Week 10. Chapter 9 1.Convolution sum & integral 1.Kronecker delta and Dirac delta 2.Impulse response and convolution 2.Impulse response & frequency response.

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Presentation transcript:

Week 10. Chapter 9 1.Convolution sum & integral 1.Kronecker delta and Dirac delta 2.Impulse response and convolution 2.Impulse response & frequency response 3.FIR 4.IIR

1.Convolution sum

1.Convolution integral

Example

1 1/2 1/3 n 0 12 y

Example

x 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 t 02 y t 02

From impulse response to frequency response An LTI system S is characterized by h, H. The two are related. Discrete-time

Continuous-time

Example

Causal systems

FIR filter 0M k h

Implementing FIR topics/convolution/implementation