[music-dsp]   Splitting audio signal into N frequency bands

Wen Xue mr.x.wen at gmail.com
Wed Nov 2 11:36:14 EDT 2011

"Filtering a signal x(t) with a LP filter H(z) then subtract the result from 
x(t) itself" is equivalent to filtering x(t) with a filter 1-H(z), which is 
a HP filter only if H(j2*pi*f) is close to 1 in the pass band (i.e. unit 
gain and zero phase). Otherwise the result after subtraction will still 
contain substantial low-frequency components. If you want to use the 
subtraction method to split your signal then you need to have some idea of 
how much LP leak is going into 1-H(z) so that you know what outcome to 

But is there any special reason why you want to do the subtraction? If it's 
perfect reconstruction you're after then quadratic mirror filters may serve 
all right. They're usually not very steep but are stable and reasonably 

From: "ThiloKöhler" <koehlerthilo at gmx.de>
Sent: Wednesday, November 02, 2011 12:09 PM
To: <music-dsp at music.columbia.edu>
Subject: Re: [music-dsp]   Splitting audio signal into N frequency bands

> Hello Thomas, Wen!
> Thank you for the quick input on this.
> 1. I found that in the 3-band case, splitting up
> the low and high band from the input and then
> generating the mid band by subtracting them
> works much better than the "salami" stategy
> (chopping off slices with a LP).
> Thanks!
> 2.
>> Subtracting the LP part makes sense only if the LP filter is zero-phase.
> I dont know if my filters are zero phase, I am not that deep
> into the filter math to tell you straight away. It is an IIRC taken from
> here:
> http://www.musicdsp.org/showArchiveComment.php?ArchiveID=259
> This one seems to work best for my purposes, but that is just
> from subjective listening wihtout any mathematical evidence.
> Is this a butterworth filter like Thomas suggests? (sorry if the question
> sounds like a noob...) In the comment they call it biquad, i dont know
> if a biquad can be butterworth or this is mutual exclusive.
> I have also tried:
> http://www.musicdsp.org/showArchiveComment.php?ArchiveID=266
> Doesnt work well for low cutoff frequencies, like <150Hz.
> I am using single precision.
> http://www.musicdsp.org/showArchiveComment.php?ArchiveID=117
> Seems to be too flat, not steep enough.
> http://www.musicdsp.org/showArchiveComment.php?ArchiveID=237
> Seems to be too flat, not steep enough.
> I think in the use case of a mulit-band compressor, perfect
> reconstruction is important. That is my I want to create
> the band by subtracting and not with independent filters.
> I assume this is a good strategy, no?
> Regards,
> Thilo
>> 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.

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