January 19, 2011 20:52
1
Homework #3, EECS 556, W11. Due
Fri. Jan. 28
, by 1:00PM
Skills and Concepts
•
Lens filtering, sampling, discretespace signals and systems
Optional Problems
Problems with “0” points are basic skill problems that anyone working with image processing should be able to solve. However,
you do not have to turn them in, nor will they be graded.
1. [0]
Prove that a LSI 2D system is BIBO stable if and only if its impulse response
h
[
n, m
]
is absolutely summable.
2. [0]
Derive the 2D associative property of convolution.
Problems
3. [5]
A circular lens with diameter 2mm is used in an optical scanner with laser illumination at a wavelength of 800nm in a
1200dpi acquisition mode. The distance between the lens and the detector is 3mm. Can aliasing occur in this system?
4. [15]
(a) [10] Find a (2D DS) FT property for upsampling (using insertion of zeros) by a factor of 2.
(b) [5] Suppose the image with spectrum
F
(
ω
X
, ω
Y
) = rect
parenleftbigg
√
ω
2
X
+
ω
2
Y
2
π
parenrightbigg
(2
π,
2
π
)
is upsampled by a factor of 2.
Carefully sketch the resulting spectrum.
5. [10]
In continuous space, if
g
(
x, y
) =
f
(
x, y
)
**
h
(
x, y
)
F
2
←→
G
(
ν
X
, ν
Y
) =
F
(
ν
X
, ν
Y
)
H
(
ν
X
, ν
Y
)
, then we have the following
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 Winter '08
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 Image processing, Digital Signal Processing, Signal Processing, Impulse response, νx, νY

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