## . Explain any differences. Repeat for a sampling rate of twice the Nyquist rate.

Sample the bandlimited periodic signal, x(t) = 8 cos(50πt) − 12 sin(80πt) at exactly its Nyquist rate over exactly one period of x(t). Find the DFT of those samples. From the DFT find the CTFS. Graph the CTFS representation of the signal that results and compare it with x(t). Explain any differences. Repeat for a sampling rate of twice the Nyquist rate. 68. An arbitrary real-valued signal is sampled 32 times to form a set of numbers, {x[0], x[1], ··· , x[31]}. These are fed into an fft algorithm on a computer and it returns the set of numbers, {X[0], X[1], ···, X[31]}. Which of these returned numbers are guaranteed to be purely real?

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