Q No. 1

a. Compute z-transform, plot poles and zeroes and RoC of x [n ]=(0.5 )n u [ n ]b. Compute z-transform, plot poles and zeroes and RoC of h [ n ]=(2 )nu [−n ]c. Is h [n ] in part (b) represent stable and causal system, comment if not? d. Using graphical method to compute linear convolution of the two signals given in parts

(a) and (b);y [ n ]=x [n ]∗h [ n ]. e. Use z-transforms computed in parts (a) and (b) and an appropriate property of z-

transform and compute convolution of these signals y [ n ]=x [n ]∗h [ n ].Q No. 2

Answer the following:

a. Perform linear convolution of x [n ]=[ 1, 2 ,−2 ] and h [ n ]=[1 ,−1 ,−1] using FIFO and Double FIFO buffer

b. Perform 3, 4, and 5 points circular convolution of the two signals given in part (a). c. Using graphical method, For the figure below compute magnitude and the phase response

at ω=π2

, π

Q No. 3

Given DTFT of a system h[n], compute z-transform H(z) and give ROC and then compute inverse z-transform of H(z).

Q No.4

Compute convolution of the two sequences using flip and drag method.

x[n]=0.5nu[n-2]-0.5nu[n-N1]

h[n]=u[-n+4]-[-n-N2]

Where N1 > 2 and N2 > 4

Q no. 5

Perform 5-point Circular Convolution of the following two 4-point sequences

x [n ]=[ a , 2a ,b ,−b ]

h [ n ]= [a ,−a , b , 2 b ]

How many values of the circular convolution matches with the values of linear convolution, give those values?

Q No 6.

a. Compute inverse z-transform of H (z ) for the pole-zero plot given below, compute first two samples of the impulse response h [ n ] .

Q No. 7

a. For the difference equation compute H (z ) and h [n ]y [ n ]=−0.9 y [ n−1 ]+x [n−10 ]+x [n−8 ]+x [n]

b. For x [n ]=δ [n] compute y [1] Q No.8

For x[x] = [1 1 1 1 1 1 ] and h[n] = [1 1 1]

Find out the y[n] by using

a. Overlap and save methodb. Overlap and add method

Show all steps of computation

Q no. 9:

For Q No. 8 find out y[n] using

a. FIFOb. Double FIFOc. Circular Bufferd. Double Circular Buffer

Q No. 10.

Repeat Q No. 8 by finding out the DFT of x[n] and h[n]. Multiply them together and find out y[n] by taking inverse DFT of the product by using properties of DFT and compare your answer.

Q No. 11

The following constant coefficient difference equation characterizes an LTI system

y[n] = 0.4y[n-1] + x[n];

a. Compute impulse response i.e. out of this system for input x[n]= [n] b. Compute output of this system for input x[n]= [n] - [n-3]