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ELEG 305 Signals and Systems

Computer Assignment 5 – Due 5/19 midnight
• This is a computer exercises for submission. You can work in pairs or groups of 3,
but not in larger groups, and should each turn in your own report. You should
create a single report that details the analytic setup, the requested plots, along
with your complete set of code in a readable format. You can use MATLAB/Octave,
Python, or Julia.
• These problems are more open ended. The goal is to learn through doing.
ABET Outcomes:
(1) An ability to identify, formulate, and solve complex engineering
problems by applying principles of engineering, science, and mathematics.
(1.5) Apply knowledge of science and math towards problems in signal
processing and communications
1. AM signal reflections (15 points)
• Consider a continuous-time communications system like an AM radio. The signal that you get from the
broadcaster arrives by many paths because the signal can bounce off objects or boundaries that reflects
radio waves. Let’s assume that there are only two paths: a direct one, and another that bounces off the
ground first. The second received signal is a replica of the transmitted signal, but it arrives delayed and
attenuated relative to the first. (Hint: Recall the discussion of comb filters in the lecture.)
• Consider the following family of systems !() described by the equations indexed by ∈ {1,2,3}! = 4 [ 1" #$%!& + 1! #$%"&],
where = '(& 6 meters, c = 300 6 10) meters/second, " = 10*meters, " = +!, seconds, ! = +", , and ! = 2(10#!")'.
A) Make a figure that contains all three plots of the magnitude (in dB) of the frequency response for
positive frequencies on the log scale from 540 kHz to 1700 kHz for each (like in a Bode plot). Use
different colors and linestyles {‘-’,‘:’,’--’} for the three and label them with a legend (label the axes).
[4 points]
B) Let = #$'(-#% + #$'((-##//")% where , = 880 kHz, make a plot that contains 10 periods of
the signal starting at t=0, choosing an appropriate sampling rate, and making sure to plot both the
real and imaginary components as separate curves. [4 points]
C) Plot the output for the three cases of ! as above. Note: you don’t need the inverse Fourier
transform, since the input is a sum of complex exponentials. [4 points]
D) Be sure your code use variables for all constants so they could be changed easily. Clearly document
any inline or stand alone functions. [3 points]
2. Moving average inverse (15 points)
or equivalently as
y=filter(1/7*ones(7,1),1,x);
A) Create the impulse response h[n] for n=0,…,10, by passing in the signal delta=[1,zeros(1,9)].
Plot the signal (make sure to label the time points starting at 0 for h[0]). [2 point]
The discrete-time inverse system of the 7-day moving average can be implemented as
x=filter(7,ones(7,1),y).
B) Plot the impulse response of the inverse system using stem (make sure to label the time points
correctly). [2 point]