IES-2010 IES Academy ET (Paper-I) Electronics Engineering (Paper-I)

India’s No 1IES AcademyIES-2010ET (Paper-I)(2) If x[n] = U( n)n⎛1⎞⎜2⎟⎝ ⎠⎛1⎞y[n] =δ ⎡⎣n ⎤⎦+a ⎜ u[n]4⎟⎝ ⎠nfor all n, then y[n] for all n is of the formwhere a is a constant.Determine the value of the constant a.1 3 7( a) ( b) ( c) ( d)None of them8 8 8Q6. The autocorrelation function of a sinusoid cos (wt) is given by(a) cos(wt) (b) 2 cos(wt) (c) 1/2 cos(wt) (d) noneQ7. The energy of the signal 2e-t/2u(t) is given by(a) 2 (b) Infinite (c) 3 (d) 4Q8. A random process is called ergodic if(a) It is ergodic in mean(c) It is ergodic in mean & autocorrelation(b) It is ergodic in autocorrelation(d) NoneQ9. If x(t) has fundamental period T, x(3t – 1) has fundamental period of …..?(a) T (b) T/2 (c) T/3 (d) Can’t be determinedQ10. We are given the following 5 facts about a discrete time singnal x[n] with Z –transform X(z):(a) x[n] is real and right sided.(b) X(z) has exactly 2 poles.(c) X(z) has 2 zeroes at the origin.π1 j(d) X(z) has a pole at z = e 32(e) X(1) = 8 3Determine X(z)2 2 2 2Z 2Z 2Z Z( a) ( b) ( c) ( d)2 Z 1 2 Z 1 2 Z 1 2 Z 1Z − + Z − + Z − + Z − +4 2 4 2 2 4 2 4⎛1⎞Q11. Determine the z-transform for ⎜ un ⎡ + 3⎤2⎟ ⎣ ⎦⎝ ⎠3 3 3 32z 4z 6z 8z( a) ( b) ( c) ( d)8−z 8−z 2−z 2−zn+1−1 −1 −1 −1Q12. Indicate the region of convergence of Z-transform of⎛1⎞⎜3⎟⎝ ⎠n−2un ⎡⎣− 2⎤⎦www.iesacademy.com Email: iesacademy@yahoo.com Page-3__25, 1 st Floor, Jia Sarai, Near IIT. New Delhi-16 Ph: 011-26537570, 9810958290