A continuous-time signal x c (t) is bandlimited to 5 kHz; i.e., X c (j) = 0

A continuous-time signal x_c(t) is bandlimited to 5 kHz; i.e., X_c(jΩ) = 0 for |Ω| ≥ 2π (5000). x_c(t) is sampled with period T, producing the sequence x[n] = x_c(nT). To examine the spectral properties of the signal, we compute the N-point DFT of a segment of N samples of x[n] using a computer program that requires N = 2^v, where v is an integer. Determine the minimum value for N and the range of sampling rates 

 F_min < 1/T < F_max

such that aliasing is avoided and the effective spacing between DFT values is less than 5 Hz; i.e., the equivalent continuous-time frequencies at which the Fourier transform is evaluated are separated by less than 5 Hz.