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What is the minimum sampling rate to avoid aliasing when a continuous time signal is given by x(t) = 10 cos 400πt?

What is the minimum sampling rate to avoid aliasing when a continuous time signal is given by x(t) = 10 cos 400πt? Correct Answer 400 Hz

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 = 400 π

fm = 200 Hz = maximum frequency of signal

Sampling frequency fs = 2 × 200 = 400 samples/sec

The concept is explained by spectrum analysis as:

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