7

a)

b)

९)

2)

0)

2)

९)

6)

84812 Pages: 3

Answer any two questions, each carries 20 marks

Find the Z transform and ROC of the following signals. (5)
(1) x[n] = 2"u[n]
(ii) S[n]
Pole zero plot for Z transform X(z) of a discrete time signal x[n] shown below. (6)
im
‘coon plane
Re

Determine the ROC in each of the following cases.

(1) x[n] is right sided

(ii) Fourier transform of x[n] converges

(iii)x[n] is left sided
Determine the DTFS coefficients for the discrete time signal (9)
x[n]=cos(~")+ sin(—)

Also plot the magnitude and phase spectra.

Consider a LTI system characterised by input output relationship
1 1

y[n] - gyn -1[ =x[n]+ 2 ೫[೫೬-- 1] (2)

(i) Compute the system function H(z). (2)

(ii) Sketch the possible ROCs for H(z).

(iii)Compute the impulse response h[n] if it is known that impulse response is (4)

left sided.
Consider a system with impulse response h[n] = (0.5)" u[n].
(i) Determine the system function 11(61%) (4)
(ii) If the input x[n] = cos (>), determine the output y[n]. (8)

List any four properties of Z-transform, state and prove the convolution property (10)
of Z transforms.

− 1
⋅ ത്തു (4)
A signal അ) has DTFT X(e ) eer 51. Determine the DTFT of
௬
x[n + 2] 8”,
Determine the DTFT of the signal x[n]=u[n]-u[n-N] (6)
೫ ೫ ಸೇ ‏بد‎

Page 3 of 3