Introduction

Impulse Response | DT Convolution | CT Convolution | Properties of LTI Systems |

Introduction | Computing Impulse Response |

### Introduction

- What does it mean?
- What is its significance for LTI Systems?

The impulse response completely characterizes an LTI System. We can find the output $H(x[n])$ for any $x[n]$ if $h[n]$ is known.

### Examples

Any input signal $x[n]$ can be written as:

(1)\begin{align} x[n]=\sum_{k=-\infty}^{\infty}x[k]\delta[n-k] \end{align}

where $x[k]$ is the value taken by the signal $x[n]$ at $n=k$

(2)\begin{align} y[n]=H(x[n])=\sum_{k=-\infty}^{\infty}x[k]h[n-k] \end{align}

The above equation is known as the **Convolution Sum** and is written as:

\begin{equation} y[n]=x[n]*h[n] \end{equation}

page revision: 3, last edited: 26 Aug 2016 16:22