File:Spectral leakage from two 8-point Hamming windows.png
Summary
| Description |
English: Comparing the discrete-time Fourier transforms of "symmetric" and "periodic" windows. The Hamming form was chosen for its non-zero end-points, one of which is discarded in the periodic version, resulting in an improved (narrower) main lobe. |
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| Date | ||||
| Source | Own work | |||
| Author | Bob K | |||
| Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following license:
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| PNG development | ||||
| Octave/gnuplot source | click to expand
This graphic was created by the following Octave script: <source lang='Matlab'> graphics_toolkit gnuplot pkg load signal N = 8; symmetric = .54 - .46*cos(2*pi*(0:N-1)/(N-1)); % 8-point Hamming window periodic = .54 - .46*cos(2*pi*(0:N-1)/N); % 8-points of a 9-point window L=64*N; dr = 60; H = abs(fft([symmetric zeros(1,L-N)])); H = fftshift(H); H = H/max(H); H = 20*log10(H); H = max(-dr,H); x = N*[-L/2:L/2-1]/L; figure plot(x, H, 'color', 'blue', 'linewidth', 2) hold on ylim([-dr 0]) H = abs(fft([periodic zeros(1,L-N)])); H = fftshift(H); H = H/max(H); H = 20*log10(H); H = max(-dr,H); plot(x, H, 'color', 'red', 'linewidth', 2); set(gca,'XTick', -N/2:N/2-1) grid on ylabel('decibels') xlabel('DFT bins') text(2, -23, '\leftarrow Symmetric', 'color', 'blue','FontSize', 14) text(.30, -26, 'Periodic \rightarrow', 'color', 'red','FontSize', 14) title('"Spectral leakage" from two 8-point Hamming windows','FontSize', 14) </syntaxhighlight> |
