M.A.M. COLLEGE OF ENGINEERING TRICHY

EC2314 DIGITAL SIGNAL PROCESSING

UNIT II DISCRETE TIME SYSTEM ANALYSIS

PART – A

1. Define Z-transform and its ROC?

2. What are the properties of ROC?

3. What is the relation between Z transform and Fourier transform?

4. Find the Z transform of unit step function

5. Find Z- transform of x(n) = (n-k) and its ROC.

PART – B

6. a) State and prove the convolution property of Z transform

b)Find the convolution of x1(n)= {3 4 6 } and

↑

x2(n) = { 1 5 2 } using Z transform

↑

7. Find the z-transform of the following signals and plot its ROC.

(i) x1(n)=an

u(n)

(ii) x2(n)=a-n

u(-n-1)

8.Find the inverse Z-transform of

(i) X(z) =1/1-1.5Z-1

+0.5Z-2

for the ROC ∣z∣ >1,

0.5˂ ∣z∣ 1˂

ii) X(z) = 4z/ z2-7z+12 for the ROC

∣z∣ >4 and ∣z∣ 3˂

9.Determine the Z-transform and ROC of

a. x(n) = rn cosω0nu(n)

b. x(n) = n2an u(n)

c. x(n) = -1/3 (-1/4)n u(n) – 4/3 (2)n u(-n-1)

d.x(n) = sinω0n u(n)