EESS 321 Signals & Systems 4(3+3)

Linear Time Invariant Systems

Dr. Hameedullah Kazi

Department of Electrical Engineering

Isra University, Hyderabad

January 2015

Linear Time-Invariant Systems

The Convolution Sum

The Convolution Integral

Properties of LTI Systems

◦ Commutative

◦ Distributive

◦ Associative

◦ Memory

◦ Invertibility

◦ Causality

◦ Stability

◦ Unit Step Response

Convolution Example 1

Convolution Example 2

Convolution Examples 2

Convolution Examples 2

Convolution Example 3

Convolution Graphical Example 3

Convolution Graphical Example 3

Convolution Graphical Example 3

Convolution Example 3

Convolution Example 4

Convolution Example 4

Commutative

1

1

( )* ( ) ( )

[ ]* [ ] [ ]

h t h t t

h n h n n