Re: filter with arbitrary and variable rolloff


Jerry Avins wrote:
Anton wrote:
...

This page http://www.firstpr.com.au/dsp/pink-noise/ contains a
cite from robert bristow-johnson:

"an equiripple approximation to the ideal pinking filter can be
realized by alternating real poles with real zeros.
A simple 3rd order solution that i obtained is: ...."

and it shows the coefficients. There must be a method to
generate the coefficients on the fly for a given slope.

If you plot R.B-J's poles and zeros on log paper, you will probably find
a constant spacing.

almost, Jerry. if i recall correctly there was some manual adjustment
of the outside poles/zeros due to edge effects. certainly if you were
making an optimized pinking filter that would be good to a zillion
octaves, there would be a lot of alternating poles and zeros (maybe
about 1/2 zillion pair) and in the middle of the list (assuming it is
sorted in order of log frequency) these alternating poles/zeros would
follow constant spacing extremely closely.

6 dB/octave up and 6 down is what makes 3 dB/octave
possible. Placing poles and zeros closer together (at log scale)
increases complexity and reduces ripple. I don't see a theoretical way
to construct long slopes that are not multiples of 3 dB/octave,
certainly not adjustable ones.

i s'pose one might try adjusting the relative spacing of the log
frequency the zeros relative to their adjacent poles. we start out
with a pole at the left and then alternate zeros and poles. the poles
are sorta fixed and equally spaced in log frequency. with the zeros
equally spaced but slidable w.r.t. their neighboring poles, one can
make an adjustment of slope from 0 dB/oct (when the equally spaced and
interspersed zeros are slid to the left right next to their left
neighbors) to -6 dB/oct (when the zeros are slid over to the right next
to their respective right neighbors). does that make any sense?

i dunno what you would have to do to make it continuously adjustable
from 0 to -12 dB/oct.

r b-j

.

Relevant Pages

  • Re: filter with arbitrary and variable rolloff
    ... sorted in order of log frequency) these alternating poles/zeros would ... Placing poles and zeros closer together ... Even if the slope is adjustable that way it would go from zero to 3 dB/octave and back to zero when they coincide th other way. ...
    (comp.dsp)
  • Re: Value of coupling caps
    ... > happining (multiple poles) an octave or so before the first -3dB ... > bandwidth of the first stage to a reasonable point. ... > And then an octave wider for the next stage and ect. ... zeros were the only considerations. ...
    (rec.audio.tubes)
  • Re: Bandpass system identification using IIRs (audio)
    ... You've specified the response relatively very far away from the ... location of the poles and zeros, and with only 6 digit precision, ... like it requires many more bits of precision to specify the ...
    (comp.dsp)
  • IIR Hilbert - Matlab help anyone
    ... I'm implement an IIR Hilbert Transformer. ... biquads (which I happen to have available in my FPGA DSP design). ... Zeros (complex) ... Poles (complex) ...
    (comp.dsp)
  • Re: Iterative Technique for PID Controller Tuning
    ... Page 5 The point to point response for my 3 poles at -2*PI*10 is plotted. ... The response is a critically damped response except for when the output is saturate. ... Notice that poles are were I put them but as I said before, the zeros can go anywhere. ... Page 8 The closed loop Bode plot. ...
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