A real-valued continuous-time segment of a signal xc(t) is sampled at a rate of 20,000 s...

A real-valued continuous-time segment of a signal x_c(t) is sampled at a rate of 20,000 samples/s, yielding a 1000-point finite-length discrete-time sequence x[n] that is nonzero in the interval 0 ≤ n ≤ 999. It is known that x_c(t) is also bandlimited such that for i.e., assume that the sampling operation does not introduce any distortion due to aliasing. X[k] denotes the 1000-point DFT of x[n]. X[800] is known to have the value X[800] = 1 + j .

(a) From the information given, can you determine X[k] at any other values of k? If so, state which value(s) of k and what the corresponding value of X[k] is. If not, explain why not.

(b) From the information given, state the value(s) of