Week 10. Chapter 9

1. Convolution sum & integral1. Kronecker delta and Dirac delta2. Impulse response and convolution

2. Impulse response & frequency response

3. FIR

4. IIR

1. Convolution sum

1. Convolution integral

Example

Example1

1/21/3

n0 1 2

y

Example

Examplex

t

1

y

t

e-t

x*y

t

1-e-t

2. The delta functions

area= 1

Impulse response and convolution (discrete-time)

eecs20/…/topics/convolution/convolution

Impulse response and convolution (cont-time)

h

t

e-t

x

t0 2

y

t0 2

From impulse response to frequency response

An LTI system S is characterized by h, H.The two are related.

Discrete-time

Continuous-time

Example

Example

Causal systems

FIR filter

0 Mk

h

Implementing FIR

topics/convolution/implementation