## SIGNALS AND SYSTEMS JNTU previous years question papers

Time: 3 hours Max Marks: 75

Answer any FIVE Questions

All Questions carry equal marks

1. (a) Write short notes on "Ideal BPF".

(b) In the following network, determine the relationship between R's and C's in order to have a distortion less attenuation while signal is transmitted through the network shown in fgure 1b. [8+7]

2. (a) State the three important spectral properties of periodic power signals.

(b) Determine theFourier series of the function shown in fgure 2b. [5+10]

3. (a) With the help of graphical example explain sampling theorem for Band limited signals.

(b) Explain briey Band pass sampling. [8+7]

4. (a) Find the Z-transform and ROC of the signal

x(n) = [4(5n) & 3(4n)] u(n)

(b) Find the Z-transform as well as ROC for the following sequences: [7+8]

i.

&1

3

fn

u(&n)

ii.

&1

3

fn

[u(&n) & u (n & 8)]

5. (a) State the properties of the ROC of Laplace transforms.

(b) Determine the function of time x(t) for each of the following laplace transforms and their associated regions of convergence. [7+8]

i. (s+1)2/ s2-s+1 Re fSg > 1/2

ii. s2- s+1/ (s+1)2 Re fSg > -1

6. (a) The rectangular function f(t) in fgure 6a is approximated by the signal 4fSin t.show that the error function fe(t) = f(t)-4/f Sin t is orthogonal to the function Sin t over the interval (0,2f).

(b) Determine the given functions are periodic or non periodic.

i. a Sin 5t + b cos 8t

ii. a Sin (3t/2) + b cos (16t/15) + c Sin (t/29)

iii. a cos t + b Sin

p

2t

Where a, b, c are real integers. [10+5]

7. (a) Determine theFourier Transf or m of a trapezoidal function and triangular RF

pulse f(t) shown in fgure 7a. Draw its spectrum.

(b) Using Parsevals theorem for power signals, Evaluate

f R

&f

e&2tu(t)dt. [10+5]

8. (a) Consider an input x[n] and an impulse response h[n] given by

x[n] =

&1

2

fn&2

u[n & 2];

h[n] = u[n + 2]:

Determine and plot the output y[n] = x[n] f h[n].

(b) Bring out the relation between Correlation and Convolution.

(c) Explain the properties of Correlation function. [7+4+4]