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

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

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

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

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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