EE 311
Hour Exam 2
Name_________________
March 6, 2015
1. Suppose the A/D converter is set up to do a 12-bit conversion on a signal that varies from 0 to
3 volts. I attached sensor to the port but the sensor only produces a signal that uses half of the
voltage range – say from 1 volt to 2.5 volts. How many volts does one-bit represent?
2. I have a sinusoid at 800 Hz which is sampled at 4 KHz. If I down sample by a factor of 4 to 1
KHz, what frequencies will be present in the range 0 to 500 Hz?
3. Write the transfer function for a 10th order moving average filter with a sample frequency of
44100Hz.
4. The step response for a linear DSP system is given below. What is the phase shift at fs/2?
Step response = {1, 3, 4, 4, 4, 4. . .}
5. For a given transfer function, if you double the sample frequency do the poles and zeros move
closer together, farther apart, or neither. Explain.
6. If you build a linear phase FIR filter for an audio system but you neglect to put on an antialiasing filter, how would you expect the output to differ from a similar system which did have
an antialiasing filter on it?
7. The two phase curves shown below are taken from a Matlab plot of two FIR filters which
have identical magnitude plots. What can you say about the relative positions of the zeros of the
two plots. The x axis is frequency in Hertz and the y axis is the phase angle in degrees.
100
50
0
-50
0
0.5
1
1.5
2
2.5
4
x 10
0
-100
-200
-300
-400
0
0.5
1
1.5
2
2.5
4
x 10
8. Circle the characteristics that apply for each of the following.
A)
B)
C)
9. Draw a pole/zero plot for a causal, stable, high pass FIR filter with a linear phase, a phase shift
of 90o at 0Hz, and a gain of 0 at fs/4. Minimize the number of poles and zeros to meet the
requirements.
10. If a step response is given by s(n) = {0.5, 0.75, 1.0, 1.5, 1.75, 1.0, 1.0, …} answer the
following questions:
A) What is the impulse response?
B) Is this an FIR or IIR filter? Explain your answer.
C) What is the transfer function for this system?
D) What is the phase shift at 0 Hz.
E) Does this filter have linear phase?