SRI BALAJI CHOCKALINGAM ENGINEERING COLLEGE

DEPT.OF ELECTRONICS & COMMUNICATION ENGG.

ME-APPLIED ELECTRONICS

MODEL EXAM

AP7101 ADVANCED DIGITAL SIGNAL PROCESSING

SEM/YEAR:I/I Duration:3hrs

DATE : MARKS : 100

PART-A(2*10=20)

ANSWER ALL QUESTIONS

1. Calculate the mean and variance for the auto correlation function of random signals.

2. State Wiener-Khintchine relation.

3. What is periodogram averaging?

4. Compare parametric and non-parametric methods of spectral estimation.

5. What is linear prediction?

6. What is meant by prediction?

7. What is need of adaptivity?

8. How will you avoid echos in long distance telephone circuits?

9. What is need for multiple signal processing?

10. What is discrete wavelet transform?

PART-B(16*5=80)

11. a. (i) Explain the concepts of Random Process with examples. (8)

(ii) State and prove the parseval’s Theorem. (8)

(OR)

b). (i) Calculate the mean and variance of the auto correlation function of random

signals (76-monson hayes) (8)

(ii) Determine the power spectra for a random processes generated by x (n) = w(n) – x(n – 2). Where w(n) is white noise process with variance σ2 . (8)

12. (a) (i) Explain the AR, MA, ARMA models. (8)

(ii) What is a Periodogram? How do you estimate the performance of a Periodogram? (8)

Or(b) Show that the Barlett estimate of the power special density is asymptotically Unbiased that the variance of the estimate decreases with the number of data Sections and the spectrum estimates are consistent.(412-monson hayes)(16)

13. (a) Explain the steps in the design of an FIR wiener filter that produces the minimum mean

square estimate of the given process.(337-monson hayes) (16)

Or(b) (i) Brief forward and backward prediction. (8) (ii) Explain Kalman filter. (8)

14. (a) Explain in detail the LMS adaptive algorithm for FIR filters with and application.

(16)(367-mathematics)

Or(b) (i) Explain adaptive noise concellation. (8)

(ii) Explain adaptive echo cancellor. (315,316-osp)

(8)

15. (a) (i) With neat sketches and necessary equations, briefly explain the time domain and frequency domain characterization of a down sampler with an integer factor of M. (12) (ii) Write short notes on Wavelet transformation. (4)

Or (b) (i) Obtain the polyphase decomposition of factor of 3 decimator using a 9-tap FIR low pass filter with symmetric impulse response. (8) (ii) With a neat block diagram, briefly explain about the subband coding of speech signals. (8)

ALL THE BEST

1)

2) The Wiener–Khinchin theorem (also known as the Wiener–Khintchine theorem and sometimes

as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem) states that the

autocorrelation function of a wide-sense-stationary random process has a spectral decomposition

given by the power spectrum of that process

For continuous time, the Wiener—Khinchin theorem [12][13] says that if is a wide-sense stationary process such that its autocorrelation function (sometimes called autocovariance)

defined in terms of statistical expected value E, exists and

is finite at every lag , then there exists a monotone function in the frequency domain such that

3),4) refer phone

5,6

Linear prediction

9) Multi-rate signal processing studies digital signal processing systems which include sample rate conversion. Multirate signal processing techniques are necessary for systems with different input and output sample rates, but may also be used to implement systems with equal input and output rates.

10) In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time).