Ans: D Ans: A Ans: C Ans: B Ans: C Ans: C Ans: A Ans: B Ans: C

Transcription

1 UNIT-I 1. The Fourier series of an odd periodic function contains only [ ] a. Odd harmonics b. even harmonics c. cosine terms d. sine terms 2. The RMS value of a rectangular wave of period T, having a value of +V for a duration, T1(<T) and V for the duration, T-T1 = T2 equals [ ] a. V b. T1-T2 V c. V/ 2 d. T1 V 3. The Trigonometric Fourier Series of a periodic time function can have only [ ] a. cosine terms b. sine terms c. cosine & sine terms d. d.c. and cosine terms 4. Which of the following cannot be the Fourier Series expansion of a periodic signal? [ ] a. x(t) = 2 cos t +3 cos 3t c. x(t) = cos t +0.5 b. x(t) = 2 cos πt +7 cos t d. x(t) = 2 cos 1.5πt + sin 3.5 πt 5. choose the function f(t); - < t < +, for which a Fourier Series cannot be defined [ ] a. 3 sin (25t) b. 4 cos(20t+3) +3 sin (10t) c. exp(- t )sin (25t) d The Trigonometric Fourier Series of an even function of time does not have [ ] a. d.c. terms b. cosine terms c. sine terms d. odd harmonic terms 7. The Trigonometric Fourier Series of a real periodic function has only [ ] P. cosine terms if it is even Q. sine terms if it is even R. cosine terms if it is odd S. sine terms if it is odd Which of the above statements are correct? a. P and S b. P and R c. Q and S d. Q and R 8. A function is given by f(t) = sin2t + cos 2t. which of the following is true? a. f has frequency components at 0 and 1/2π Hz b. f has frequency components at 0 and 1/π Hz c. f has frequency components at 1/2π Hz and 1/π Hz d. f has frequency components at 0, 1/2π Hz and 1/π Hz 9. A half wave rectified sinusoidal waveform has a peak voltage of 10 V. Its average value and the peak value of the fundamental component are respectively given by: [ ] a. 20 V, 10 V π 2 b. 10 V, 10 V π 2 c. 10 V, 5 V π d. 20 V, 5 V π

2 10. Which of the following signals is/are periodic? [ ] a. s(t) = cos 2t + cos 3t + cos 5t b. s(t) = exp(j8πt) c. s(t) = exp(-7t)sin 10πt d. s(t) = cos 2t cos 4t, B &D 11. The PSD and the power of a signal g(t), are respectively, Sg(w), Pg. The PSD and the power of the signal a g(t) are, respectively, a. a2sg(w), a2 Pg b. a2sg(w), a Pg c. asg(w), a2 Pg d. asg(w), a Pg 12. The Fourier Transform of a real valued time signal has a. Odd symmetry b. Even symmetry c. conjugate symmetry d. no symmetry 13. The amplitude spectrum of a Gaussian pulse is a. Uniform b. a sine function c. Gaussian d. an impulse function 14. If a signal f(t) has energy E, the energy of the signal f(2t) is equal to a. E b. E/2 c. 2E d. 4E UNIT-II 1. The Fourier Transform of a conjugate symmetric function is always [ ] a. Imaginary b. conjugate anti-symmetric c. real d. conjugate symmetry 2. Hilbert Transform of [cosw1t + sinw2t] is [ ] a. sinw1t- cosw2t b. cosw1t + sinw2t c. cosw1t sinw2t d. sinw1t + sinw2t 3. If G(f) represents the Fourier Transform of a signal g(t) which is real and odd symmetric in time, then a. G(f) is complex b. G(f) is imaginary c. G(f) is real d. G(f) is real and non-negative 4. The Fourier Transform of a signal h(t) is H(jw) = (2 cos w)(sin 2w)/w. The value of h(0) is a. ¼ b. ½ c. 1 d. 2 [ ] 5. Let x(n)=(1/2)^n u(n), y(n)=(x(n))^2 and Y(exp(jw)) be the Fourier transform of y(n).

