User:Caswto

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9-27-2004

Todd Caswell
509-374-2820

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How a CD Player Works

First, a digital signal $x(kt)$ is read from the CD and then convolved with a pulse function $p(t)$ in the D/A converter. The result in the time domain looks like this:

$\hat{x}(t)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}x(kT)p(t-kT)=p(t)*\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}x(kT)\delta (t-kT)$

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency.

$\hat{X}(f)=1/T\sum _{n=-\mathrm{\infty }}^{\mathrm{\infty }}X(f-n/T)\cdot P(f)$

where

$P(f)=\underset{-T/2}{\overset{T/2}{\int }}{e}^{j2\pi ft}dt=Tsinc(fT)$

The low pass filter then knocks the high frequencies out of the signal coming from the D/A converter, which smoothes out the edges of the reproduced sine wave $\hat{x}(t)$ in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors:

Todd Caswell

Aric Goe