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Summary

Description Kaiser Window Function for different parametric values
Date 2007-09-18, revised 2019-03-21 by Bob K
Source Own work
Author RetoGalli
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
SVG development
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The SVG code is valid.
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This vector image was created with GNU Octave.
Octave/gnuplot source
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click to expand

This graphic was created by the following Octave script:

pkg load signal
graphics_toolkit gnuplot

clear all; close all; clc
betas = [1 2 4 8 16];
alphas = betas/pi
colors = [0 0 1; 0 1 0; 1 0 0; 0 1 1; 1 0 1]; %blue green red cyan magenta

hfig = figure;
grid on; hold on; box on
N = 128;	% Relative curve shapes are not sensitive to this number
set(gca, "XTick",[0 : 1/8 : 1]*N,...
         "XTickLabel",[" 0"; " "; " "; " "; " "; " "; " "; " "; "N  "])
xlim([0 N])
ylim([0 1.05])

for k = 1:length(betas)
  w = besseli(0,betas(k)*sqrt(1-(2*(0:N)/N -1).^2))/besseli(0,betas(k));
  plot(0:N, w, "color", colors(k,:), "linewidth", 2)
end

title("Parametric family of Kaiser windows")
ylabel(" ")             % create left margin
text(3, .99, 'W_n', "fontsize", 14)
text(56, -0.05, '\leftarrow   n   \rightarrow')

h = legend(['\pi\alpha=  ' num2str(betas(1),'%2i') '; \alpha=' num2str(betas(1)/pi,'%4.2f')],...
           ['\pi\alpha=  ' num2str(betas(2),'%2i') '; \alpha=' num2str(betas(2)/pi,'%4.2f')],...
           ['\pi\alpha=  ' num2str(betas(3),'%2i') '; \alpha=' num2str(betas(3)/pi,'%4.2f')],...
           ['\pi\alpha=  ' num2str(betas(4),'%2i') '; \alpha=' num2str(betas(4)/pi,'%4.2f')],...
           ['\pi\alpha='   num2str(betas(5),'%2i') '; \alpha=' num2str(betas(5)/pi,'%4.2f')],...
           "location","south");
legend boxoff
set(h, "fontsize",10);

% The following print() converts plain-text Greek characters in text() strings into Symbol font,
% but legend() crashes it.  The set() succeeds, but generates warnings, some of which are 
% diabled by warning().
% print(hfig,"-dsvg","-color",'C:\Users\BobK\KaiserWindow.svg')
  warning("off", "Octave:missing-glyph");
  set(h, "fontname","Symbol");

Captions

Kaiser Window Function for different parametric values

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File history

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

Date/TimeThumbnailDimensionsUserComment
current16:58, 24 March 2019Thumbnail for version as of 16:58, 24 March 2019700 × 525 (78 KB)Bob Kmore space between ylabel and axis
16:43, 24 March 2019Thumbnail for version as of 16:43, 24 March 2019700 × 525 (78 KB)Bob Kmore whitespace above peak value
16:31, 24 March 2019Thumbnail for version as of 16:31, 24 March 2019700 × 525 (78 KB)Bob Kchange x-limit from N-1 to N
21:50, 22 March 2019Thumbnail for version as of 21:50, 22 March 2019700 × 525 (79 KB)Bob KThis version has a full border.
17:00, 22 March 2019Thumbnail for version as of 17:00, 22 March 2019700 × 525 (75 KB)Bob KChange legend to display α and β=πα.
22:09, 18 September 2007Thumbnail for version as of 22:09, 18 September 2007560 × 420 (29 KB)RetoGalli{{Information |Description=Kaiser Window Function for different alpha values |Source=self-made with Matlab |Date=18-September-2007 |Author= RetoGalli }}

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