A rectangular pulse of duration T is applied to a filter matched to this input. The output of the filter is aa) Rectangular pulse of duration Tb) Rectangular pulse of duration '2Tc) Triangular pulsed) Sine functionCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Matching Filter Response to Rectangular Pulse

A matching filter is a filter designed to maximize the signal-to-noise ratio of a signal by matching the filter's impulse response to the input signal. In this case, a rectangular pulse of duration T is applied to a filter matched to this input.

Output of the Filter

The output of the filter is a triangular pulse, which is option C. This is because the matched filter's impulse response is a time-reversed and scaled version of the input signal. In this case, the matched filter's impulse response is a triangular pulse.

Explanation

When a rectangular pulse is applied to a filter, the filter's impulse response is a triangular pulse that ramps up and then ramps down to zero. This is because the rectangular pulse contains a wide range of frequencies, and the filter's impulse response is designed to match these frequencies. As a result, the filter's output is a triangular pulse.

Conclusion

In conclusion, when a rectangular pulse of duration T is applied to a filter matched to this input, the output of the filter is a triangular pulse. This is because the matched filter's impulse response is a time-reversed and scaled version of the input signal, which in this case is a triangular pulse.

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