3 Then Y(exp(j0)) is [GATE-2005] (a) 1/4 (b) 2 (c) 4 (d) 4/3 6. For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2) is given by [ (a) (1/2) x(t/2) exp(j3*pi*t) (b) (1/3) x(t/3) exp(-j4*pi*t/3) (c) 3 x(3t) exp(-j4*pi*t) (d) x(3t+2) 7. The 4-point discrete Fourier transform (DFT) of a discrete time sequence {1, 0, 2, 3) is (a) [0, -2+2j, 2, -2-2j] (b) [2, 2+2j, 6, 2-2j] (c) [6, 1-3j, 2, 1+3j] (d) [6, -1+3j, 0, -1-3j] 8. The Fourier Transform of a real valued time signal has a. Odd symmetry b. Even symmetry c. conjugate symmetry d. no symmetry 9. The Fourier Transform F{e-t u(t)} is equal to 1/(1+j2πf). Therefore F{1/(1+j2πt)} is [ ] a. efu(f) b. e-fu(f) c. efu(-f) d. e-fu(-f) 10. If G(f) represents the Fourier Transform of a signal g(t) which is real and odd symmetric in time, then a. G(f) is complex b. G(f) is imaginary c. G(f) is real d. G(f) is real and non-negative 11. The Fourier Transform of a signal h(t) is H(jw) = (2 cos w)(sin 2w)/w. The value of h(0) is a. ¼ b. ½ c. 1 d. 2 [ ] 12. A signal x(t) has a Fourier Transform X(w). If x(t) is a real and odd function of t, Then X(w) is (a) a real and even function of w (b) an imaginary and odd function of w (c) an imaginary and even function of w (d) a real and odd function of w

4 UNIT-V LAPLACE TRANSFORMS: 1. If the Laplace transform of a signal y(t) is Y(s)= 1/(s(s-1)), then its final value is (a) -1 (b) 0 (c) 1 (d) Unbounded 2. The Laplace Transforms of the functions t u(t) and u(t) sin(t) are respectively [ ] a. 1/s2, s/( s2+1) b. 1/s, 1/( s2+1) c. 1/s2, 1/( s2+1) d. s, s/( s2+1) 3. The Laplace Transforms of the function f(t)u(t),where f(t) is periodic with period T, is A(s) times the L.T. of its first period. Then [ ] a. A(s) = s b. A(s) = 1/(1-exp(-Ts)) c. A(s) = 1/(1+exp(-Ts)) d. A(s)= exp(ts) 4. In what range should Re(s) remain so that the L.T. of the function e(a+2)t+5 exists? [ ] a. Re(s) > a+2 b. Re(s) > a+7 c. Re(s) <2 d. Re(s) > a+5 5. If F(s) = L[f(t)] = 2(s+1) then the initial and final values are respectively [ ] S 2 +4s+7 a. 0,2 b. 2,0 c. 0, 2/7 d. 2/7,0 6. Given that F(s) is a one sided L.T. of f(t), the L.T. of ( ) 0 is [ ] a. sf(s)-f(0) b. 1/s F(s) c. ( ) 0 d. 1/s[F(s)-f(0)] 7. In what range should Re(s) remain so that the L.T. of the function e(a+2)t+5 exists? [ ] a. Re(s) > a+2 b. Re(s) > a+7 c. Re(s) <2 d. Re(s) > a+5 8. The Laplace Transforms of the function f(t)u(t),where f(t) is periodic with period T, is A(s) times the L.T. of its first period. Then [ ]

5 a. A(s) = s b. A(s) = 1/(1-exp(-Ts)) c. A(s) = 1/(1+exp(-Ts)) d. A(s)= exp(ts) Z-TRANSFORMS 1. The region of convergence of the z-transform of a unit step function is (a) IzI > 1 (b) IzI < 1 (c) (Real part of z) > 0 (d) (Real part of z) < 0 Answer: A 2. The z-transform of a system is H(z)= z/(z-0.2) If the ROC is IzI<0.2, then the impulse response of the system is (a) (0.2)^n u[n] (b) (0.2)^n u[-n-1] (c) -(0.2)^n u[n] (d) - (0.2)^n u[-n-1] Answer: B 3. The z-transform X[z] of a sequence x[n] is given by X[z]= 0.5/(1-2z^(-1)). It is given that the region of convergence of X[z] includes a unit circle. The value of X(0) is (a) -0.5 (b) 0 (c) 0.25 (d) 0.5 Answer: B 4. The z- Transform of the function Σ( ) =0 is [ ] a. (z-1)/z b. z/(z-1)2 c. z/(z-1) d. (z-1)2/z Answer: C 5. The Z-transform F(z) of the function f(nt)=a^(nt) is (a) z/(z-a^t) (b) z/(z+a^t) (c) z/(z-a^(-t)) (d) z/(z+a^t) Answer: A