In real continuous-time signal x c (t) is bandlimited to frequencies below 5 kHz; i.e., X c (j) = 0 for || 2(5000). The

In real continuous-time signal x_c(t) is bandlimited to frequencies below 5 kHz; i.e., X_c(jΩ) = 0 for |Ω| ≥ 2π(5000). The signal x_c(t) is sampled with a sampling rate of 10,000 samples per second (10kHz) to produce a sequence x[n] = x_c(nT) with T = 10⁻⁴.

Let X[k] be the 1000-point DFT of x[n].

(a) To what continuous-time frequency does the index k = 150 in X[k] correspond?

(b) To what continuous-time frequency does the index k = 800 in X[k] correspond?