Roll Number: Name:

Thapar University, Patiala Department of Electrical and Instrumentation Engineering

BE- EE (VI Semester) Mid-Sem UEI503 DIGITAL SIGNAL PROCESING AND

Examination APPLICATIONS MARCH 2015 (12/03/2015)

Time: 2 Hours; MM: 60 (50%) Name of Faculty: Dr. Smarajit Ghosh

1 Q1. Find the inverse z—transform of the function X(z)--=

for the 1-1.8z-1 + 0.8z— 2

following ROCs:

1, (1i) < 0.8 and (iii) 0.8 < Izi < 1

[7]

Q2. Determine the cross correlation [Rxy(/)] using mathematical equations of the following

two sequences

x(n) = {1,2,-3,4,5,7,-9,3} and y(n) = {1,-2,3,2,7,-6,9) [12]

Q3. Prove the relation y(n) = x(n)*h(n). Prove the properties of convolution. [10]

Q4. Find the circular convolution of x(n) = { 1,3,5,7) and h(n) = {2,7,9,4} graphically. Verify

the result by matrix method. Also verify the result by DFT and IDFT techniques. [14]

z z Q5. (a) Prove that if xi (n)<-> Xl

(z) and x2 (n) <-4 X2 (z) then

(n)* x2 (n)<—>Xi(z) X2(z)

(b) Derive the necessary condition for causality and stability in terms of z-transform.

Q6. Prove the following:

(a) x(n)8(n — no ) = x(no ) and (b) x(n)*8(n — no ) = x(n — no )

Also explain graphically the difference between (a) and (b) when x(n) = {1,1,2,4} . [7]

NOTE: PLEASE SEE YOUR EVALUATED ANSWER SCRIPT ON 16-03-2015 AT 5:15 PM IN D-206.