[pulseaudio-discuss] New Module: module-lfe-lp

[Alexander E. Patrakov]

2013/3/19 Justin Chudgar <justin at justinzane.com>:
> I've created a module to ensure that only low frequencies are sent to devices
> at the end of an "lfe"/"subwoofer" channel. This module allows the user to
> select the master channel, the low pass cutoff frequency (aka corner freq, -3dB
> freq) and the number of filter poles.

I have received this e-mail and will review the DSP-related part of
the file later today (when I return from work). However, even based on
this short description and a cursory examination of the file, I can
say that some of my criticisms are not addressed.

First, it is said nowhere in the comments that you implement a
Butterworth IIR filter.

Second, you copy the non-LFE channels straight from input to output,
and this is a Bad Thing if any filtering is applied to LFE. Please
calculate the delay introduced by the filter and apply it to other
channels if you still want to copy them (but see below).
Unfortunately, I don't know the formula that allows one to calculate
the phase delay introduced by the Butterworth filter (don't confuse
this with group delay). Still, given some paper, pen, and some time,
it should be possible to derive from the transfer function using the
low-frequency limit. However, due to the objection below, it is
pointless.

I still maintain that filtering LFE (and only LFE) is the wrong thing
to do at all. It doesn't help with 5.0 concert recordings (as found on
music BluRays) and 2.0 recordings (found on audio CDs) where low
frequencies are in the non-LFE channels (and should be moved to the
LFE channel). Yes, this is a different problem from the one you are
trying to fix (you assume that there is some non-LFE content in the
LFE channel and try to filter it out). A correct implementation of a
digital crossover filter is what will help both of our cases.

Given that you now have Butterworth filters (congratulations! but I
still have to check it for correctness), implementing a LR4 crossover
filter should be easy. According to
http://en.wikipedia.org/wiki/Linkwitz–Riley_filter , you have to:

1. Implement a 2nd order (this is not a user-adjustable parameter due
to phase considerations, it really must be 2nd order) Butterworth
lowpass filter and a 2nd order Butterworth highpass filter for the
same user-selected cut-off frequency.

2. Instantiate 4N copies of the filter, where N is the number of
channels of the acoustic system. Connect one lowpass filter and one
highpass filter to each input channel. After each filter, insert
another filter of the same kind. Note that applying a 2nd order
Butterworth filter twice is not the same as applying a 4th order
Butterworth filter once.

3. Now you have 2N filtered signals: twice-highpass-filtered left,
twice-lowpass-filtered left, twice-highpass-filtered right,
twice-lowpass-filtered right, ... , twice-highpass-filtered LFE,
twice-lowpass-filtered LFE.

4. For non-LFE outputs, give them the sum of the corresponding
twice-highpass-filtered input channel and 1/(N-1) of the
twice-highpass-filtered LFE input channel.

5. For the LFE output, give it the sum of all twice-lowpass-filtered
inputs (both LFE and non-LFE). Note: this can clip, it needs
additional discussion what is the correct thing to do with it in
PulseAudio context. Applying 1/(N-1) gain to all final outputs
(including step (4)) is definitely safe, but users may complain that
the filter loses a lot of volume. Maybe a configurable parameter is
what's needed.

If you want to implement a LR2 crossover instead, do this:

1. Implement a 1st order (this is not a user-adjustable parameter due
to phase considerations, it really must be 1st order) lowpass filter
and a 1st order highpass filter for the same cut-off frequency.

2. Instantiate 4N copies of the filter, where N is the number of
channels of the acoustic system. Connect one lowpass filter and one
highpass filter to each input channel. After each filter, insert
another filter of the same kind.

3. Now you have 2N filtered signals: twice-highpass-filtered left,
twice-lowpass-filtered left, twice-highpass-filtered right,
twice-lowpass-filtered right, ... , twice-highpass-filtered LFE,
twice-lowpass-filtered LFE.

4. For non-LFE outputs, give them the sum of the corresponding
inverted twice-highpass-filtered input channel and 1/(N-1) of the
non-inverted twice-highpass-filtered LFE input channel.

5. For the LFE output, give it the sum of all twice-lowpass-filtered
non-inverted inputs (both LFE and non-LFE).

In both cases, I have sent the (misplaced) high-frequency portion of
the LFE channel to all remaining speakers. Feel free to send it only
to the center (without the 1/(N-1) factor) or maybe discard, as you
did in your module. Or make this an option.

-- 
Alexander E. Patrakov