DavidsCD

CD Players Explained!

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As seen above storing voice samles on a cd only involves a couple of steps. First the data must be passed through a low pass filter incase there are any unwanted high frequencies. In our case we would need a filter to pass anything under 22kHz. If we pass anything higher than this then there will be alaising. Next an analog to digital converter (ADC) samples the data at 44000kHz. It does this by basically picking the closest sampling value to the analog value. Next this data is stored on a CD.

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Data is taken from the CD player and is represented mathmatically as $\sum _{k=-\infty }^{\infty }\ x(kT)\delta (t-KT)$. When the data goes through the Digital to Analog Converter (DAC) it is convolved with p(t) to get ${\tilde {x}}(t)=\sum _{k=-\infty }^{\infty }\ x(kT)p(t-KT)$ as shown below.

File:BarnsaDA.jpg

In the frequency domain you can see that this relates to multipliing ${\tilde {\frac {1}{T}}}\sum _{n=-\infty }^{\infty }X(f-{\frac {n}{T}})\cdot$ by P(f) and results in a quite distored X(f).

where

$P(f)=\int _{-{\frac {T}{2}}}^{\frac {T}{2}}e^{j2\pi ft}\,dt=Tsinc(fT)$

File:Barnsasample.jpg

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