Sample the bandlimited periodic signal, x(t) = 8 cos(50?t) ? 12 sin(80?t) 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.

What will be an ideal response?


The highest frequency in the signal is 150 Hz. Therefore the Nyquist rate is 300 Hz. The period of the signal is the LCM of the two periods of the sinusoidal components, 1/150 and 1/100. The LCM is 1/50. Therefore the period of the signal is 1/50 second. Sampling for 1/50 second at 300 Hz requires 6 samples. If the samples begin at t = 0, they are

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