Audio signal processing is taking an audio recording, represented as a wave function of amplitude against time, and mathematically manipulating it, often in order to improve the quality.

Transposing the pitch of an audio recording is easy if you allow for changes in the length of the file. If you shorten the time of the wavefunction the frequency increases, and similarly if you lengthen the time of the audio file you decrease the frequency of the wavefunction. However, it is much more computationally intensive to transpose an audio file without changing its length. Fourier analysis is used to change the wavefunction from the time domain to the frequency domain, changing the frequencies represented, then using the inverse Fourier transform to return it to the time domain without lengthening the time of the file. You cannot simply linearly shift all of the frequencies represented in the Fourier transform because the harmonic ratios must remain intact.

This can be used for many reasons, entertainment being common, but there are scientific reasons as well; such as studying infrasonic and ultrasonic waves. The study of ultrasonic waves brings about some issues with computers. To capture ultrasound waves the sampling rate must be considered in order to avoid aliasing of frequencies above the nyquist frequency.

We are going to represent ultrasonic sound waves in the audible range.

by: Juan Vasquez & Robert Sciortino