**ADVANCED DIGITAL SIGNAL PROCESSING**B.E ECE, 6TH SEM

ANSWER THE FOLLOWING:

PART A-(10*2=20)

1. Define statistical variance and covariance.

2. How do you compute the energy of a discrete signal in time and frequency domains?

3. Define sample autocorrelation function. Give the mean value of this estimate.

4. What is the basic principle of Welch method to estimate power spectrum?

5. How do find the ML estimate?

6. Give the basic principle of Levinson recursion.

7. Why are FIR filters widely used for adaptive filters?

8. Express the Widrow- Hoff LMS adaptive algorithm. State its properties.

9. What is meant by image smoothing and image sharpening?

10. Give the two channel wavelet filter banks to decompose the input signal into frequency bands

.PART-B (5*16=80)

11. (a) 1. Define the following terms :

(i) Uniform noise.

(ii) Wiener – Khintchine theorem.

(iii) Power spectrum

(iv) Physical significance of spectral factorization.

2. Define Hilbert space and orthogonal projection . How does it help in estimation.

(Or)

(b) Consider a discrete random process X(n) = Acos(2?f0n+?)+?(n). where A and f0 are constants , ? is a random variable with pdf f0 (?) = B 0=?=2?

= 0 elsewhere ?(n). is an independent white noise. Determine the autocorrelation and power spectrum of this random process. And Assume a Gaussian random process with narrow band spectrum zero mean and variance s2. Prove that the two quadrature components of it are uncorrelated and possess equal variance.

12. (a) (i) Define cross correlation and cross spectrum. Relate the output cross spectrum in terms of input cross spectrum.

(ii) Explain about smoothed spectral estimation.

(Or)

(b) Present the model based approach to power spectral estimation. Define AR,MA, and ARMA models. And Illustrate the ARMA model for spectrum estimation.

13 (a) (i) Give the properties of linear estimators and the Cramer-Rao bound.

(ii) Briefly explain the estimation of a non stationary process by a Kalman filter.

(Or)

(b) (i) Describe the basics of forward linear prediction . Give the schematic of FIR filter and Lattice filter for first order predictor.

(ii) Derive the recursive predictor coefficients for optimum lattice predictor by Levinson –Durbin algorithm.

14(a) What do you understand by an adaptive filter? Discuss the minimum MSE criterion to develop an adaptive FIR filter

(Or)

(b) Explain the adaptive channel equalization in detail.

15 (a) Define 2D DFT and state its separability and peridiocity properties. Explain its role in the image smoothing and sharpening operations.

(Or)

(b) Explain the multisolutional analysis of wavelets . Explain the application of wavelets in signal compression.