need to visualise this comb filter

I need to visualise this schroeder comb filter - y_n=x_(n-tau)+g*y(n-tau). I have that the z-transfer function is H(z)=1/(z^tau - g).

I don't really know how to do this - any help would be greatly appreciated.

Many thanks

[Matt Fig]

Tom's question

I need to visualise this schroeder comb filter - y_n=x_(n-tau)+g*y(n-tau). I have that the z-transfer function is H(z)=1/(z^tau - g).

I don't really know how to do this - any help would be greatly appreciated.

Many thanks

Answer 1

[Wayne King]

You can visualize it in pole-zero form, or the phase, magnitude etc, which evaluates it on the unit circle.

However, you should rewrite it in the form:

H(z) = z^{-\tau}/1-gz^{-\tau}

I'll assume tau = 3 here and g = 1/2. The actual value of g will determine whether the filter is stable and therefore whether it has a Fourier transform. The first element of the numerator, B, and denominator, A, coefficient vectors is the 0-th order term in the Z-transform.

   g = 1/2;
   B = [0 0 0 1]; 
   A = [1 0 0 -g];
   %pole-zero plot
   zplane(B,A)
   % magnitude and phase response
   freqz(B,A)

Answer 2

[Wayne King]

You have to know tau. In your example, tau is 1, just as long as that is correct. Also, the sign on g is incorrect and you don't need to feed freqz a frequency vector. Finally, h is complex-valued, so you want to plot the magnitude or phase.

   fs = 11025;
   g = 0.8;
   b = [0 1];
   a = [1 -g];
   [h,f] = freqz(b,a,fs); 
   plot(f,abs(h)); grid on;
   xlabel('Hz');

The b values are the coefficients on the x-side of the difference equation. The a's are the coefficients on the y-side

y(n)-g y(n-1) = x(n-tau)

1 and -g are the only nonzero a coefficients, 1 is the only nonzero b coefficient. To use freqz(), you want the power of z to be negative.