# HW 06

From Class Wiki

## Contents

## Problem

Figure out why seems to equal an imaginary odd function of frequency, but there is no j.

## Background

This is the incorrect solution derived in class. Cosine is incorrect, because a real odd function of time, ,should map to an imaginary odd function of frequency.

### Proof

Euler's identity | ||

Even function integrates out over symmetric limits | ||

Time integrates out |

- The odd function of time has no component (ie. 0) of frequency. Thus it is an even function in frequency.

### Functions

- Even*Even=Even
- Odd*Odd=Even
- Odd*Even=Odd