File:8-point windows.gif
8-point_windows.gif (574 × 390 pixels, file size: 18 KB, MIME type: image/gif, 0.1 s)
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Summary edit
Description8-point windows.gif |
English: We illustrate two different ways to generate Bartlett 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: Comparison of symmetric and periodic triangular window functions.svg | |||
GIF development InfoField | This GIF 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 Triangle window
window = triang(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
hfig = figure
plot(0:7, symmetric, 'color', 'red', '.') % plot the symmetric coefficients
hold on % same axes for next 3 plots
plot(0:7, periodic, 'color', 'blue', '.') % plot the periodic coefficients
% 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(5.2, 0.74, str, 'color', 'blue', 'FontSize',12)
title('Two 8-point Bartlett window functions','FontSize', 14);
xlabel('\leftarrow n \rightarrow')
% Or use the export function on the GNUPlot figure toolbar.
print(hfig,"-dsvg", "-S574,390","-color", 'C:\Users\BobK\8-point windows.svg')
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File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 01:06, 12 April 2016 | 574 × 390 (18 KB) | Bob K (talk | contribs) | Change window title. "Bartlett" is more specific than "triangular". | |
22:06, 5 April 2016 | 574 × 391 (19 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. | ||
21:47, 26 August 2013 | 594 × 374 (13 KB) | Bob K (talk | contribs) | extend continuous plots to the x-axis | ||
03:55, 25 August 2013 | 591 × 399 (13 KB) | Bob K (talk | contribs) | Color code the 3 graphs, and superimpose them on one axis system. | ||
20:25, 22 August 2013 | 571 × 634 (13 KB) | Bob K (talk | contribs) | User created page with UploadWizard |
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GIF file comment | Created with GIMP |
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