A part of a communication system consists of an amplifier of effective noise temperature, $$Te = \,\,21\,\,{}^ \circ K\,$$, and a gain of 13 dB, followed by a cable with a loss of 3 dB. Assuming the ambient temperature to be $$300{}^ \circ \,K$$, we have for this part of the communication system,

Zero mean Gaussian noise of variance N is applied to a half wave rectifier. The mean squared value of the rectifier output will be:

A source produces 4 symbols with probabilities $${1 \over 2},\,{1 \over 4},\,{1 \over 8}\,\,and\,\,{1 \over 8}.$$ For this source, a practical coding scheme has an average codeword lenght of 2 bits/symbols. The efficiency of the code is :

For the input signal, x(t), shown in Fig.

(a) Sketch the impulse response, h(t), of the matched filter.
(b) Sketch the output, y(t), of the matched filter. Fully label your diagram.
(c) If the input to the matched filter consists of the signal, x(t), plus additive white noise of two sided spectral density of $${10^{ - 6}}$$ watts/Hz, find the maximum output SNR of the matched filter.