Subtracting the LP part makes sense only if the LP filter is zero-phase. I believe the typical way is to directly construct a series of steep band-pass filters to cover the whole frequency range. This is very flexible but usually means the individual parts do not accurately add up to the original signal. On the other hand, if perfect sum is desirable you may wish to take a look at mirror filters, such as QMF. These are pairs of LP and HP filters designed to guarantee perfect reconstruction.

--------------------------------------------------
From: "Thilo Köhler" <koehlerth...@gmx.de>
Sent: Monday, October 31, 2011 10:47 AM
To: <music-dsp@music.columbia.edu>
Subject: [music-dsp] Splitting audio signal into N frequency bands

Hello all!

I have implemented a multi-band compressor (3 bands).
However, I am not really satisfied with the splitting of the bands,
they have quite a large overlap.

What I do is taking the input singal, perfoming a low pass filter
(say 250Hz) and use the result for the low band#1.
Then I subtract the LP result from the original input and do
a lowepass again with a higher frequency (say 4000Hz).
The result is my mid band#2, and after subtracting again the remaining
signal is my highest band#3.

I assume this proceedure is appropriate, please tell me otherwise

The question is now the choise of the filter.
I have tried various filters from the music-dsp code archive,
but i still havent found a satisfiying filter.

I need a steep LP filter (12db/oct or more),
without resonance and fewest ringing possible.
The result subtracted from the input must works as a HP filter.

Are there any concrete suggestions how such a LP filter should look like,
or is there even a different, better way to split the audio signal
into 3 bands (or N bands)?

I know I can use FFT, but for speed reasons, I want to avoid FFT.

Regards,

Thilo Koehler

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