[PD] 8 point average filter with biquad and raw filters?

[David Medine]

I'm not sure how to do it with biquads, but I'm sure it's possible. It 
is absolutley possible to design an IIR filter that approximates this 
and then build it out of biquad sections, but I would have to look long 
and hard at my DSP theory texts to figure it out.

I /do/ know how to do it with [czero~] objects, though. The difference 
equation for a mean across m samples is:

y(n) = 1/m * (x(n) + x(n-1) + ... + x(n-m+1))

so the z-transform is:

h(z) = 1/m * (1+ z^(m-1) +  z^(m-2) + ... + z)

This is a polynomial in z and the roots of this polynomial (which are 
complex) are the locations of the zeros. I'm bad at algebra, so I used 
octave (the function is called roots) to find the roots. It turns out 
that whatever the value is for m, you will have n zeros spaced at equal 
intervals around the unit circle for the mean filter /except/ for an 
absent zero at 1 (m-1 zeros in all). So for an m=8, your zeros would be 
at [.707, .707] [0,1] [ -.707, .707] [-1, 0] etc. I attach the pole-zero 
plot of the filter for m=8.

Your biquad-based solution to the 4 point average is very clever. It is 
very challenging (for me anyway) to generalize this filter design 
problem with biquads, so I have something to think about when I'm on the 
bus for a little while. If I come up with anything I'll post it.

Cheers,
David

On 9/7/2015 9:00 PM, Alexandre Torres Porres wrote:
> Hi, I was able to implement a 4 point average filter with raw filters 
> and biquad~ in Pd (find attached patch). I'm struggling to finda a way 
> to implement an 8 point average filter with biquads~ and raw filters...
> Anyone can help?
>
> thanks
>
>
>
>
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