBA and CABS, I'll just refer to both of them as the "plane-wave approach".

Celestinos' thesis is arguably the definitive work on the plane-wave approach. In it, he makes use of a simulation technique called the Finite-Difference Time-Domain (FDTD) method. This method is often used in the analysis of electromagnetic field problems. Celestinos adapts it for use in room acoustics. This simulation method uses a rectangular grid of points, uniformly spaced in three dimensions throughout the room. These points must be spaced closely enough to accurately simulate the spatial variations of the sound throughout the room at the highest frequency simulated. For each grid point, a time-domain waveform is computed, so the technique is capable of detailed analysis of the time-domain behavior of the system at every point on the grid throughout the room. Frequency response information at each grid point is derived in an indirect way, by performing an FFT on the simulated time-domain waveform at that point.

Celestinos' analysis demonstrates the high performance of the plane wave approach, both in terms of the frequency and time domains, as well as the seat-to-seat frequency response variation. It's very worthwhile reading for those with an interest in the topic and a background in Engineering, Math or Physics.

For a practical example and discussion of a DBA, see this AVSForum post.

Dirac Live Bass Control (DLBC)

Dirac Live Bass Control is a more recent development that's gaining in popularity. Though there are no engineering-level articles about how its algorithm works, there is a white paper in PDF format called the "Dirac Live Bass Control User Guide" that has some interesting details. This user guide states that:

"...the present Bass Control solution provides a fine-tuning of the levels, delays and phase responses of individual subwoofers, under a criterion that the variations across space are minimized in a selected band of frequencies. Fig. 5 shows the result of such a fine-tuning, where a gain factor and two all-pass bi-quad filters have been applied to each subwoofer."

So it appears to use digital signal processing whose magnitude response is independent of frequency (delays, all-pass filters and attenuators) for each sub.

One welcome feature introduced by DLBC is the ability to "optimize the splice" between the subs and all satellites in an automated way.

If you have a miniDSP DDRC-88A with DDRC-88BM plugin or miniDSP Flex HTx, this could in theory be done manually (and rather tediously) with MSO as described in the reference manual's theory and practice sections on this topic. I wouldn't want to try it though. That article was written mainly to counter some misinformation being put forth on the topic in online forums.

Software Differences Between the Plane-Wave Approach and SFM/DLBC/MSO

The software requirements for subwoofer optimization using the plane-wave approach are much simpler than for SFM, DLBC and MSO.

In the former case, most of the work involves small adjustments to the level and delay of the rear subwoofer array relative to the front. The software is made with the assumption of a DBA or CABS configuration, and this assumption greatly simplifies the code. The problem could get somewhat more complicated if the rear array is different from the front one, but overall, it is not a complex optimization problem. If one were to mix subwoofer driver types within a planar array, the software could admittedly get quite messy, but doing that is inadvisable.

In the case of SFM, DLBC and MSO, there are no assumptions being made about sub locations or behavior, other than that the subs are separated enough so as not to be coincident. The algorithm must improve performance for any physical configuration of subs meeting the separation requirement. Such systems are unlikely to be able to achieve the level of performance of a plane-wave-based approach, but the use of such software can provide quite large improvements over the un-optimized case for typical rooms for which the user may have few choices for sub location. Common sense dictates that not everyone's domestic situation or budget can accommodate rebuilding their room just for their subwoofer arrangement.

For a hypothetical product supporting both the plane-wave approach and arbitrary sub locations, completely different optimization code bases would be required for the two scenarios.

Trinnov Waveforming

The Trinnov Waveforming system is a recent entrant into the hardware and software market for optimization of multi-sub systems. This product has yet to be officially released, and the information here is based on a June 24, 2024 webinar video called "Expanding Waveforming Applications", as well their online written material.

They vehemently claim that their Waveforming system is "not a DBA". To back up this dubious claim, they show a block diagram of their processing, illustrating that it's capable of controlling each subwoofer driver of the front and rear arrays independently.

For such systems, best performance is obtained by achieving the best possible plane wave, and ensuring its propagation is "straight front-to-back" without being redirected in any way. When identical drivers are used for the front and rear arrays, the best approximation of a plane wave is achieved by supplying the same signal to all drivers of a given array. With identical drivers, it's not possible to produce a "better plane wave" by providing different signals to each driver. One cannot compensate for the presence of unavoidable obstructions of the wave such as the seating and audience by providing unequal signals to the drivers either. Under certain conditions, such as non-identical drivers, unequal drive signals could be justified, but figuring out the different drive signals would require near-field measurements, not the far-field ones they specify. Even if they were able to do this properly, one might rightly wonder who the target users are that are willing to rebuild their rooms to accommodate the sub arrays, but not willing to use identical drivers within a given array.

Their approach seems to be using a DBA to minimize software complexity and cost, claiming that their system is not a DBA, then claiming that the performance improvement that's due to the DBA should be attributed it to their proprietary processing instead. It's a remarkably deceptive approach.