## SIGNALS AND SYSTEMS JNTU previous years question papers

Time: 3 hours Max Marks: 75

All Questions carry equal marks

1. (a) Derive polarFourier series from the exponentialFourier series representation and hence prove that Dn= 2jCn j.
(b) Determine the trigonemetric and exponential Fourier series of the function shown in fgure 1b. [5+10]

2. (a) Write short notes on \orthogonal vector space".
(b) A rectangular function f(t) is defned by:
f(t) =
f
1
&1
0 < t < f
f f t < 2f
Approximate above function by a fnite series of Sinusoidal functions. [8+7]

3. (a) Using the Power Series expansion technique, fnd the inverse Z-transform of the following X(Z):
i. X(Z) = Z
2Z2&3Z+1 jZj < 1
2
ii. X(Z) = Z
2Z2&3Z+1 jZj > 1
(b) Find the inverse Z-transform of
X(Z) = (Z+1)(
Z(Z&1)(Z&2) jZj > 2. [8+7]

4. (a) Determine the inverse Laplace transform for the following Laplace transform and their associated ROC.
i. s+1
(s2 +5s+6) & 3 < Refsg < &2
ii. (s2 +5s+6)
(s+1 )2 Refsg > &1
(b) Explain the constraints on ROC for vari ous classes of signals, with an example.[9+6]

5. (a) Find theFourier Transf or m for the following functions shown in fgure
(b) Find the total area under the function g(t) = 100 Sin c ((t-8)/30). [10+5]

6. (a) Explain briey detection of periodic signals in the presence of noise by correlation.
(b) Explain briey extraction of a signal from noise by fltering. [8+7]

7. (a) Find the transfer function of Lattice network shown in fgure 7a.
(b) Sketch the magnitude and phase characteristic of H(j!). [8+7]

8. Determine the Nyquist sampling rate and Nyquist sampling interval for the signals.
(a) sinc(100ft).
(b) sinc2(100ft).
(c) sinc(100ft) + sinc(50ft).
(d) sinc(100ft) + 3 sinc2(60ft). [3+4+4+4]

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