ANALYSIS OF DISCRETE LINEAR TIME INVARIANT SYSTEMS

systemX(n) y(n)

the behavior or response of a linear system to a given input signal

One method is based on the direct solution of the input-output equation for the system.

the second method is to decompose the input signal into a sum of elementary signals. Then, using the linearity property of the system, the responses of the system to the elementary signals are added to obtain the total response of the system.

Convolution method

The impulse response:

Finite impulse response

infinite impulse response

system

FIR system

IIR system

The linear time invariant systems are characterized in the time domain by their response to a unit sample sequencean LTI system is causal if and only if its impulse response is zero for negative values of n.

Imp resp is noncausal and stable

Imp resp is causal and unstable

h(n) h(n)

Impulse response is non causal and stable

h(n)

h(n)

Various forms of impulse response

Impulse response is causal and stable

h(n)

Impulse response is causal and unstable

Example :Find the impulse response of the system described by the following difference equation y(n)=1.5 y(n-1)-0.85 y(n-2) +x(n), is this system is FIR or IIR

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