The following facts are given about the signal x[n] and its Fourier transform: 1. x[n]

Chapter 7, Problem 7.16

(choose chapter or problem)

The following facts are given about the signal x[n] and its Fourier transform:

1. x[n] is real.

2. \(X\left(e^{j \omega}\right) \neq 0 \text { for } 0<\omega<\pi\).

3.\(x[n] \sum_{k=-\infty}^{\infty} \delta[n-2 k]=\delta[n] .\).

Determine x[n]. You may find it useful to note that the signal \(\left(\sin \frac{\pi}{2} n\right) /(\pi n)\) satisfies two of these conditions.