Properties of LSI Impulse Response 1.2 2004/07/13 13:42:48 GMT-5 2004/07/22 11:01:48.979 GMT-5 Richard G. Baraniuk richb@rice.edu Richard G. Baraniuk richb@rice.edu Robert Ahlfinger ahlfing@rice.edu ELEC 301 LSI An overview of the properties of LSI impulse responses.

Causality An LSI system is causal if the current output is a function of only current and past input values.

What is the constraint on h ?

Causality of LTI Systems When, in addition to LTI, is a system causal? Causal y n o depends on x n only for n n o . Causality h n 0 for all h 0

Causal or Non-Causal?

No

Yes

Yes

No

No

FIR - Finite Impulse Response An LSI system is FIR if the current output is the function of only a finite number of input values.

Otherwise it is called IIR - infinite impulse response. What are the constraints on h to be FIR?

Impluse Response Duration

y n k - x k h n k

Type 1: Finite Impulse Response (FIR) N 1 and N 2

sum in convolution is finite practical.

Type 2: Infinite Impluse Response (IIR) Either N 1 or N 2 or both

sum in convolution is infinite impractical.