Signal Processing Toolbox

Chebyshev Window

The Chebyshev window minimizes the mainlobe width, given a particular sidelobe height. It is characterized by an equiripple behavior, that is, its sidelobes all have the same height. The chebwin function, with length and sidelobe height parameters, computes a Chebyshev window.

n = 51;
Rs = 40;                 % Sidelobe height in decibels
w = chebwin(n,Rs);
stem(w); title('Length 51 Chebyshev Window');
xlabel('Sample Number');

As shown in the plot, the Chebyshev window has large spikes at its outer samples. Plot the frequency response to see the equiripples at -40 dB.

[W,f] = freqz(w,1,512,2);
plot(f,20*log10(abs(W)/sum(w))), grid
title('Chebyshev Window Magnitude Response');
xlabel('Normalized Frequency (Nyquist = 1)');
ylabel('Normalized Magnitude (dB)');

For a detailed discussion of the characteristics and applications of the various window types, see Oppenheim and Schafer [2], pgs. 444-462, and Parks and Burrus [3], pgs. 71-73.

Kaiser Window

Parametric Modeling