Unformatted text preview: Professor BJ Trivedi
Exam 2B Fall 2011 Solutions
True or False a. Consider the IIR filter specified by the difference equation:
The System Function H(Z) is FALSE b. An LTI system with the transfer function given below is a second order FIR filter FALSE the transfer function is one of an IIR filter. Professor BJ Trivedi
Exam 2B Fall 2011 Solutions
c. Given the transfer function below, the system is stable. True, are no poles outside the unit circle. P 212
d. An FIR filter has the frequency response
is applied to the FIR filter. The corresponding output signal is False. . The input signal x[n] = Professor BJ Trivedi
Exam 2B Fall 2011 Solutions MATLAB Question: You are asked to write MATLAB codes to perform a filtering operation in this
question. You may simply provide the right sequence of MATLAB commands with proper arguments to
perform the required operations. There is no need to write MATLAB functions. You must make sure that
your MATLAB commands are syntactically correct.
a. Suppose that an input signal has already been generated and entered into a vector named xx.
Given the transfer function
. Write the MATLAB code
necessary to put the transfer function into a vector hh, and the output signal of xx applied to hh
in the vector yy. hh = [1 3 3 0 4 2];
yy = conv(hh,xx); b. Write the MATLAB code to plot the magnitude and phase responses of the filter described in
part (a) in two subplots, one on the top and one on the bottom. Be sure to properly label the
axes of your plots. w = pi:pi/100:pi;
Hz = freqz(hh,1,w);
subplot(2,1,1);
plot(w/pi, abs(Hz));
ylabel(‘Magnitude Response’);
subplot(2,1,2);
plot(w/pi, angle(Hz));
ylabel(‘Normalized Radian Frequency’); Professor BJ Trivedi
Exam 2B Fall 2011 Solutions Free Response 1
Concept Being Tested: Filter Design (Chapter 6 & 7), ABET Outcome A
Question: Consider a 6 point simple moving average (MA) filter
a. Calculate the transfer function H(Z) b. Show the polezero diagram for H(Z). Hint: User the standard result for this filter class to
determine the poles and zeroes.
p. 181 c. Sketch the Magnitude of the filter frequency response and identify all null points in the [π, π]
interval. d. To transform this system into a bandpass filter with a center frequency at
, determine K0
such that the new pole zero plot is obtained by rotating the above polezero plot counterclockwise by
show the new polezero plot. Professor BJ Trivedi
Exam 2B Fall 2011 Solutions
e. Develop an additional modified polezero plot such that it yields a bandpass filter with a center
frequency at
and real coefficients. What is the new transfer function H1(z) based on this
new polezero plot? f. Write the impulse response function h1[n] for the filter in part e. g. You are involved with the design of a digital AM radio tuner circuit. Assume that the radio
spectrum occupies the interval [505 kHz – 2505 kHz] and each radio station uses a band of
10kHz contiguously spaced in the spectrum. Assume also that the digital tuner utilizes a
sampling frequency of 3150 kHz. You are to implement the tuner with an L point MA filter. To
tune into a particular station the passband of the filter would shift to correspond with the
location of the station in the AM spectrum specified above. Determine the value of L necessary
for such a tuner. h. The tuner in part g needs to tune into WUFG with a center frequency of 2000kHz. Determine the
value of k0 needed to shift the filter passband to this position. Use the definition of K0 implied
by part d above. [Hint: first determine the center frequency as radians.] Professor BJ Trivedi
Exam 2B Fall 2011 Solutions Free Response 2
Concept Being Tested: Standard LTI Systems Question (Chapter 7), ABET Outcome 3
Question: Consider the signal
a. If this signal acts as the input to a CtoD converter what is the output signal x[n] if fs=1000
samples/sec? b. For this LTI System there is a system function
of the system? , what is the output , c. Determine an expression for y(t),if the output of the previous section is placed into a DtoC
converter. d. If a new signal
is placed into a system with the same system function in
the previous step. Show how to calculate y[n] in MATLAB, n is already given below.
nn
xn
bn
yy =
=
=
= [0:29];
cos((1/5)*pi*nn)– (pi/6));
[1 1 3 3];
conv(bn,xx); ...
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 Fall '08
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 Digital Signal Processing, Signal Processing, Professor BJ Trivedi

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