"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
expect.
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
well-behaved.
--------------------------------------------------
From: "ThiloKöhler" <koehlerth...@gmx.de>
Sent: Wednesday, November 02, 2011 12:09 PM
To: <music-dsp@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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