A bandlimited periodic continuous-time signal is sampled at twice its Nyquist rate over exactly one fundamental period at f s = 220 Hz with the first sample occurring at t = 0 and the samples are {1, ? 2, ? 4, 6, 3, 5, 9,7} .
(a) What is the maximum frequency at which the continuous-time signal could have any signal power?
(b) What is the fundamental period T 0 of the continuous-time signal?
(c) If sample 1 occurs at time t = 0 and the sampling continued indefinitely, what would be the numerical value of sample 317 and at what time would it occur?
(a) What is the maximum frequency at which the continuous-time signal could have any signal power?
Nyquist rate is 110. Therefore highest frequency cannot be greater than 55 Hz.
(b) What is the fundamental period T0 of the CT signal?
Time between samples is 1/220 seconds. There are 8 samples in one fundamental period. Therefore the fundamental period is 8/220 = 0.0364 seconds.
(c) If sample 1 occurs at time t = 0 and the sampling continued indefinitely, what would be the numerical value of sample 317 and at what time would it occur?
Value of sample 317 is the same as the value of sample 317 – 8n where n is any integer. 317 = 8x39+5. Therefore sample 317 is the same as sample 5 which is 3. If sample 1 occurs at time that means sample 317 occurs at time 316T= 31/220=1.436 seconds.
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