File:Spectral leakage from a sinusoid and rectangular window.png

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Spectral_leakage_from_a_sinusoid_and_rectangular_window.png ‎(508 × 412 pixels, file size: 47 KB, MIME type: image/png)

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Transferred from en.wikipedia to Commons by Maksim.

The original description page was here. All following user names refer to en.wikipedia.

Summary

Description
English: This is a portion of the DTFT for a rectangularly-windowed sinusoid. The actual frequency of the sinusoid is indicated as "0" on the horizontal axis. Everything else is leakage. The unit of frequency is "DFT bins"; that is, the integer values on the frequency axis correspond to the frequencies sampled by the DFT. So the figure depicts a case where the actual frequency of the sinusoid happens to coincide with a DFT sample, and the maximum value of the spectrum is accurately measured by that sample. When it misses the maximum value by some amount [up to 1/2 bin], the measurement error is referred to as scalloping loss (inspired by the shape of the peak). But the most interesting thing about this case is that all the other samples coincide with nulls in the true spectrum. (The nulls are actually zero-crossings.) So in this case, the DFT creates the illusion of no leakage.
Date
Source Own work     I created this image myself, using Matlab tools and PowerPoint to annotate the graph and create a png file.
Author Bob K
Permission
(Reusing this file)
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File:Spectral leakage caused by "windowing".svg is a vector version of this file. It should be used in place of this PNG file when not inferior.
File:Spectral leakage from a sinusoid and rectangular window.png → File:Spectral leakage caused by "windowing".svg
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Matlab code

N=128;
k=0:N-1;
dr = 60;
w = ones(1,N);
% 
H = abs(fft([w zeros(1,7*N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
x = -4.5*8 : 7.5*8;
H = H(x + 1+4*N);
%
figure
h = area(x/8,H,'FaceColor', [.871 .49 0], 'Linestyle', 'none')
set(h,'BaseValue',-dr)
ylim([-dr 0])
set(gca,'XTick', -4:7)
grid on
ylabel('decibels')
xlabel('DFT bins')
title('"Leakage" from a sinusoid (rectangular window)')


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date/time username edit summary
01:47, 17 December 2005 en:User:Bob K (I created this image myself, using Matlab tools.)

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17 December 2005

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Date/TimeThumbnailDimensionsUserComment
current07:25, 17 December 2011Thumbnail for version as of 07:25, 17 December 2011508 × 412 (47 KB)wikimediacommons>Bob KRemove gray border. Annotate sidelobes, main lobe, sidelobe level.

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