Suppose xc(t) is a periodic continuous-time signal with period 1 ms and for which the Fo...

Suppose x_c(t) is a periodic continuous-time signal with period 1 ms and for which the Fourier series is

The Fourier series coefficients a_k are zero for |k| > 9. x_c(t) is sampled with a sample spacing T = 1/6 × 10⁻³ s to form x[n]. That is,

(a) Is x[n] periodic and, if so, with what period?

(b) Is the sampling rate above the Nyquist rate? That is, is T sufficiently small to avoid aliasing?

(c) Find the DFS coefficients of x[n] in terms of a_k.