A real continuous-time signal xc(t) is bandlimited to frequencies below 5 kHz; i. e., Xc(jΩ) = 0 for |Ω| >= 2π(5000). The signal xc(t) is sampled with a sampling rate of 10,000 samples per second (10 kHz) to produce a sequence x[n] = xc(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?