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Original file (SVG file, nominally 700 × 525 pixels, file size: 111 KB)
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Summary
| Description | Spectra of Kaiser windows for different parametric values. Note that the downward spikes in the side lobes should actually spike all they way to -infinity, since at these points the amplitude goes to zero. The fact that the minima are finite is an artifact of the finite plotting resolution. | |||
| Date | 2007-09-19, revised 2019-03-21 by Bob K | |||
| Source | Own work | |||
| Author | RetoGalli | |||
| Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following license:
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| SVG development |  This vector image was created with GNU Octave. |
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| Octave/gnuplot source | click to expand
This graphic was created by the following Octave script: pkg load signal
graphics_toolkit gnuplot
N = 2^17;
n = 0:N-1;
P = 15; % Maximum bin index drawn
dr = 100; % dynamic range of plot
M = 32; % Fourier transform size as multiple of window length
k = ([1:M*N]-1-M*N/2)/M;
k2 = [-P : 1/M : P];
% Uncomment warning() if a text() call includes ("fontname", "Symbol")
% warning("off", "Octave:missing-glyph");
h = figure;
hold on
box on
set(gca,'FontSize',10)
beta=4; alpha = beta/pi
w = besseli(0,beta*sqrt(1-(2*n/(N-1) -1).^2))/besseli(0,beta);
H = abs(fft([w zeros(1,(M-1)*N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
H2 = interp1 (k, H, k2);
plot(k2, H2, "color", "blue", "linewidth", 2)
xlim([-P P])
ylim([-dr 6])
set(gca,"YTick", [0 : -10 : -dr])
grid("on")
ylabel("decibels")
xlabel("DFT bins")
%text(4.26, -36, '\pi\alpha=4; \alpha=1.27', "color", "blue", "fontsize", 12)
%But let's do it the instructive way:
str = ['\pi\alpha=' num2str(beta,'%1i') '; \alpha=' num2str(beta/pi,'%4.2f')];
text(4.26, -36, str, "color", "blue", "fontsize", 12)
beta=8; alpha = beta/pi
w = besseli(0,beta*sqrt(1-(2*n/(N-1) -1).^2))/besseli(0,beta);
H = abs(fft([w zeros(1,(M-1)*N)]));
H = fftshift(H);
H = H/max(H);
H = 20*log10(H);
H = max(-dr,H);
H2 = interp1 (k, H, k2);
plot(k2, H2, "color", "red", "linewidth", 2)
%text(2.5, -19.5, '\pi\alpha=8; \alpha=2.55', "color", "red", "fontsize", 12)
%But let's do it the less "manual" way:
str = ['\pi\alpha=' num2str(beta,'%1i') '; \alpha=' num2str(beta/pi,'%4.2f')];
text(2.5, -19.5, str, "color", "red", "fontsize", 12)
title("Fourier transforms of two Kaiser windows")
% The following print() converts plain-text Greek characters in text() strings into Symbol font.
% Therefore it isn't necessary to include ("fontname", "Symbol") in the text() calls above,
% and doing so causes warnings, some of which can be suppressed by warning().
print(h,"-dsvg","-color",'C:\Users\BobK\Kaiser-Window-Spectra.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 | |
|---|---|---|---|---|---|
| current | 21:25, 22 March 2019 | | 700 × 525 (111 KB) | Bob K | Use definition of α from Window function article. |
| 19:46, 19 September 2007 |  | 560 × 420 (143 KB) | RetoGalli | {{Information |Description=Spectra of Kaiser windows for α of 4 and 8. Note that the downward spikes in the side lobes should actually spike all they way to -infinity, since at these points the amplitude goes to zero. The fact that the minima are finite |
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