# User:Goeari

Aric Goe

## Signals & Systems

### Introduction

#### Becoming familiar with Wiki

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

#### Practicing TEX

Simple Transformer Equation
${\displaystyle {\frac {Ep}{Tp}}={\frac {Es}{Ts}}}$

## How a CD Player Works

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

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

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

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

where

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

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 ${\displaystyle {\hat {x}}(t)}$ in time. This output waveform then drives the speaker, thereby recreating the original sound stored on the CD.

Contributing Authors: