User:Goeari

Aric Goe

Signals & Systems

Introduction

Becoming familiar with Wiki

Well, it all seems a little too convenitent 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 adn then convolved with a pulse function $p(t)$. 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 is frequency space. Note that convolution in time means multiplication in frequency.

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

where

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

The low pass filter then knocks the high frequencies out of the signal to be sent to the speaker.