y[n] is the output of a stable LTI system with system function H(z) = 1/(z − bz−1),...

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

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]?