EE114
Introduction to Speech and Image Processing
Winter Quarter, 2011
Page 1 of 8
EE114 Midterm Exam Solutions
Notes:
 For all problems please circle or otherwise clearly indicate your answers!
The use of calculators or other electronic devices with calculatorlike functionality is not
permitted on this test.
1. Signal processing basics (25 points)
1a) Sampling and Reconstruction (7 points)
Suppose that a signal consisting of a pure cosine at 4000 Hz is subject to ideal sampling at a
sampling frequency of 5000 Hz, and then subject to reconstruction using an ideal low pass filter
with a cutoff of 2500 Hz. What is the frequency of the resulting cosine?
Answer:
1000 Hz. The spectrum of the original cosine is a pair of delta functions at plus and minus 4 KHz.
After sampling, these delta functions will be replicated at intervals of 5 KHz. The delta function
locations in KHz will then be
. . . .11,9,6, 4, 1,1, 4, 6, 9, 11, 14, 16 . . .
After application of the low pass filter, only those delta functions at plus and minus 1KHz will
remain.
1b)
1D Convolution (12 points)
Figure 1 below shows a triangle function that starts on the horizontal axis at position 4, rises to a
maximum height of 1 at 5, and then declines again until it reaches a value of zero again
horizontal axis position 6.
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 Spring '11
 VanSchaar
 Image processing, Digital Signal Processing, Signal Processing, Cartesian product, Lowpass filter

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