way to generate FIR from desired spectra data

[[email protected]]

I am trying to create a custom spectra noise signal from 20 to 20khz.
Its got various peaks and valleys. I have a plot of the desired
frequency response in about 2hz increments. Is there some way to
generate an FIR filter from this data? Or should I say, generate the
coefficients? Do all FIR filters come in the form:

b0 = 0.99765 * b0 + white * 0.0990460;
b1 = 0.96300 * b1 + white * 0.2965164;
b2 = 0.57000 * b2 + white * 1.0526913;
tmp = b0 + b1 + b2 + white * 0.1848;

 

[Ben Jackson]

I am trying to create a custom spectra noise signal from 20 to 20khz.
Its got various peaks and valleys. I have a plot of the desired
frequency response in about 2hz increments.

Matlab can do this with firls. Octave-forge (an addon to Gnu Octave,
which is very matlab-like) can do it with fir2. You'll want to iterate
by making a filter, examining its frequency response (freqz can do this),
and adjusting the order of the filter to trade off computational complexity
vs adherence to your input. If your shape has sharp peaks and valleys,
especially in the low frequency range, you will need a high order filter.

b0 = 0.99765 * b0 + white * 0.0990460;
b1 = 0.96300 * b1 + white * 0.2965164;
b2 = 0.57000 * b2 + white * 1.0526913;
tmp = b0 + b1 + b2 + white * 0.1848;

No, that looks like some kind of gaussian noise. For one thing, a FIR
filter would not destroy the historical input samples. Although, if
the input is noise, I'm not sure if it matters. Good puzzler for DSP
guys.

 

[Tom Bruhns]

As I though we had agreed on earlier, what you posted is an IIR filter,
not an FIR filter. An FIR filter will have the form

out = sum-from-i=1toN( coefficient(i) * input(k+1-i) )

or in words, the current input times a coefficient plus the previous
input times another coefficient plus the next earlier input times yet
another coefficient... until you exhaust the set of coefficients.
Next input sample, you slide your set of saved input samples over by
one and do the same set of multiply-and-accumulates, which is how a DSP
can do the filter very efficiently. A typical DSP will fetch a new
coefficient and a new input from a circular buffer, multiply them
together, and add them into an accumulator, all in one instruction
cycle, and in many cases, the instruction can auto-repeat for N times
with practically no additional overhead.

But if the filter needs to have a lot of "memory" -- if its impulse
response takes a long time to die out -- then implemented as an FIR it
will take a long buffer, a lot of coefficients, and a relatively long
time to calculate unless you can do the multiplications and additions
all in parallel (such as digitally with an FPGA or in analog domain
with weighting resistors). And the IIR filter you have shown below has
a lot of "memory". If you hit it with an impulse, each of b0, b1 and
b2 becomes non-zero and will take a long time to die out. With no
further input, b0 will decay only 0.235 percent per sample. That means
it will take 295 sample periods for it to decay to half its original
value, and over a thousand sample periods to get down to 1/256th of the
amplitude of the input impulse. Depending on how accurately you wanted
to emulate the behaviour of that IIR filter, then, you'd probably need
a few hundred stages of sample delay, and a few hundred coefficients.
MAYBE you can do it in a much shorter FIR filter that will give you
acceptable performance, but it depends a lot on what's "acceptable."

Cheers,
Tom

 

[[email protected]]

[email protected] skrev:

I am trying to create a custom spectra noise signal from 20 to 20khz.
Its got various peaks and valleys. I have a plot of the desired
frequency response in about 2hz increments. Is there some way to
generate an FIR filter from this data? Or should I say, generate the
coefficients? Do all FIR filters come in the form:

b0 = 0.99765 * b0 + white * 0.0990460;
b1 = 0.96300 * b1 + white * 0.2965164;
b2 = 0.57000 * b2 + white * 1.0526913;
tmp = b0 + b1 + b2 + white * 0.1848;

This should be to do exactly that and more;
http://www.iowegian.com/scopefir.htm

-Lasse

 

[Genome]

I am trying to create a custom spectra noise signal from 20 to 20khz.
Its got various peaks and valleys. I have a plot of the desired
frequency response in about 2hz increments. Is there some way to
generate an FIR filter from this data? Or should I say, generate the
coefficients? Do all FIR filters come in the form:

b0 = 0.99765 * b0 + white * 0.0990460;
b1 = 0.96300 * b1 + white * 0.2965164;
b2 = 0.57000 * b2 + white * 1.0526913;
tmp = b0 + b1 + b2 + white * 0.1848;

I know **** all but there might be something in the idea of taking your
frequency response thing and inverse ffting it or ffting it or whatever and
then you end up with the coefficients of your FIR filter to do what you want
to do.

DNA