Question: 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

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

The Fourier series coefficients αk are zero for |k| > 9.xc(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 discrete Fourier series coefficients of x[n] in terms of αk.

arei(2zk!/10 *) X, (1) = k=-9 n10-3 x[n] = x, 6.

arei(2zk!/10 *) X, (1) = k=-9 n10-3 x[n] = x, 6.

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