Wikimore

Description

English: Kaiser-Bessel derived (KBD) window function for different alpha values.

Date

27 February 2013

Source

Own work

Author

Bob K

Permission
(Reusing this file)

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.

Category:Self-published work#Kbd-window.jpg Category:PD-self#Kbd-window.jpg

Other versions

File:Kbd-window.svg is a vector version of this file. It should be used in place of this JPG file.Category:Superior vector version available

File:Kbd-window.jpg → File:Kbd-window.svg

For more information, see Help:SVG.

In other languages

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Source code

N

This JPG graphic was created with GNU Octave by Bob K.

Category:PNG created with Octave code#Kbd-window.jpg

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

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

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]]}}

Uploaded with derivativeFX Category:Uploaded with derivativeFX

Category:Signal processing Category:Images with Octave source code