Jump to content

File:Two 8-point Gaussian window functions.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 652 × 372 pixels, file size: 36 KB)

Summary

Description
English: Two different ways to generate Gaussian window functions (σ=0.4) for spectral analysis applications. MATLAB calls them "symmetric" and "periodic". The latter is also called "DFT Even" in the classic Frederic Harris paper.
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:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

Other versions Derivative works of this file:  Comparison of symmetric and periodic Gaussian windows.svg
SVG development
InfoField
 
The source code of this SVG is invalid due to an error.
V
 
This W3C-invalid vector image was created with GNU Octave.
Gnu Octave 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

function out=gauss(sigma,M)
out=exp(-.5*(((0:M)-M/2)/(sigma*M/2)).^2);
endfunction

 M=5600;        % big number, divisible by 7 and 8
 window = gauss(0.4,M);   % M+1 samples of a Gaussian window
 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;
%symmetric8 = window(1+(0:7)*sam_per_hop_7);
 symmetric8 = exp(-.5*(((0:7)-7/2)/(.4*7/2)).^2); % Equivalent method

% Scale the abscissa. 0:M samples --> 0:8 "hops", and take 8 asymmetrical hops, from 0 to 7
 sam_per_hop_8 = M/8;
%periodic8 = window(1+(0:7)*sam_per_hop_8);
 periodic8 = exp(-.5*(((0:7)-8/2)/(.4*8/2)).^2); % Equivalent method

% Compare equivalent noise bandwidths (info only)
 ENBW_symmetric8 = N*sum(symmetric8.^2)/sum(symmetric8)^2                            % 1.6233
 ENBW_periodic8  = N*sum(periodic8.^2) /sum(periodic8)^2                             % 1.4533

%------------------------------------------------------------------
% Plot the points
figure("position", [100 200 700 400])

 plot(0:7, symmetric8,  "color","red",   ".", "markersize",14)
 hold on
 plot(0:7, periodic8,   "color","blue",  ".", "markersize",14)

% 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, "xgrid","on")
set(gca, "ygrid","on")
set(gca, "ytick",[0:.25:1])
set(gca, "xtick",[0:8])

title("Two 8-point Gaussian window functions", "fontsize",14, "fontweight","normal");
xlabel('\leftarrow  n  \rightarrow', "fontsize",14)

text(2.96, .56, 'Matlab "symmetric" \rightarrow', 'color', 'red', 'FontSize',12)
str = {'\leftarrow Matlab "periodic"','     ("DFT-even")'};
text(5.1, .813, str, 'color', 'blue', 'FontSize',12)

#{
% After this call, the cursor units change to a normalized ([0,1]) coordinate system
% Draw an annotated right-to-left arrow.
annotation("textarrow", [.683 .644], [.738 .738],...
        "color", "blue", "string", {'Matlab "periodic"','     ("DFT-even")'}, "fontsize",10,...
        "linewidth",1, "headstyle","vback1", "headlength",5, "headwidth",5)

% Draw an annotated left-to-right arrow.
% Bug alert:  Unlike the right-to-left arrow, it centers the text at the arrow start point.
% So the string of blanks in the 1st continuation line is a work-around for that.  
annotation("textarrow", [.565 .62], [.542 .542],...
        "color", "red", "string", {'Matlab "symmetric"            '}, "fontsize",10,...
        "linewidth",1, "headstyle","vback1", "headlength",5, "headwidth",5)
#}

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

28 September 2019

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current01:42, 29 September 2019Thumbnail for version as of 01:42, 29 September 2019652 × 372 (36 KB)Bob Kincrease size of annotation font
00:39, 29 September 2019Thumbnail for version as of 00:39, 29 September 2019652 × 372 (36 KB)Bob KUser created page with UploadWizard

The following page uses this file:

Metadata