Audio Aliasing Explorer
Introduction   Demo   Investigate   Reading   Credits   Home

Introduction

This application allows to user to simulate the effects of aliasing in audio. Aliasing occurs when a signal is sampled at a frequency too low to capture the highest frequencies in that signal. For instance, sampling a 1000 Hz tone with a sampling rate (Fs) of 10000 Hz would be able to capture the necessary number of samples per period of the waveform in order to allow perfect reconstruction. In this case there would be 10 samples captured for each period of the waveform. If however the Fs were 1000 Hz, then only one sample per period would be captured at the same phase position--which would look like a DC offset, or straight line. If the Fs were 750 Hz, then the signal originally at 1000 Hz, would reappear at 250 Hz! (These effects can also be visually demonstrated with the Sampling Explorer.)

The tool

This tool is similar to the Fourier Explorer, in that is lets you move a window across the data to watch the Fourier spectrum. The bottom left plot is the time domain plot of the loaded signal. The two red bars represent a window, which you can drag across the signal. The spectrum of the windowed segment is computed and displayed in the top left plot. The scroll bar at the top of the spectrum plot changes the range of frequencies displayed. The scroll bar to the left scales the amplitudes displayed

Once you have loaded a signal you can choose to downsample it, thereby reducing the effective Fs. This is done with the menu at the upper right. In the above example I have loaded a 10 kHz sine wave, sampled at 44.1 kHz. I then downsampled it by 2 (throwing away every other sample), which makes the effective Fs = 22,050 Hz. That is still adequate for perfect reconstruction, but as can be seen the alias of the tone is moving closer to the Nyquist frequency--shown by the red line at 11,025 Hz.

Things to investigate

1. In the image above, why does it appear the alias is folding over? What frequency is the alias at?
2. What will the frequency become of this tone with a downsampling factor of 3, 4, and 10?
3. Load the sound "OldManPurple.wav", and choose a downsample factor of 5. Why does it still sound good? What parts of the speech can you hear the folding? Why?
4. Repeat the same process for the sound "clarinet.wav"? Why is there such a difference at a factor of 5?

Further reading

Credits

The code to make the slidable window and updated spectrum was taken and improved upon from the MAD program "wavspect."

Produced by Bob L. Sturm and Dr. Jerry Gibson
Release date: January 21, 2004
Copyright 2004 University of California, Santa Barbara