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) 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:
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
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.
(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.
(c) sinc(100ft) + sinc(50ft).
(d) sinc(100ft) + 3 sinc2(60ft). [3+4+4+4]