File:DFT-even_Hann_window_&_spectral_leakage.png
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![File:DFT-even Hann window & spectral leakage.png](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9b/DFT-even_Hann_window_%26_spectral_leakage.png/399px-DFT-even_Hann_window_%26_spectral_leakage.png)
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Summary
DescriptionDFT-even Hann window & spectral leakage.png |
English: The main point is to illustrate that the N-point DFT (discrete Fourier transform) of an N-point DFT-even Hann window function has only 3 non-zero coefficients. The other N-3 samples of the DTFT (bottom figure) coincide with zero-crossings of the DTFT. Higher-order "Cosine-sum windows" have more non-zero DFT coefficients. Wikipedia article Window function contains a link to this figure. |
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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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Other versions | Derivative works of this file: Odd-length, "DFT-even" Hann window & spectral leakage.png | |||
PNG development InfoField | ![]() This PNG graphic was created with LibreOffice. |
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Octave/gnuplot source InfoField | click to expand
This graphic was created with the help of the following Octave script: pkg load signal
graphics_toolkit gnuplot
clc
M=4096;
window = hann(M)'; % row vector
N=16; % window size, in samples
dx = M/N; % decimation factor for 16 hops (17 samples)
periodic = window(1+(0:15)*dx); % take 16 of 17 symmetrical samples
%Plot the points
figure
plot(0:15, periodic, 'color', 'blue', '.', 'MarkerSize',14)
hold on
%Connect the dots
x = (0:M-1)*N/M;
plot(x, window, 'color', 'blue') % periodic
xlim([0 16])
set(gca, 'xgrid', 'on');
set(gca, 'ygrid', 'on');
set(gca, 'ytick', [0:.25:1]);
set(gca, 'xtick', [0:16]);
title('DFT-even Hann window function');
xlabel('\leftarrow n \rightarrow','FontSize', 14)
%Now compute and plot the DTFT
M=64*N;
dr = 80;
H = abs(fft([periodic zeros(1,M-N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
x = N*[-M/2:M/2-1]/M;
figure
plot(x, H, 'color', 'blue');
hold on
%Plot the 3 non-zero points
plot(-1:1, H((N/2-1:N/2+1)*M/N), 'color', 'blue', '.', 'MarkerSize',14)
ylim([-dr 0])
xlim([-N/2 N/2-1])
set(gca,'XTick', -N/2:N/2-1)
grid on
ylabel('decibels','FontSize', 14)
xlabel('DFT bins','FontSize', 12)
title('Non-zero DFT coefficients of Hann window')
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Captions
Top: 16 sample ''DFT-even'' Hann window. Bottom: Its discrete-time Fourier transform (DTFT) and the 3 non-zero values of its discrete Fourier transform (DFT).
Items portrayed in this file
depicts
6 March 2017
image/png
6c36cd8391d5d1c65166ad52e9b560344ef10de9
34,936 byte
842 pixel
560 pixel
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:51, 10 August 2020 | ![]() | 560 × 842 (34 KB) | Bob K | change a figure title and x-limits. |
12:42, 7 March 2017 | ![]() | 560 × 841 (29 KB) | Bob K | Changed a script parameter (M) to better-align zero-crossings with grid lines. Use plot parameter "MarkerSize" to control size of dots. | |
12:05, 7 March 2017 | ![]() | 560 × 841 (62 KB) | Bob K | Enlarge the "dots". That is accomplished by choosing "Font" from the "Options" menu in the gnuplot windows created by the script. | |
02:42, 7 March 2017 | ![]() | 560 × 837 (62 KB) | Bob K | User created page with UploadWizard |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Metadata
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If the file has been modified from its original state, some details may not fully reflect the modified file.
PNG file comment |
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Horizontal resolution | 118.11 dpc |
Vertical resolution | 118.11 dpc |
File change date and time | 16:49, 10 August 2020 |