Anna University - DIGITAL SIGNAL PROCESSING (DSP) - Version 2 - April / May 2008 Question Paper

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2008.

Fifth Semester

(Regulation 2004)

Electronics and Communication Engineering

EC 1302 -  DIGITAL SIGNAL PROCESSING
(Common to B.E. (Part-Time)
Fourth Semester Regulation 2005)
Time : Three hours

Maximum: 100 marks

Answer ALL questions.

PART A - (10 x 2 = 20 marks)

1. Define the properties of convolution.
2. Draw the basic butterfly diagram of radix - 2 FFT.
3. What are the merits and demerits of FIR filters?
4. What is the relationship between analog and digital frequency in impulse invariant transformation?
5. What are the three types of quantization error occurred in digital systems?
6. What is meant by limit cycle oscillations?
7. What is a periodogram?
8. Determine the frequency resolution of the Bartlett method of power spectrum
estimates for a quality factor Q = 15. Assume that the length of the sample
sequence is 1500.
9. What is meant by pipelining?
10. What is the principal feature of the Harvard architecture?

PART B - (5x16=80marks)

11. (a) (i) Discuss in detail the important properties of the Discrete Fourier Transform. (8)
(ii) Find the 4 point DFT of the sequence (8)

x(n)=Cosnπ/4.

Or

(b) (i) Using decimation-in-time draw the butterfly line diagram for 8 point FFT calculation and explain. (8)

(ii) Compute an 8 point DFT using DIF FFT radix 2 algorithm. (8)
X (n) = {1, 2, 3, 4, 4, 3, 2, 1}

12. (a) (i) Determine the magnitude response of an FIR filter (M = 11) and
show that the phase and group delays are constant (8)

(ii) If the desired response of a low-pass filter is

Determine H (eiw) for M = 7 using a Hamming window.

Or

(b) (i) For the analog transfer function H(s) = 1 

determine  using impulse invariant technique. Assume T = 1s. (6)

(ii) Design a digital Butterworth filter that satisfies the following constraint using bilinear transformation (T = 1s) (10)

13. (a) (i) Discuss in detail the Truncation error and Round-off error for sign magnitude and two’s complement representation. (8)

(ii) Explain the quantization effects in converting analog signal into digital signal. (8)
Or

(b) (i) A digital system is characterized by the difference equation

y(n)= O.9y (n-1)+x(n)

With x (n) = O and initial condition y (-1) = 12. Determine the dead band of the system. (4)
(ii) What is meant by the co-efficient quantization? Explain. (12)

14. (a) (i) Explain the Barlett method of averaging periodograms. (8)
(ii) What is the relationship between autocorrelation and power spectrum? Prove it. (8)

Or

(b) (i) Derive the mean and variance of the power spectral estimate of the Blackman and Tukey method. (8)
(ii) Obtain the expression for mean and variance of the auto correlation function of random signals. (8)

15. (a) (i) Describe the multiplier and accumulator unit in DSP processors. (6)
(ii) Explain the architecture of TMS 320 C5X DSP processor. (10)

Or

(b) (i) Discuss in detail the four phases of the pipeline techniques. (8)
(ii) Write short notes on:
(1) Parallel logic unit (4)
(2) Circular registers. (4)

Anna University - DIGITAL SIGNAL PROCESSING (DSP) - April / May 2008 - Question Paper

B.E./B.Tech. DEGREE EXAMINATION, APRIL/MAY 2008.

Fifth Semester

Electronics and Communication Engineering

EC 333 - DIGITAL SIGNAL PROCESSING

(Common to Bio-Medical Engineering)

Time: Three hours

Maximum: 100 marks
Answer ALL questions.

PART A - (10x2 = 20 marks)

1. Check for linearity and ausa1ity of the system y(n) = Cos wnT.
2. State two properties of Z-transform.
3. Prove that convolution in the time domain is multiplication in the frequency domain.
4. Draw the basic butterfly of DIT - FFT structure.
5. ‘What is limit cycle oscillation?
6. State the advantages and disadvantages of FIR filters.
7. Write the expression for Hanning window.
8. When do you decimate a signal?
9. What is interpolation?
10. What is quantization noise?

Part B

11. (a) (i) Represent the signal y(n) = x(2n)+x(n —1)where x(n) is the input and y(n) is the output. (8)
(ii) Explain the procedure to perform linear and circular convolution. (8)

Or

(b) Explain in detail the steps in the computation of FFT using DIF algorithm. (16)
12. (a) Design a FIR filter with the following characteristics using rectangular
window with M = 7 and determine h (n) (16)

Or

(b) Discuss the various window functions available for constructing linear phase FIR filters. (16)

13. (a) Design Butterworth filter with the following characteristics using bilinear transformation method using T = 1 s. (16)

Or

(b) Explain briefly how Cascade and parallel realization of filters are done. (16)

14. (a) Explain fixed and floating point representation in detail. (16)

Or

(b) Explain the various errors that occur in a DSP system. (16)

15. (a) With a neat block diagram explain decimation and interpolation. (16)

Or

(b) Discuss mean, variance, co-variance of a Discrete Random signal. (16)