Consider an envelope detectorthat would be used to detect the message sent in an AM system. Consider the envelope detector as a system composed of the cascading of two sys-tems one which computes the absolute value of the input, and a sec-ond one that low-pass filters its input. A circuit that is used as an envelope detector consists of a diode circuit that does the absolute value operation, and an RC circuit that does the low-pass filtering. The following is an implementation of these operations in the discrete-time time.

Let the input to the envelope detector be a sampled signal x(nT_s) = p(nT_s) cos(20? nT_s) where

p(nT_s) = u(nT_s) ? u(nT_s ? 20) + u(nT_s ? 40) ? u(nT_s ? 60)

two pulses of duration 20 and amplitude equal to one.

(a)?Choose T_s = 0.01, and generate 10,000 samples of the input signal x(nT_s) and plot it.

(b)?Consider then the subsystem that computes the absolute value of the input x(nT_s) and compute and plot 10,000 samples of y(nT_s) = ?x(nT_s)?.

(c)?Let the low-pass filtering be done by a moving-averager of order 15, i.e., if y(nT_s) is the input, then the output of the filter is

Implement this filter using the function filter, and plot the result. Explain your results.

(d) Is this a linear system? Come up with an example using the script developed above to show that the system is linear or not.

Transcribed Image Text:

14 1 z(nT,) Ey(nT, – kT,) 9.75 k=0