The graph below shows a linear phase response of FIR Hilbert transformer with a constant diff of -0.06135923. I am not sure if I understand the concept of the phase response correctly, but as the quadrature is the input signal shifted by PI/2, why is the phase response not a straight horizontal line at PI/2?
The code to generate the figure was copied directly from Scipy's documentation (the example at the bottom of the page) except that I did not unwrap the phase angle and I used the following filter coefficients:
N = 10 b = [2*np.sin(np.pi*n/2)**2/(np.pi*n) for n in range(1, N+1)] b = np.append(-1*np.flip(b, 0), np.append(, b))*np.hamming(2*N+1)
I tried the same with different values of N and each time the behavior of the phase response line was the same, just the steepness was varying.