We have a function which describes a frequency response correction to piezo devices we use. To flatten the FFT, it is similar to:
Cdis_t = .5
N = 8192
for n in range(8192):
B3 = n * 2560 / N
Fc(n) = 1 / ((B3/((1/(Cdis_t*2*pi))**2+B3**2)**0.5)*(-0.01*log(B3) + 1.04145))
In practice it really only matters for low frequencies.
I suggested that we might be able to do a time domain correction as a forward-reverse FFT filter using the function, but another said it can also be applied in the time domain using a bilinear transform.
So, can one use
and, how does one generate b,a from the given Fourrier domain flattening function?