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File:Comparison of periodogram and Welch methods of spectral density estimation.png

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Summary

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Description
English: The power spectral density of a segment of music is estimated by two different methods, for comparison.
The factual accuracy of this description or the file name is disputed.
Reason: The script below uses the two-sided spectrum, which produces a mirrored copy of the spectrum (from a purely real input signal), which would correctly be plotted at negative frequencies. Falsely, the x-axis goes beyond the Nyquist frequency of 22.5 kHz and places the copy at higher frequencies. Ideally, simply a one-sided spectrum should be used instead.
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Source Own work
Author Bob K
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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.

PNG development
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This PNG graphic was created with LibreOffice.
Octave/gnuplot source
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This graphic was created with the help of the following Octave script: 

graphics_toolkit gnuplot
pkg load signal

load 'music.mat'    % adds variables wavedata and samplerate to the workspace
whos                % displays the workspace
%{music.mat was created by these steps in program Audacity:
  • Open a stereo mp3 file.
  • Right-click on the filename, and choose Split Stereo to Mono in the drop-down menu.
  • Delete one channel.
  • Highlight a section to be exported.
  • Choose Export Selected Audio.
  • Choose Save As Type:  Other Uncompressed Files.
  • Under Options, set Header=MAT5 and Encoding=Signed 16-bit PCM
%}
periodogram (wavedata, [], 512, samplerate, 'twosided')
grid on
xlim([0 samplerate])
title("Periodogram",'FontSize', 14)
xlabel('Frequency (Hz)','FontSize', 14)
ylabel('Amplitude (dB)','FontSize', 14)

figure
pwelch(wavedata, hann(512), 0.25, 512, samplerate, 'twosided', 'dB')
grid on
xlim([0 samplerate])
ylim([-60 60])
title("Welch's method",'FontSize', 14)
xlabel('Frequency (Hz)','FontSize', 14)
ylabel('Amplitude (dB)','FontSize', 14)

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Date/TimeThumbnailDimensionsUserComment
current20:07, 24 October 2016Thumbnail for version as of 20:07, 24 October 2016544 × 662 (33 KB)Bob K (talk | contribs)User created page with UploadWizard

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