# A matched filter is used for the reception of the pulse g t = e-at , 0 = t = T in an AWGN channel…

A matched filter is used for the reception of the pulse g t
= e__t , 0 _ t _ T in an AWGN channel with zero mean and
PSD N0/2 W/Hz.

a. Find and sketch the impulse response of the filter which
is matched to the pulse g(t). b. Derive an expression for the maximum output
SNR in terms of the parameters _, T and N0. c. Consider the signalling
scheme characterized by s0(t) = _g(t) and s1(t) = g(t) for 0 _ t
_ T, with equal probability, in a AWGN channel with PSD N0/2 watts/Hz.
Sketch the pdf of the decision variable corresponding to s0(t) and s1(t), and
derive the probability of error. d. Repeat

A matched filter is used for the reception of the pulse g t
= e__t , 0 _ t _ T in an AWGN channel with zero mean and
PSD N0/2 W/Hz.

a. Find and sketch the impulse response of the filter which
is matched to the pulse g(t). b. Derive an expression for the maximum output
SNR in terms of the parameters _, T and N0. c. Consider the signalling
scheme characterized by s0(t) = _g(t) and s1(t) = g(t) for 0 _ t
_ T, with equal probability, in a AWGN channel with PSD N0/2 watts/Hz.
Sketch the pdf of the decision variable corresponding to s0(t) and s1(t), and
derive the probability of error. d. Repeat (a)(c) for g(t) = 2 t/T, 0 _
t _ T

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