CD Player

A CD is a digitally recorded sound wave. Since the CD is digital it must have deffinate numerical values for the magnitude of that wave at any given time, and since there is only a finite amout of storage on a CD those deffinite values only change every so often. So if you were to look at a what is stored on the CD you would see a stair stepping function similar to the one below.

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The basic idea of turning this stair step into the smooth sound wave that it used to be is to run it through a digital to analog converter then through a low pass filter WHY?? and then out to a speaker. While this would work you signal would be substantially distorted due to its conversion to and then from a digital signal. We will look at a few diferent ways to compensate for this.

The following is only included for my sake, so I can look at the syntax.

The Fourier Series

A Fourier series is an expansion of a periodic function $f$ in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.

$f(t)=\sum _{k=-\infty }^{\infty }\alpha _{k}e^{\frac {j2\pi kt}{T}}$.

see also:Orthogonal Functions

Principle author of this page: Aric Goe