EE354
Exam 2
EE 354 Exam 2 Make Up
Due Date: Friday, 15 April, 2016, in class.
Objective: Reinforce the topics that were the most troublesome on Exam 2, namely superheterodyne,
probability, and baseband signaling/power spectral density.
Honor Statement: This assignment shall be treated like an Exam for the purposes of the Brigade Honor
Concept. The assignment is Open Book and Open (your personal) Notes; no other resources (except
those expressly mentioned in Problem 2) are permitted beyond the Matlab Help Files/Documentation.
You may not discuss this assignment, in whole or in part, with anyone other than the instructor. The sole
exception is that you may discuss basic Matlab questions and issues with other students and faculty;
however, sharing of code (in whole or in part) is prohibited.
Assignment: You have the opportunity to recover points lost on Exam 2 by re-working the following
three problems and then confirming your results via simulation in Matlab. Credit will only be given for
those problems that have an accompanying simulation; full credit requires a detailed and documented
solution (Exam 2 Instructions 4-7 are still in effect), fully documented code, and results that convince the
instructor that simulations and calculations match to within 10% margin of error.
1. (7 points) A dual-band receiver operates at 1800-1900 MHz. Each band contains signals that
are spaced 500 kHz apart and have 200 kHz bandwidth. The IF for the receiver is 250 MHz,
the LO is tunable from 1900 – 2250 MHz. Additional stations in the area are operating at 23502400 MHz and 1600-1700 MHz.
Your capstone partner decided to use a double-conversion receiver (shown below) with
f IF1 = 70 MHz and f IF2 = 10.7 MHz . Determine all image frequencies present at the RF input
to the receiver and whether (and why) their design will experience operational issues.
IF1
RF1
LO
1731
MHz
IF2
RF2
To
Demodulator
LO
80.7
MHz
(a) Calculate the four (4) frequencies that could be received and downconverted to IF2 and
explain why the receiver will experience issues.
(b) Simulate the operation of this double-conversion receiver. To avoid memory errors in
Matlab, divide the frequency values by a factor of 100. Use narrowband AM or FM for the
RF signals. Generate a plot of the frequency spectrum at IF2 clearly showing the overlap of
the four signals and clearly differentiating each signal (colors, linestyle, etc.). Full credit
requires all axes labels, units, proper plot ranges, clear delineation of signals, descriptive
titles, and crisp (not fuzzy) image(s).
EE354
Exam 2
2. (9 Points) A Virginia Tech Extracurricular Activity (VT SEED) manages a $6.3 Million portion
of the university’s investment portfolio. They have a moderately conservative investment
strategy with an expected rate of return of µ = 7.5% and variance of σ 2 = 324 .
(a) If the Rate of Return of their portfolio is Uniformly Distributed, calculate the probability that
SEED will lose at least 10% of their invested capital in any given year.
(b) If the Rate of Return of their portfolio is Gaussian Distributed, calculate the probability that
SEED will lose at least 25% of their invested capital in any given year.
(c) Perform a Monte Carlo simulation of Parts (a) and (b) in Matlab to verify your predictions
above. Monte Carlo simulations involves running many (typically thousands or more) trials of
a random experiment and then using the Law of Large Numbers to compute the probability of
an event.
The Matlab Command rand() can be used to generate numbers based on a Standard Uniform
PDF, and the command randn() can be used to generate numbers based on a Standard
Gaussian PDF. You will need to use a Random Variable Transformation on order to generate a
PDF that corresponds to the problem space – consult your EE353 notes/text, or type “doc
rand” or “doc randn” at the Matlab Command Prompt for more info.
For Parts (a) and (b), generate a plot that clearly compares the theoretical and actual PDF from
the Monte Carlo simulation; subplots may be necessary to convince the instructor that you have
met the 10% margin of error criteria. To generate a PDF based on your simulation trials,
assume that you have created a vector “data” that contains the outcomes of your random
experiments. You can use the hist() command (see “doc hist” for more info) to generate
an estimated PDF via a code segment like the one below (this is for a normal distribution).
n = length(data(:,2));
bins = 20;
% Use a minimum of 20 bins in the Histogram, 40 is better.
% This block gets PDF parameters from the histogram
[N, x]=hist(data(:,2),bins); % Get histogram data from function
del_x = x(3)-x(2);
% Determine bin width for PDF calculation
pdf_hist = N/n/del_x;
% get probability from histogram
% Generate Theoretical Gaussian PDF
gauss_pdf = #####;
% Equation for Gaussian PDF
plot(x,gauss_pdf,'k-')
% Plots theory PDF
hold on
plot(x,pdf_hist,'X') % Plots simulated PDF
Turn in the two plots above as well as your Matlab computed probabilities and comparisons to
predicted. Full credit requires all axes labels, units, proper plot ranges, clear delineation of signals,
descriptive titles, and crisp (not fuzzy) image(s).
EE354
3.
Exam 2
(9 Points) The information in an Analog Signal is A/D Converted and encoded into Binary
PCM. The PCM signal is then encoded into an M=4 Level baseband signal for transmission
across the channel. The analog input signal has a bandwidth of BW = 3.0 kHz and
SQNR ≥ 35 dB .
(a) Determine the Bit Rate and Symbol Rate ( Rb and Rs ) of the PCM signal.
(b) Determine the minimum required bandwidth of the baseband channel assuming rectangular
pulses.
(c) Determine the Power Spectral Density of the baseband transmission for b ∈ [ −2, − 1, 1, 2]
Volts, assuming BNRZ, all symbols are equally likely and assuming rectangular pulse shapes.
(d) Simulate the baseband digital signal and generate both a time-domain and Power Spectral
Density plot; compare the PSD to the theoretical prediction above. Use at least 10
samples/symbol and at least 1,000 symbols (better 10,000 or more) in your simulation in order
to get clear and crisp results. Note that the spec_analysis() function generates a Power
Spectrum; to compare the two you will need to convert from the PSD equation to a Power
Spectrum.
The following code snippet is an example of how to do the PSD  Power Spectrum conversion.
fs = #######; % Sampling frequency
sam_per_sym = ##;
% Samples per Symbol
% freq is the frequency vector output from spec_analysis()
% psd_linear is the power from spec_analysis() converted into linear
Psd_linear = #####;
% Equation for PSD
power_linear = psd_linear.*(fs./length(freq_BNRZ)).*sam_per_sym;
Turn in the two plots above (time domain and Spectrum comparison). Full credit requires all axes
labels, units, proper plot ranges, clear delineation of predicted and simulated signals, descriptive
titles, and crisp (not fuzzy) image(s).