Revision as of 14:07, 26 September 2008 by Cztan (Talk)

Defining the DT LTI system

$ x[n] \rightarrow system \rightarrow y[n] = 5x[n] $

a) Finding the unit impulse response h[n] and the system function F(z).

$ x[n] = \delta [n] \rightarrow system \rightarrow y[n]=5\delta [n] $

Therefore the unit impulse response, $ h[n] = 5\delta [n] $

For a DT LTI system,

$ Z^n \rightarrow system \rightarrow F(z)Z^n $

Output of the system, $ F(z)Z^n = h[n]*Z^n = \sum_{m=-\infty}^{\infty} h[m]Z^{n-m} = Z^n\sum_{-\infty}^{\infty}h[m]Z^{-m} $

Therefore, $ F(z) = \sum_{-\infty}^{\infty}h[m]Z^{-m} $

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