Figure P7.28(a) shows a system that converts a continuous-time signal to a discrete-time...

Figure P7.28(a) shows a system that converts a continuous-time signal to a discrete-time signal. The input x(t) is periodic with a period of 0.1 second. The Fourier series coefficients of x(t) are

The lowpass filter H(jω) has.the frequency response shown in Figure P7.28(b). The sampling period second.

(a) Show that x[n] is a periodic sequence, and determine its period.

(b) Determine the Fourier series coefficients of x[n].