File:Example of spectral "folding" caused by sampling a real-valued waveform.png

Summary

Description
English: When a continuous-time function is sampled, it becomes indistinguishable from other functions (called aliases) that match the same set of samples. In the frequency domain (Fourier transform), the aliases appear as new frequencies that aren't in the original function. In this example, the original frequency content is between 0 and 22050 Hz. The region [22050,44100] contains new content caused by sampling at 44100 samples/sec. The mirror image effect is referred to as "folding".
Date
Source Own work
Author Bob K
PNG development
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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

% This did not work
% load 'music.mat'    % adds variables wavedata and samplerate to 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
%}

%This did work
[wavedata,samplerate] = audioread('music.ogg');

pwelch(wavedata, hann(512), 0.25, 512, samplerate, 'whole', 'dB')
xlim([0 samplerate])
grid
title('Spectral folding, caused by sampling','FontSize', 14)
xlabel('Frequency (Hz)','FontSize', 14)
ylabel('Amplitude (dB)','FontSize', 14)

Licensing

Bob K, the copyright holder of this work, hereby publishes 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.

Category:CC-Zero#Example%20of%20spectral%20%22folding%22%20caused%20by%20sampling%20a%20real-valued%20waveform.pngCategory:Self-published work
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Category:Graph images that should use vector graphics#%20Example%20of%20spectral%20%22folding%22%20caused%20by%20sampling%20a%20real-valued%20waveform.pngCategory:PNG that should use vector graphics Category:Digital signal processing Category:Created with GNU Octave Category:Images with Octave source code Category:Images with Gnuplot source code
Category:CC-Zero Category:Created with GNU Octave Category:Digital signal processing Category:Graph images that should use vector graphics Category:Images with Gnuplot source code Category:Images with Octave source code Category:PNG created with Octave Category:PNG that should use vector graphics Category:Self-published work