Consider a real-valued sequence x[n] for which X(ejω) = 0 for ≤ |ω| ≤ π. One sequence v...

Consider a real-valued sequence x[n] for which X(e^jω) = 0 for ≤ |ω| ≤ π. One sequence value of x[n] may have been corrupted, and we would like to recover it approximately or exactly. With g[n] denoting the corrupted signal,

and g[n₀] is real but not related to x[n₀]. In each of the following two cases, specify a practical algorithm for recovering x[n] from g[n] exactly or approximately.

(a) The exact value of n₀ is not known, but we know that n₀ is an odd number.

(b) Nothing about n₀ is known.