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BIM 251
Medical Image Analysis
Winter 2009
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Homework #1
Due January 14
1. There is a periodic random process
0
() c
o
s
)
(
fx
x
ω
θ
=
+
, where
is a uniform random variable
(rv) over the interval [0,2 )
π
and
0
is a constant.
a) Find the expectation {()
}
Efx
.
b) Find the autocorrelation function
12
)
(,
Rx
x
.
c) Is f(x) widesense stationary (WSS)?
2. Consider the random process
0
()
c
o
s
(
)
gx
x
A
+
=
, where
A
is a real rv with a Rayleigh pdf,
2
pr( )
exp(
/ 2),
0
AA
A
A
=−
≥
,
is a uniform rv over the interval [0,2 )
and
0
is a constant.
A
and
θ
are independent. This is a mathematical model of ultrasonic and MR echo signals for
some realistic situations.
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This note was uploaded on 10/15/2010 for the course BIM BIM251 taught by Professor Buonocore during the Spring '09 term at UC Davis.
 Spring '09
 Buonocore

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