File:8-point Hann windows.png
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8-point_Hann_windows.png (620 × 392 pixels, file size: 41 KB, MIME type: image/png)
This is a file from the Wikimedia Commons. Information from its description page there is shown below. Commons is a freely licensed media file repository. You can help. |
Summary
Description8-point Hann windows.png |
English: We illustrate two different ways to generate Hann window functions for spectral analysis applications. MATLAB calls them "symmetric" and "periodic". The latter is also called "DFT Even" in the classic Frederic Harris paper. |
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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: 8-point Hann windows.svg,
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PNG development InfoField | N This PNG graphic was created with GNU Octave. |
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Octave/gnuplot source InfoField | click to expand
This graphic was created by the following Octave script: pkg load signal
graphics_toolkit gnuplot
clear all; close all; clc
M=5600; % big number, divisible by 7 and 8
% Generate M+1 samples of a Hann window
window = hann(M+1);
N=8; % actual window size, in "hops"
% Sample the window.
% Scale the abscissa. 0:M samples --> 0:7 "hops", and take 8 symmetrical hops, from 0 to 7
sam_per_hop_7 = M/7;
symmetric = window(1+(0:7)*sam_per_hop_7);
% Scale the abscissa. 0:M samples --> 0:8 "hops", and take 8 asymmetrical hops, from 0 to 7
sam_per_hop_8 = M/8;
periodic = window(1+(0:7)*sam_per_hop_8);
% Compare equivalent noise bandwidths (info only)
ENBW_symmetric = N*sum(symmetric.^2)/sum(symmetric)^2 %
ENBW_periodic = N*sum(periodic.^2) /sum(periodic)^2 %
%Replace above with the equivalent formulaic versions
%This step just proves that formulas match window() array.
symmetric = .5*(1-cos(2*pi*(0:7)/7));
periodic = .5*(1-cos(2*pi*(0:7)/8)); % aka "DFT Even"
%Compare equivalent noise bandwidths (info only)
ENBW_symmetric = N*sum(symmetric.^2)/sum(symmetric)^2 % 1.7143
ENBW_periodic = N*sum(periodic.^2) /sum(periodic)^2 % 1.5
%Plot the coefficients as dots
figure
plot(0:7, symmetric, 'color', 'red', '.', 'MarkerSize', 10)
box off % no border around plot
hold on % same axes for next 3 plots
plot(0:7, periodic, 'color', 'blue', '.', 'MarkerSize', 10)
% Connect the dots
hops = (0:M)/sam_per_hop_8;
plot(hops, window, "color","blue") % periodic
hops = (0:M)/sam_per_hop_7;
plot(hops, window, "color","red") % symmetric
xlim([0 8])
set(gca,'FontSize',14)
set(gca, "yaxislocation", "origin")
set(gca, 'xgrid', 'on')
set(gca, 'ygrid', 'on')
set(gca, 'ytick', [0:.25:1])
set(gca, 'xtick', [0:8])
text(3.3, 0.27, 'Matlab "symmetric" \rightarrow', 'color', 'red', 'FontSize',12)
str = {'\leftarrow Matlab "periodic"',' ("DFT-even")'};
text(5.5, 0.74, str, 'color', 'blue', 'FontSize',12)
title('Two 8-point Hann window functions', 'FontSize',12);
xlabel('\leftarrow n \rightarrow')
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Original upload log
Date/Time | Dimensions | User | Comment |
---|---|---|---|
27 August 2013, 04:03:10 | 636 × 374 (12992 bytes) | Bob K (talk · contribs) | User created page with UploadWizard |
Items portrayed in this file
depicts
5 April 2016
image/png
87b6f0454f417c201b3e5d9be13761d7ff3d908c
41,897 byte
392 pixel
620 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 | 22:36, 5 April 2016 | 620 × 392 (41 KB) | Bob K | Enlarge the dots on the graph. | |
20:56, 5 April 2016 | 623 × 394 (41 KB) | Bob K | The formula from Harris' paper (called "DFT Even") is the same as MATLAB's formula (called "periodic"). Therefore only two plots are needed, not three. | ||
18:04, 2 August 2014 | 636 × 374 (15 KB) | GifTagger | Bot: Converting file to superior PNG file. (Source: 8-point_Hann_windows.gif). This GIF was problematic due to non-greyscale color table. |
File usage
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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 | 28.35 dpc |
Vertical resolution | 28.35 dpc |
File change date and time | 22:35, 5 April 2016 |
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