Impulse response of a linear shift-invariant discrete-time system

In earlier lectures, we emphasized sinusoidal input signals. There is another very important input signal, called the impulse. The response of a system to an impulse is called the impulse response. The impulse response is an alternative characterization of the system, like the frequency response.

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Discrete-time impulse signal

Impulse response of a linear shift-invariant system

Causal linear shift-invariant system

A system is causal if the impulse response h[n]=0 for n<0. This implies that the system does not anticipate the application of the impulse. In the sequel we will assume that systems are causal.

Finite-impulse-response (FIR) system

Infinite-impulse-response (IIR) system

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