I am working at a Karplus-Strong sound synthesis technique where an excitation impulse is subjected to a delay with feedback and a one pole LP filter in the feedback line. The process is simply y=(x+ky)[-n] Where x is the input signal, y is the output signal, n is the delay length in samples in the circular delay buffer and k is the feedback factor from 0 to 1. If no filtering is applied at the feedback line, the resulting frequency will be
sample rate / n.
If I apply a simple one pole LP filter in the feedback line, which is very effective for simulation of plucked strings, of form
where f is the filtering factor from 0 to 1, I get a frequency shift which is in some manner proportional to f (the higher f, the higher the shift downwards in frequency).
My problem is, I have no means to quantify this shift, the underlying math is likely too complex for me. But I would like to discover the exact relationship linking f and n so I can compensate n in function of f in order to avoid detuning (n is not integer but a real number becsuse I am using interpolation to read my samples from the circular buffer). The only thing I discovered is that such function D m=D(n,f) always passes by 0 for f=0 and by 1 for f=0.5 and likely goes to infinity for f=1 but it is neither a suitably scaled hyperbole nor exponential but something else.. Thanks in advance