# Question: The input to a filter consists of a half sinusoidal

The input to a filter consists of a half- sinusoidal pulse

plus zero- mean white Gaussian noise.

(a) Suppose the impulse response of the filter is rectangular, h (t) = rect (t / ta). What should the width of the rectangle, ta, be in order to maximize the SNR at the output? At what point in time does that maximum occur?

(b) Suppose the impulse response of the filter is triangular, h (t) = tri (t / tb). What should the width of the triangle, tb, be in order to maximize the SNR at the output? At what point in time does that maximum occur?

(c) Which filter (rectangle or triangle) produces the larger SNR and by how much? Specify your answer in decibels (dBs).

plus zero- mean white Gaussian noise.

(a) Suppose the impulse response of the filter is rectangular, h (t) = rect (t / ta). What should the width of the rectangle, ta, be in order to maximize the SNR at the output? At what point in time does that maximum occur?

(b) Suppose the impulse response of the filter is triangular, h (t) = tri (t / tb). What should the width of the triangle, tb, be in order to maximize the SNR at the output? At what point in time does that maximum occur?

(c) Which filter (rectangle or triangle) produces the larger SNR and by how much? Specify your answer in decibels (dBs).

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