Question: A square pulse of width to = 1s plus zero- mean white Gaussian noise is input to a filter with impulse response, h (t) =

A square pulse of width to = 1µs plus zero- mean white Gaussian noise is input to a filter with impulse response, h (t) = exp (–t / t1) u (t).
(a) Find the value of the constant such t1 that the SNR at the output of the filter will be maximum.
(b) Assuming the square pulse is non- zero over the time interval (0, t0) at what sampling time will the SNR at the output of the filter be maximized?

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