# 10/3,6 - The Game

From Class Wiki

## Contents

## The Game

The idea behind the game is to use linearity (superposition and proportionality) and time invariance to find an output for a given input. An initial input and output are given.

Input | LTI System | Output | Reason |

Given | |||

Time Invarience | |||

Proportionality | |||

Superposition |

With the derived equation, note that you can put in **any** to find the given output. Just change your t for a lambda and plug n chug.

## Example 1

Let

Let thus | ||

The order of integration switched due to changing from | ||

Different notation | ||

Different notation |

## Example 2

Let

From Example 1 | ||

Different notation |

## Questions

- How do eigenfunction and basisfunctions differ?
- Eigenfunctions will "point" in the same direction after going through the LTI system. It may (probably) have a different coefficient however. Very convenient.