64226-mt----detection & Estimation Theory

NR

Code No: 64226/MT

M.Tech. – II Semester Regular Examinations, September, 2008 DETECTION & ESTIMATION THEORY (Wireless & Mobile Communication) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.a)

Compute the Fourier transform for the discrete time signal n

1   [u(n+3)-u(n-2)]. 2 b) Consider a discrete

time

LTI

system

with

impulse

response

n

1 h(n)=   u (n) . 2

Use F T to determine the response to the i/P signal

n

1 x ( n ) = ( n + 1)   u ( n )  4 2.a) b)

The PSD of random process 0 given by S xx ( w) =

A −k < w< k 0 otherwise

find its auto correction function. A Rayleigh density function is given by f x ( x) = x e − x 2 x ≥ 0 =0 x<0 p(0.5 < x ≤ 2) Find i) ii) E(x) and E(x2)

3.a)

b) 4.a) b)

The signal y(t) is observed in the presence colored noise with the 1 − s2 spectrum. φv ( s ) = No . Find the optimum matched filter and 2 − s2 determine the output SNR. Explain the neymen-pearson criterion for radar detection of constant amplitude signal. Derive an expression for the probability of error for the detection of equal energy, orthogonal signals observed in additive white noise. What is matched filter? Explain in detail with relevant mathematical expressions.

Contd….2 Code No: 64226/MT

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5.

Find out MAP and NMSE estimate of x1 from the observation Z=x1+x2 where x1 and x2 are independent and are Rayleigh distributed with parameters σ 12 and σ 22 .

6.a) b)

Explain about uniformly minimum variance unbiased estimation. A signal x(t) i) sampled at regular intervals to give a sequence of amplitudes x1,x2 ……….xn. The xis moderate a carrier and are received in a T-second interval in additric Gauss ion write noise with zero mean and spectral height No/2. The received signal in the jth T-second internal a) Z(t)_=xj Sin Wct+V(t) jT ≤ t ≤ ( j + 1) T How can you estimate xj in the sence of ML.

7.a) b)

Explain the fundamental role of optimum liner filter. Discuss the Numerical accuracy of adaptive algorithms.

8.

Write short notes on: i) Linearized Kalman filter ii) Bounds of MAP Estimates.