Choice of Kaiser Window

w = kaiser(M,beta); % Kaiser window returned in "linear phase form"
w = w'; % prefer row vectors for printing
wzp = [w,zeros(1,N-M)]; % zero pad out to FFT size
W = fft(wzp);
Wp = [W(N/2+2:N), W(1:N/2+1)]; % plot (-) freqs on the left
Wpn = abs(Wp); Wpn = Wpn/max(Wpn);
plot(f,20*log10(Wpn)); grid;
s = sprintf(...
  'Kaiser Window Transform, FFT size = %d, Window length = %d',N,M);
title(s); 
xlabel('Normalized Frequency (cycles/sample)'); 
ylabel('Gain (dB)')
if dopause, disp 'Pausing... RETURN to continue'; pause; end;
if saveplots, saveplot('KaiserFR.eps'); end;

The function saveplot above is simply defined (for Matlab) as

function saveplot(filename)
% SAVEPLOT - Save current plot to disk in a Post Script file.
%            This version is compatible only with Matlab.

cmd = ['print -deps ',filename];
disp(cmd); eval(cmd);

In Octave, the body may be defined instead as

gset output filename
gset terminal postscript
replot

Note that in Octave you can also set the output terminal to fig, which is an ASCII file format understood by the xfig drawing program for X Windows systems such as Linux.

kzero = N/2; % index of frequency 0
kshow = 2*k1;
krange = kzero-kshow : kzero+kshow;
frange = (krange - kzero)/N;
plot(frange,20*log10(Wpn(krange))); grid;
s = sprintf(['Close Up on Kaiser LF Response, FFT size = %d',...
             ' Window length = %d'], N, M);
title(s); 
xlabel('Normalized Frequency (cycles/sample)'); 
ylabel('Gain (dB)')
if saveplots, saveplot('KaiserZoomFR.eps'); end;
if dopause, disp 'Pausing... RETURN to continue'; pause; end;
wzp = [w((M+1)/2:M), zeros(1,N-M), w(1:(M-1)/2)]; % zero-phase 

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Order a Hardcopy of Spectral Audio Signal Processing

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Next: Windowing an ``Ideal'' Impulse Response

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.