User:Goeari

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Aric Goe

Signals & Systems

• Signals and Systems

Introduction

Aric's Homepage,

Becoming familiar with Wiki

Well, it all seems a little too convenient to me.

Practicing TEX

Simple Transformer Equation

$\frac{Ep}{Tp}=\frac{Es}{Ts}$

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.

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

where

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

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