Signals and Systems - Electrical Engineering

Problems 509

absolute value of the input, and a second 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

system.

Let the input to the envelope detector be a sampled signal,

x(nTs)=p(nTs)cos( 2000 πnTs)

where

p(nTs)=u(nTs)−u(nTs− 20 Ts)+u(nTs− 40 Ts)−u(nTs− 60 Ts)

where two pulses of duration 20 Tsand amplitude equal to one.
(a) ChooseTs=0.01, and generate 100 samples of the input signalx(nTs)and plot it.
(b) Consider then the subsystem that computes the absolute value of the inputx(nTs)and compute and
plot 100 samples ofy(nTs)=|x(nTs)|.
(c) Let the low-pass filtering be done by a moving averager of order 15—that is, ify(nTs)is the input, then
the output of the filter is

z(nTs)=

1

15

∑^14

k= 0

y(nTs−kTs)

Implement this filter using the MATLAB functionfilter, 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.