Let x c (t) be a real-valued, bandlimited signal whose Fourier transform x c (j) is zero

Let x_c(t) be a real-valued, bandlimited signal whose Fourier transform x_c(jΩ) is zero for |Ω| ≥ 2π (5000). The sequence x[n] is obtained by sampling x_c(t) at 10 kHz. Assume that the sequence x[n] is zero for n < 0 and n > 999.

Let X[k] denote the 1000-point DFT of x[n]. It is known that X[900] = 1 and X[420] = 5. Determine X_c(jΩ) for as many values of Ω as you can in the region |Ω| < 2π (5000).