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Problem Set 2
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
1.
Consider the binary hypothesis testing problem:
H0 : y = v,
H1 : y = A + v,
where 0 < A < 1 is a known constant and noise v is uniformly distributed over [1/2
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Problem Set 3
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
1. [OPTIONAL - do it only if you have time] We reviewed (real) m-dimensional Gaussian vector x and ndimensional Gaussian vector y and underlined that if x and y
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Problem Set 5
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
1.
Let cfw_Yk , 1 k N be N independent uniformly distributed random variables over [0, X ], so the density of
each Yk takes the form
1/X,
f (y |X ) =
0,
0yX
o
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Problem Set 4
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
Periodogram (or implement your own spectrum analyzer!)
Consider observations
Y (t) = Zc cos (0 t) + Zs sin (0 t) + V (t),
(1)
for 0 t N 1 of a sinusoidal signal
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Mid Term
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
Problem 1 (Warmup) [1/9]
H1
You are given a test L(y) for a binary hypothesis testing problem, with hypotheses H0 and H1 . This test
provides probability of detection
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Problem Set 1
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
1.[WARMUP]
Consider the binary hypothesis testing problem:
H0 :Y = V,
H1 :Y = X + V,
where X, V are two independent exponential random variables with parameters
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Problem Set 6
TEL 603 Detection & Estimation, Fall 2009
ECE Dept., Technical Univ. of Crete
1.
In digital communications, it is sometimes necessary to determine whether a communication link is active or
not. Suppose that we are trying to decide whether