A continuous-time signal xc(t) is bandlimited to 5 kHz; i.e., xc(t) is sampled with peri...

A continuous-time signal x_c(t) is bandlimited to 5 kHz; i.e., 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

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.