Deemed University 2009 A.M.I.E.T.E Electronics

i. For a causal linear time invariant system, the impulse response for t < 0 is equal to

(A) Unity (B) Infinity
(C) Zero (D) None

j. The ROC associated with the system function for a causal system is a

(A) Right half plane (B) Left half plane
(C) Middle of plane (D) None of the above


ans any 5 ques. out of 8 ques..
every ques. carries 16 marks.


Q.2 a. obtain out whether signal is an energy signal or a power signal. Also obtain if is an energy signal or a power signal. (8)

b. obtain out the response of a continuous –time system to unit step input provided the impulse response, . (8)

Q.3 a. obtain the trigonometric Fourier series for the waveform shown in Fig.1. (8)





b. Determine the fourier series coefficients for a discrete-time periodic signal provided as , where . (8)

Q.4 a. Determine the continuous-time fourier transform of a continuous –time signal, . (8)

b. obtain the fourier transform of the pulse shown in Fig.2 beneath (8)















Q.5 a. Using discrete time fourier transform, determine the frequency response and impulse response of a causal discrete-time LTI system that is characterised by, . (8)


b. Determine the discrete-time frequency transform of the discrete-time periodic signal, , with fundamental frequency . (8)

Q.6 a. The frequency response for a causal and stable continuous time LTI system is provided by, .
(i) obtain the magnitude of .
(ii) Determine which of the subsequent statement is actual about , the group delay of the system
1.
2.
3. (8)

b. obtain the Nyquist rate and Nyquist interval for the continuous-time signal, . (8)

Q.7 a. obtain the z-transform and ROC for the signal sequence . (6)



b. State initial value theorem for z-domain transfer function. obtain the initial
value of the corresponding sequence, s(n) having a z-transform . (6)

c. Determine the sequence s(n) whose z-transform . (4)

Q.8 a. A binary source generates digits one and 0 randomly with probabilities 0.6 and 0.4 respectively.
(i) What is the probability that 2 1s and 3 0s will occur in a five-digit sequence?
(ii) What is the probability that atleast 3 1s will occur in a five-digit sequence? (6)

b. The pdf of a random variable X is provided by,
where, K is a constant
(i) Determine the value of K.
(ii) Let a = -1 and b=2. compute . (6)
c. Consider a random process X(t) provided by, where is a random variable uniformly distributed in the range . Show that the process is ergodic in the mean. (4)

Q.9 Write short notes on:

(i) Joint probability.
(ii) Conditional probability.
(iii) Cross spectral density.
(iv) White noise. (44 = 16)

Earning:   Approval pending.