[music-dsp] Re: EQ through Wavelets

[Olli Niemitalo]

On Mon, 25 Nov 2002, Payan, Remi wrote:

> [EQ through Wavelets]
>
> I tried this a year ago also.
> The problem I faced was that wavelets are based on the fact that hp/lp
> filters are complementary. This means there is an interdependency
> between each level of the decomposition; if you try and modify
> the gain in one sub-band, or filter it, it will have some side
> effects on all upper levels of the decomposition.

Here's a workaround, which looks good on paper, but which I have not yet
implemented:

  http://www.student.oulu.fi/~oniemita/DSP/multi.gif

The idea is to avoid aliasing by keeping a frequency headroom, that is,
not sampling critically. Linear phase windowed-ideal halfband and
quarterband filters are exceptionally cheap and fit the job well, because
you can for example turn a lowpass into a highpass by negating all taps
and adding 1 to the middle tap, and because there are plenty of zero
coefficients. Here are the filters I'm planning to use with this scheme:

  http://www.student.oulu.fi/~oniemita/DSP/fir.gif

Coefficients for those two filters are attached.

Minimum phase versions could be interesting, too.

-olli

Attached filter coefficients:
-------------------------------------------------------------------------
LOWPASS
-------
Passband: 0..Nyquist/3, very low equiripple.
Stopband: Nyquist*2/3..Nyquist, -96 dB equiripple.
Total 35 coefficients of which 10 unique non-zero.
Symmetrical. Middle coefficient and right side coefficients:

0.50000000000, 0.31433885029, 0.00000000000, -0.09470958687,
0.00000000000, 0.04627105082, 0.00000000000, -0.02406468568,
0.00000000000, 0.01202958319, 0.00000000000, -0.00546305257,
0.00000000000, 0.00213211241, 0.00000000000, -0.00065578126,
0.00000000000, 0.00012920359

BANDSTOP
--------
Passband: 0..Nyquist/6, very low equiripple.
Stopband: Nyquist/3..Nyquist*2/3, -100 dB equiripple.
Passband: Nyquist*5/6..Nyquist, very low equiripple.
Total 69 coefficients of which 10 unique non-zero.
Symmetrical. Middle coefficient and right side coefficients:

0.50000000000, 0.00000000000, 0.31416923397, -0.00000000000,
0.00000000000, 0.00000000000,-0.09424822482, -0.00000000000,
0.00000000000, 0.00000000000, 0.04564070856, -0.00000000000,
0.00000000000, 0.00000000000,-0.02341535571, -0.00000000000,
0.00000000000, 0.00000000000, 0.01148470813, -0.00000000000,
0.00000000000, 0.00000000000,-0.00508548751, -0.00000000000,
0.00000000000, 0.00000000000, 0.00192002613, -0.00000000000,
0.00000000000, 0.00000000000,-0.00056493048, -0.00000000000,
0.00000000000, 0.00000000000, 0.00010420789
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