Discussion
What is the significance of the matched filter being the time-reverse of the pulse?
Answer: C
Time-reversal is exactly what makes the contributions add coherently. Convolving a pulse with its own time-reverse brings every frequency component into phase at one instant, so the signal builds to a peak there while the noise, being uncorrelated, adds in power only - which is why the signal-to-noise ratio at that instant is the best any linear filter can achieve. It cannot remove noise; it optimises the ratio, which is a different and achievable goal. Bandwidth is set by the transmitted pulse. And the output shape is the pulse's autocorrelation, which is generally rounded rather than rectangular.
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