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Consider the sinusoidal signal  Suppose this signal is sampled at w, frequency. If this impulsesampled signal is applied as the input to an ideal lowpass filter with cutoff frequency w ωs/2, the resulting output is: 

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Answer (Detailed Solution Below)

Option 1 :
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Concept:

We are given a sinusoidal signal:

This signal is sampled at frequency . After sampling, the signal becomes an impulse train containing frequency components centered at multiples of .

If this sampled signal is passed through an ideal lowpass filter with cutoff frequency , only baseband components (centered around 0 Hz) are retained.

Calculation:

Using the trigonometric identity:

After lowpass filtering, the component is removed because it lies at or above the cutoff frequency and is attenuated. Only the baseband term remains.

Thus, the output is:

Final Answer:

✅ The resulting output after ideal lowpass filtering is:

Correct Option: (1)

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