A 2.5 seconds long segment of a continuous time signal is uniformly sampled with

Question

A 2.5 seconds long segment of a continuous time signal is uniformly sampled without aliasing and generating a finite length sequence containing 2501 samples. Answer the following questions.       

What is the sampling interval (T)?

What is the sampling frequency (fs)?

What is the Nyquist rate?

What is the highest frequency component that could be present in the continuous time signal?

What is the Nyquist frequency?

What is the folding frequency?

What is the Nyquist band?

What possible types of sampling could have been done here? (Over, Under or Critical)

Explanation / Answer

Thanks for choosing chegg!! here's the answer..

The sampling interval would be = (message signal duration)/(number of samples) = (2.5 seconds)/(2500 samples) = 1 milli second. (Here we have taken the number of samples to be 2500 since the first sample represents zero as the message signal duration is from 0s to 2.5s)

The sampling frequency(Fs) would be = 1/(sampling interval) = 1/(1millisecond) = 1000Hz.

The frequency of the message signal is 1/2.5 = 0.4 Hz

The nyquist rate would be to sample at a frequency twice the frequency of the message signal that would be 0.8 Hz

the highest frequency component that could be present in the continuous time signal could be half of the sampling rate that woulf be 1000/2 = 500Hz

The nyquist frequency is sampling frequency / 2 = 1000/2 = 500Hz

The folding frequency would be equal to the nyquist frequency that is 500Hz.

The nyquist band would be from 500Hz and any frequency above it.

The samling that could be done over here is over sampling as the sampling rate is higher than the nyquist frequency.

Thank you!! Happy learning! :)

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