File:Kbd-window.jpg

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Kbd-window.jpg ‎(510 × 425 pixels, file size: 126 KB, MIME type: image/jpeg)

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Description
English: Kaiser-Bessel derived (KBD) window function for different alpha values.
Date
Source Own work
Author Bob K
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(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.
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File:Kbd-window.svg is a vector version of this file. It should be used in place of this JPG file.
File:Kbd-window.jpg → File:Kbd-window.svg
For more information, see Help:SVG.
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This JPG graphic was created with GNU Octave by Bob K.

Matlab

graphics_toolkit gnuplot
N = 129;
M = N-1;
colors = [0 0 1; 0 1 0; 0 1 1; 1 0 1];
alphas = [0.64 2.56 7.68 32];

figure
title('Kaiser-Bessel-derived window functions')
xlim([0 2*M-1])
ylim([0 1.1])
grid on
ylabel(' ')             % create left margin
set(gca,'XTick', [0 : 1/8 : 1]*(2*M-1))
set(gca,'XTickLabel',[' 0'; ' '; ' '; ' '; ' '; ' '; ' '; ' '; '2M-1 '])
set(gca,'YTick', [0 0.2 0.4 0.6 0.707 0.8 1.0])
text(2, 1.05, 'd_n', 'fontsize', 14)
text(100, -0.05, '\leftarrow   n   \rightarrow')

hold on
for graph = 1:4
    alpha = alphas(graph);
    color = colors(graph,:);

    w = besseli(0,pi*alpha*sqrt(1-(2*(0:M)/M -1).^2))/besseli(0,pi*alpha);

    d = zeros(1,2*M);
    for n=0:M-1
    d(1+n) = sum(w(1+(0:n)));
    end

    for n=M:2*M-1
    d(1+n) = sum(w(1+(0:2*M-1-n)));
    end

    d = sqrt(d/sum(w(1+(0:M))));
    plot(0:2*M-1, d, 'color', color, 'linewidth', 2)
end
hold off

text(96, .47, '\alpha=0.64')
text(96, .40, '\alpha=2.56')
text(96, .33, '\alpha=7.68')
text(96, .26, '\alpha=32')

Source code
InfoField

SVG code

Source code 
graphics_toolkit gnuplot
N = 129;
M = N-1;
colors = [0 0 1; 0 1 0; 0 1 1; 1 0 1];
alphas = [0.64 2.56 7.68 32];

figure
title('Kaiser-Bessel-derived window functions')
xlim([0 2*M-1])
ylim([0 1.1])
grid on
ylabel(' ')             % create left margin
set(gca,'XTick', [0 : 1/8 : 1]*(2*M-1))
set(gca,'XTickLabel',[' 0'; ' '; ' '; ' '; ' '; ' '; ' '; ' '; '2M-1 '])
set(gca,'YTick', [0 0.2 0.4 0.6 0.707 0.8 1.0])
text(2, 1.05, 'd_n', 'fontsize', 14)
text(100, -0.05, '\leftarrow   n   \rightarrow')

hold on
for graph = 1:4
    alpha = alphas(graph);
    color = colors(graph,:);

    w = besseli(0,pi*alpha*sqrt(1-(2*(0:M)/M -1).^2))/besseli(0,pi*alpha);

    d = zeros(1,2*M);
    for n=0:M-1
    d(1+n) = sum(w(1+(0:n)));
    end

    for n=M:2*M-1
    d(1+n) = sum(w(1+(0:2*M-1-n)));
    end

    d = sqrt(d/sum(w(1+(0:M))));
    plot(0:2*M-1, d, 'color', color, 'linewidth', 2)
end
hold off

text(96, .47, '\alpha=0.64')
text(96, .40, '\alpha=2.56')
text(96, .33, '\alpha=7.68')
text(96, .26, '\alpha=32')

Original upload log

[edit]

The 5/1/2009 version is a derivative work of the following image:

  • File:Kbd-window.svg licensed with PD-self
    • 2008-02-29T21:14:28Z RetoGalli 560x420 (32379 Bytes) {{Information |Description=Kaiser-Bessel derived (KBD) window |Source=self-made with Matlab |Date=02/29/2008 |Author= [[User:RetoGalli|RetoGalli]]}}

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File history

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Date/TimeThumbnailDimensionsUserComment
current00:03, 1 March 2013Thumbnail for version as of 00:03, 1 March 2013510 × 425 (126 KB)Bob K (talk | contribs)Add title and tickmark @ y=0.707
21:01, 27 February 2013Thumbnail for version as of 21:01, 27 February 2013502 × 390 (121 KB)Bob K (talk | contribs)Upload version that can be regenerated from new Octave script (to be attached).
23:55, 30 April 2009Thumbnail for version as of 23:55, 30 April 2009512 × 411 (61 KB)Bob K (talk | contribs){{Information |Description=Kaiser-Bessel derived (KBD) window |Source=*File:Kbd-window.svg |Date=2009-05-01 00:54 (UTC) |Author=*File:Kbd-window.svg: RetoGalli *derivative work: ~~~ |Permission=see below |other_versions= }}

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