User:Caswto

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9-27-2004


Todd Caswell
509-374-2820



How a CD Player Works

Description


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:


Description


\hat x(t) = \sum_{k=-\infty}^\infty x(kT)p(t - kT) = p(t) *\sum_{k=-\infty}^\infty x(kT) \delta (t - kT)


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


Description


\hat X(f) = 1/T \sum_{n=-\infty}^\infty X(f - n/T) \cdot P(f)

where

P(f) = \int_{-T/2}^{T/2} e^{j2\pi ft} \, dt = T sinc(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