Question: Y[n] is the output of a stable LTI system with system function H(z) = 1/(z bz 1 ), where b is a known constant.

Y[n] is the output of a stable LTI system with system function H(z) = 1/(z – bz ^–1), where b is a known constant. We would like to recover the input signal x[n] by operating on y[n]. The following procedure is proposed for recovering part of x[n] from the data y[n]:

1. Using y[n], 0 ≤ n ≤ N – 1. Calculate Y[k], the N-point DFT of y[n].

2. Form

V[k] = (W – bW)Y[R]. N.

3. Calculate the inverse DFT of V[k] to obtain v[n].

For which values of the index n in the range n = 0, 1 ….. N – 1 are we guaranteed that

x[n] = v[n]?

V[k] = (W bW)Y[R]. N.

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