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Window Method applied to Bandlimited Ideal Impulse Response

Further Design Parameters:

f1 = 530;       % lower passband limit (Hz)
N = 2^(nextpow2(8*fs/f1)) % FFT size from xition width
if N<8*M, N = 8*(M-1); end; % spectral interpolation

Bandlimited ``Ideal'' Hilbert transformer frequency response (FR), including transition bands $ \Delta$ matched to FFT size $ N$ such that $ N\gg f_s/\Delta$ :

H = [ ([0:k1-2]/(k1-1)).^8,ones(1,k2-k1+1), ...
   ([k1-2:-1:0]/(k1-1)).^8,zeros(1,N/2-1)];
Hp = [H(N/2+2:N), H(1:N/2+1)]; // pos. freqs only
f = [-0.5 + 1/N : 1/N : 0.5]; normalized freq axis
plot(f,Hp); grid; ...


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``The Window Method for FIR Digital Filter Design}'', by Julius O. Smith III, (From Lecture Overheads, Music 421).
Copyright © 2020-06-27 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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