File:8-point Hann windows.png
8-point_Hann_windows.png (620 × 392 pixels, file size: 41 KB, MIME type: image/png)
Captions
Summary
[edit]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
[edit]Date/Time | Dimensions | User | Comment |
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27 August 2013, 04:03:10 | 636 × 374 (12992 bytes) | Bob K (talk · contribs) | User created page with UploadWizard |
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:36, 5 April 2016 | 620 × 392 (41 KB) | Bob K (talk | contribs) | Enlarge the dots on the graph. | |
20:56, 5 April 2016 | 623 × 394 (41 KB) | Bob K (talk | contribs) | 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 (talk | contribs) | Bot: Converting file to superior PNG file. (Source: 8-point_Hann_windows.gif). This GIF was problematic due to non-greyscale color table. |
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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 |