CDPlayerJEW

How a CD Player Works

A CD player reads a dicrete set of data off a CD. In short, a CD player takes this data and sends it through a digitla to analog converter, then through a low pass filter, and finally is output through speakers. A simple diagram illustrates this below.

When an audio CD is recorded, the music has an infinite amount of data points and can be represented as a continuous function of time $x(t)$. Because a medium, such as a CD, has a finite amount of space, it will not be able to hold $x(t)$ since it has an infinite amount of data. Instead, the music is sampled at intervals to create a discrete function of time $x(nT)$ where $n$ is an integer and $T$ is the interval between samples.

This discrete signal can be represented mathematically by:

$\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}x(nT)\delta (t-nT)$

Then, the discrete signal is convolved by the D/A converter with a function $p(t)$:

$p(t)=u(t+\frac{T}{2})-u(t-\frac{T}{2})$

$\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}x(nT)\delta (t-nT)*p(t)=\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}x(nT)p(t-nT)$

This convolution, which is the convolution of the discretized signal and $p(t)$, a pulse function, will yield a graph that is no longer discrete, but is stepped. The following is an example:

In the frequency domain, the above stepped signal will look like the following:

- Principle author of this page: Jeffrey Wonoprabowo

- Image of CD Player Diagram and Convolution by Aric Goe or Todd Caswell (not sure which since both of them had it on their pages)