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A continuous time signal is given by x(t) = 5 cos 100πt. What is the minimum sampling rate required to avoid aliasing.

A continuous time signal is given by x(t) = 5 cos 100πt. What is the minimum sampling rate required to avoid aliasing. Correct Answer 100 samples/sec

Concept:

Nyquist sampling theorem: Any bandlimited continuous-time signal can be completely represented by its samples if the signal is sampled at a sampling frequency greater than 2 times the maximum frequency present in the signal.

Minimum sampling rate to avoid aliasing:

fs = 2fm = (Nyquist rate)

Calculation:

Given that, ωm = 100 π

ωm = 2πfm

fm = 50 Hz = maximum frequency of signal

Sampling frequency fs = 2 × 50 = 100 samples/sec

The concept is explained by spectrum analysis as:

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