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# gausswin() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

### Alternatives / See Also

### Reference

w = gausswin(N) returns an N-point Gaussian window in a column vector, w. N is a positive integer.w = gausswin(N,Alpha) returns an N-point Gaussian window with Alpha proportional to the reciprocal of the standard deviation. The width of the window is inversely related to the value of α. A larger value of α produces a more narrow window. The value of α defaults to 2.5.Note If the window appears to be clipped, increase N, the number of points.

w = gausswin(N)w = gausswin(N,Alpha)

Gaussian WindowOpen This Example Create a 64-point Gaussian window. Display the result in wvtool. L = 64; wvtool(gausswin(L)) Gaussian Window and the Fourier TransformOpen This Example This example shows that the Fourier transform of the Gaussian window is also Gaussian with a reciprocal standard deviation. This is an illustration of the time-frequency uncertainty principle. Create a Gaussian window of length 64 by using gausswin and the defining equation. Set , which results in a standard deviation of 64/16 = 4. Accordingly, you expect that the Gaussian is essentially limited to the mean plus or minus 3 standard deviations, or an approximate support of [-12, 12].N = 64; n = -(N-1)/2:(N-1)/2; alpha = 8; w = gausswin(N,alpha); stdev = (N-1)/(2*alpha); y = exp(-1/2*(n/stdev).^2); plot(n,w) hold on plot(n,y,'.') hold off xlabel('Samples') title('Gaussian Window, N = 64') Obtain the Fourier transform of the Gaussian window at 256 points. Use fftshift to center the Fourier transform at zero frequency (DC).nfft = 4*N; freq = -pi:2*pi/nfft:pi-pi/nfft; wdft = fftshift(fft(w,nfft)); The Fourier transform of the Gaussian window is also Gaussian with a standard deviation that is the reciprocal of the time-domain standard deviation. Include the Gaussian normalization factor in your computation.ydft = exp(-1/2*(freq/(1/stdev)).^2)*(stdev*sqrt(2*pi)); plot(freq/pi,abs(wdft)) hold on plot(freq/pi,abs(ydft),'.') hold off xlabel('Normalized frequency (\times\pi rad/sample)') title('Fourier Transform of Gaussian Window')