MBStereophony

Marc Joliet marcec@gmx.de

Introduction

This is a simple implementation of a Regalia-Mitra filter bank using 3rd order Cauer low-pass filters as the base designs. There are four filter bank programs available which are described below. MBStereophony itself is a demo effect that down-mixes a stereo signal separately per frequency band. It also has four versions as described below.

For implementations in MATLAB, Python and C++ – the latter of which does not work – see this repository.

Compilation

You can either use the provided SCons based build system, whose invocation would typically look like

scons -j<N> all

<N> is the number of parallel builds. Instead of "all", you can also specify any of the group targets mbstereophony or rmfb, or any of the individual targets mbstereophonyd_syn, mbstereophonyd_sum, etc.. That way you can build only the program you actually want to use. The SCons build system will automatically pass appropriate options to the FAUST compiler, such as -vec to produce auto-vectorisable code. See the output of scons --help for more details.

This relies on an SCons FAUST tool available here. It is a submodule of this repository and is initialised by executing

git submodule update --init

Of course, you can always just use any of the myriad of faust2* scripts that are distributed with FAUST. This requires more knowledge of the FAUST options, though (see faust --help).

NOTE: it turns out that on my computer (AMD Athlon64 X2 4200+ from late 2006) clang++ produces faster binaries than g++. MBStereophony uses about 15% CPU on average when compiled with g++ (with CFLAGS="-O3 -march=native"), while it only uses about 9% CPU on average when compiled with clang++.

Usage

There are two groups of applications: RMFB* and MBStereophony*. Each comes in four versions which follow the following naming scheme:

• "d" and "s" (e.g., "rmfbd_sum") stand for "dynamic" and "static", respectively. The static filter banks have constant edge frequencies, whereas the dynamic filter banks let you vary the edge frequencies.
• "sum" and "syn" suffixes (e.g., "rmfbs_syn") defines how the filter bank reconstructs the signal: by using the all-pass complementary property and simply summing the frequency bands up ("sum") or by using a synthesis filter bank ("syn").

The static versions have their edge frequencies set to 220, 880, 1760, 3520, and 7040 Hz, so are partially octave filter banks. Some of the bands were left out due to the exponential increase in compilation time for each additional band.

The reason for the four versions are:

1. dynamic filter banks require long compilation times, so you don't have to compile them if you don't want to, and
2. reconstruction by summing the bands requires only half as much CPU, while the using a synthesis filter bank results in the overall transfer function of the system becoming invariant to changes in edge frequency (see the references below).

So select from them depending on your requirements.

NOTE: the master branch of FAUST recently received a modification that greatly reduces the total compilation time of all of the programs below. On my computer all 8 programs now compile in about 3:30 minutes vs. about 60 minutes for the original set of 5 programs (before commit 290a6018591a98e2e0eea279e4947f764cc0e9e2).

RMFB*

These are four filter bank applications that split a signal into six frequency bands.

All four of the applications have 7 audio inputs and 7 audio outputs: The first input is for the input signal, while the first 6 outputs are from the analysis filter bank. Correspondingly, the last 6 inputs belong to the reconstruction filter bank, while the last output is the reconstructed signal. Here a graphical representation:

Input                   |  Analysis Band 1
Reconstruction Band 1   |  Analysis Band 2
...                     |  ...
Reconstruction Band N-1 |  Analysis Band N
Reconstruction Band N   |  Output

MBStereophony

This is a demo effect for demonstrating the use of the filter banks. For each frequency band there is a slider that controls whether the band should be left in full stereo (1), down-mixed to mono (0), or anything in-between.

References

The original paper (and some accompanying papers) can be downloaded from Pillip Regalias home page.

P. A. Regalia, P. P. Vaidyanathan, M. Renfors, Y. Neuvo, and S. K. Mitra, "Tree-structured complementary filter banks using all-pass sections," IEEE Trans. Circuits and Systems, vol. 34, no. 12, pp. 1470–1484, December 1987.