TIME DOMAIN ANALYSIS

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Stability

Stability

CausalityCausality

ExampleExample 2/2b

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Stability of Systems

• Given Impulse response stability of Systems can be checked by computing the sum

n

khS

stableissystemthenSIf ,• Ideal delay system• MA system• Forward Difference System• Backward Difference System

• Stable Systems-h[n] has finite no of non zero samples• FIR Systems• Accumulator (Infinite Impulse Response) – Unstable

system IIR System 4/4

Causality of LTI Systems

• Ideal delay system – Causal • MA system – • Forward Difference System-Causal• Backward Difference System- Non Causal

• Accumulator - Causal

, Non Causal

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causalissystemthennfornhIf ,00][

ond ond

021 MandoMforCausal

Difference Equations

Difference Equations 5/6

Finite Impulse Response (FIR): for causal, FIR systems:

Mnandnnh 0 0

1

0

M

kknxkhny

Convolution reduces to:

Infinite Impulse Response (IIR):

Finite impulse responseFinite Impulse Response6/12

Infinite Impulse Response7/6

IIR: AccumulatorIIR: Accumulator

(BIBO) stable 9/13

LTI Summary