# User:Goeari

## Signals & Systems

### Introduction

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

Let's look at this result in frequency space. Note that convolution in time means multiplication in frequency. $\hat X(f) = \frac{1}{T} \sum_{n=-\infty}^\infty X(f - \frac{n}{T}) \cdot P(f)$

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

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:

Aric Goe