Which Of The Following Signals Can Be Downsampled By Factor

Which of the following signals can be down sampled by a factor of 2 using the system in Figure without any loss of information?

(a) x[n] = δ[n – n0], for n0 some unknown integer 

(b) x[n] = cos(π n/4)

(c) x[n] = cos(π n/4) + cos(3π n/4)

(d) x[n] = sin(π n/3) / (π n/3) 

(e) x[n] = (–1)n sin(π n/3) / (π n/3)

Which of the following signals can be downsampled by a factor

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