SUDHARSAN ENGINEERING COLLEGE

ROEVER COLLEGE OF ENGINEERING & TECHNOLOGY

ELAMBALUR, PERAMBALUR 621 220DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERINGEE6403 Discrete time system and signal processingClass & Sem: II-EEE&IV

Date: 17-02-2015Time: 3hours

Maximum: 100 marks

Answer ALL Questions

PART A

(10 x 2 = 20 Marks)1. Test whether the system governed by the relation y(n)= is linear time invariant or not?

2. What is aliasing effect?

3. Give the continuous time signal x(t)=2cos500. What is the Nyquist rate and fundamental frequency of the signal?

4. Determine whether x(n)=u(n) is power signal or energy signal.

5. Find the Z transform and its ROC of the discrete time signals x(n)=-anu(-n-1), a>0.

6. Find the stability of the system whose impulse response h(n)=nu(n).

7. Prove the convolution property of Z-transform.

8. Mention four properties of ROC in Z-transform.

9. What is zero padding? What are its uses?

10. Draw the basic butterfly diagram for DIT and DIF algorithm.PART B

(5 x 16 = 80 Marks)11. (a) i) what is energy and power signals? Determine whether the following signals are (6)

power or energy or neither of these two.

1. x(n)=(1/5)nu(n)

2. x(n)=3(0.5)nu(n)

ii) Explain the following with respect to discrete time system:

(6)

1. casuality

2. stability

3. dynamic system

iii) Explain what is meant by quantization?

(4)

Or

(b) i) What is system? Explain the classification of systems.

(5)

ii) What is sampling? Explain the operation of sampling process.

(7)

iii) What is meant by spectral density? Explain.

(4)

12. (a) i) Given y(n)=x(n)2. Determine whether the system is linear, time invariant, memory

less and causal.

(8)

ii) State the stability property of LTI system and check if the system defined by

y (n)=x(n)=nx(n+1) is stable, liner and causal.

(8)

Or

(b) i) Explain the time invariant property of the system and find if the system

y (n)=x(n)= x(n-1) is time invariant, linear and causal.

(8) ii) Explain the process of quantitation during analogy to digital conversion and error

associate with it.

13. (a) i) Find the linear convolution of x(n)={1,2,3,4,5,6,7} with h(n)={2,4,6,8}.

(8)

ii) Find the Z-transform of x(n)=rncos(n)u(n).

(8)

Or

(b) i) Find the inverse Z Transforms of X(Z)=4Z/(Z+1)2(Z+3) for all possible ROCs.(8)

ii) Determine the Z-transform of the signal x(n)=(coson)u(n).

(8)

14. (a) i) Find the Z transform and its associate ROC for the following discrete time signal

x(n)=(-1/5)nu(n)+5(1/2)-nu(-n-1).

(8)

ii) Evaluate the frequency response of the system described by system function

H(Z)=1/(1-0.5z-1) .

(8)

Or

(b) Using Z-transform determine the response y(n) for n>0 if y(n)=1/2y(n-1)+x(n),

x(n)=(1/3)nu(n) and y(-1)=1.

(16)

15. (a) i) Obtain the 8-point DFT of the sequence x(n)={1,1,1,1}.

(8)

ii)Find DFT of the sequence x(n)={1,2,3,4,4,3,2,1}. Using decimation in time

algorithm.

Or (b) i) Explain the important features of decimation in frequency FFT algorithm. (8)

ii) Find the 4 point inverse DFT of X(k)={10,-2+2j,-2,-2-2j}.

(8)SUBJECT IN CHARGE HOD/EEE