File:Spectral leakage from two 8-point Poisson windows.png

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Spectral_leakage_from_two_8-point_Poisson_windows.png (742 × 424 pixels, file size: 49 KB, MIME type: image/png)

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English: Comparing the discrete-time Fourier transforms of "symmetric" and "periodic" windows. The Poisson form was chosen for its non-zero end-points, one of which is discarded in the periodic version, with a noticeable performance degradation.
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Author Bob K
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The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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This PNG graphic was created with GNU Octave.
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This graphic was created with the help of the following Octave script: 

graphics_toolkit gnuplot
pkg load signal

N = 8;
symmetric = exp(-abs(((0:N-1) - (N-1)/2))*2/N);  % 8-point Poisson window
periodic  = exp(-abs(((0:N-1) - N/2))*2/(N+1));  % 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(-1.13, -36.6, '\leftarrow Symmetric', 'color', 'blue','FontSize', 14)
text(-2.1, -19, 'Periodic', 'color', 'red','FontSize', 14)
title('"Spectral leakage" from two 8-point Poisson windows','FontSize', 14)

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Date/TimeThumbnailDimensionsUserComment
current22:43, 6 April 2016Thumbnail for version as of 22:43, 6 April 2016742 × 424 (49 KB)Bob K (talk | contribs)User created page with UploadWizard

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