A signal of bandwidth 3.5 kHz has peak-to-peak and rms amplitudes of 4 V and 0.2 V, respectively. This signal is passed through a linear PCM coder and then transmitted over a channel capable of supporting a transmission rate of 60 kbps. Calculate the maximum signal-to-quantization-noise ratio that can be obtained using this system.

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.

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 :

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