Consider the system in Figure. The input x[n] and corresponding output x_d[n] are given for a specific choice of M/L in each of the following parts. Determine a choice for M/L based on the information given, and specify whether your choice is unique.

(a) x[n] = sin (π n/3) / (π n/3). x_d[n] = sin (5π n/6) / (5π n/6)

(b) x[n] = cos (3π n/4). x_d[n] = cos(π n/2)

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Interpolator Decimator Lowpass filter Gain = 1 Cutoff = 1!M ä,(1)] Lowpass filter Gain = L. Cutoff = niL | x,\r] x;(n} x(n] Sampling period: T т т L. L. L. (a) Lowpass filter Gain = L Cutoff = min (7/L, T/M) x[n] x„[n] Sampling period: TM L. L. (b)