1. Analysis of Discrete Linear Time Invariant Systems
y(n)
X(n)
system
the behavior or response of a linear system to a given input signal
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.
One method is based on the direct solution of the input-output equation for the system.
Convolution method

2. The impulse response: Finite impulse response
infinite impulse response
FIR system
system
IIR system

3. The linear time invariant systems are characterized in the time domain by their response to a unit sample sequence
an LTI system is causal if and only if its impulse response is zero for negative values of n.
h(n)
h(n)
Imp resp is noncausal and stable
Imp resp is causal and unstable

4. Various forms of impulse response
h(n)
h(n)
h(n)
Impulse response is non causal and stable
Impulse response is causal and unstable
Impulse response is causal and stable

5. 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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