Signals & Systems Gate Complete Question Set

8/10/2019 Signals & Systems Gate Complete Question Set

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GATE QUESTIONS ON SIGNALS & SYSTEMS

1. The Fourier Series of an odd periodic function, contains only [ ]

a. Odd harmonics b. even harmonics c. cosine terms d. sine terms

Ans: D GATE 19942. The RMS value of a rectangular wave of period T, having a value of +V for a duration, T1(


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Ans: B GATE 2009

9. A halfwave 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

2

b. 10 V, 10 V

2

c. 10 V, 5 V

d. 20 V, 5 V

Ans: C GATE 1987

10.Which of the following signals is/are periodic? [ ]

a. s(t) = cos 2t + cos 3t + cos 5t b. s(t) = exp(j8t) c. s(t) = exp(-7t)sin 10t

d. s(t) = cos 2t cos 4t

Ans: A, B &D GATE 1992

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), a2Pg b. a2Sg(w), a Pg c. aSg(w), a2Pg d. aSg(w), a Pg

Ans: a GATE 2001

12.The Fourier Transform of a real valued time signal has

a. Odd symmetry b. Even symmetry c. conjugate symmetry d. no symmetry

Ans: C GATE 1996

13.The amplitude spectrum of a Gaussian pulse is

a. Uniform b. a sine function c. Gaussian d. an impulse function

Ans: C GATE 1998

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

Ans: B GATE 2001

15.The Fourier Transform F{e-tu(t)} is equal to 1/(1+j2f). Therefore F{1/(1+j2t)} is[ ]

a. efu(f) b. e-fu(f) c. efu(-f) d. e-fu(-f)

Ans: C GATE 2002


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16.The Fourier Transform of a conjugate symmetric function is always [ ]

a. Imaginary b. conjugate anti-symmetric c. real d. conjugate symmetry

Ans: C GATE 2004

17.Hilbert Transform of [cosw1t + sinw2t] is [ ]

a. sinw1t- cosw2t b. cosw1t + sinw2t c. cosw1tsinw2t d. sinw1t + sinw2t

Ans: A GATE 2000

18. 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

Ans: B GATE 1992

19.The Fourier Transform of a signal h(t) is H(jw) = (2 cos w)(sin 2w)/w. The value of h(0) is

a. b. c. 1 d. 2 [ ]

Ans: C GATE 2012

20.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)

Ans: C GATE 1987

21. 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)

Ans: B GATE 1988

22. 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) a+5

Ans: A GATE 2005

23. If F(s) = L[f(t)] = 2(s+1) then the initial and final values are respectively [ ]

S2+4s+7

a. 0,2 b. 2,0 c. 0, 2/7 d. 2/7,0

Ans: B GATE 2011

24. Given f(t) = L-13+

+4 +(3). If lim

() 1, then the value of K is [ ]

a. 1 b. 2 c. 3 d. 4

Ans: D GATE 2010

25. Given that F(s) is a one sided L.T. of f(t), the L.T. of ()

0is [ ]


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a. sF(s)-f(0) b. 1/s F(s) c. ()

0 d. 1/s[F(s)-f(0)]

Ans: B GATE 2009

26. consider the function f(t) having the L.T. [ ]

F(s) = w0 Re[s]>0 the final value of f(t) would be

( s2+ w0 2)

a. 0 b. 1 c. -1 f() 1 d.

Ans: C GATE 2006

27. The first six points of the 8point DFT of a real valued sequence are 5, 1-j3, 0, 3-j4, 0,

and 3+j4. The last two points of the DFT are respectively [ ]

a. 0, 1-j3 b. 0, 1+j3 c. 1+j3, 5 d. 1-j3,5

Ans: B GATE 2011

28.The z- Transform of the function ()=0 is [ ]a. (z-1)/z b. z/(z-1)2 c. z/(z-1) d. (z-1)2/z

Ans: C GATE 1998

29.The z Transform of the sequence x[n] is given by X[z] =0.5

2. it is given that the region of

convergence of X[z] includes the unit circle. The value of x[0] is [ ]

a. -0.5 b. 0 c. 0.25 d. 0.5

Ans: B GATE 2007

30.The Z-transform F(z) of the function f(nT)=a^(nT) is [GATE-1999]

(a) z/(z-a^T) (b) z/(z+a^T) (c) z/(z-a^(-T)) (d) z/(z+a^T)

Answer: a

30.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 [GATE-1999]

(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

Answer: b

31. A system with an input x(t) and output y(t) is described by the relation: y(t)=t x(t).


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This system is [GATE-2002]

(a) linear and time-invariant

(b) linear and time varying

(c) non-linear and time-invariant

(d)non-linear and time-varying

Answer: b

32. The region of convergence of the z-transform of a unit step function is

(a) IzI > 1 [GATE-2002]

(b) IzI < 1

(c) (Real part of z) > 0

(d) (Real part of z) < 0

Answer: a

33. 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 [GATE-2002]

Answer: b

34. Let x(t) be the input to a linear, time-invariant system. The required output is

4x(t-2). The transfer function of the system should be [GATE-2003]

(a) 4exp(j4*pi*f) (b) 2exp(-j8*pi*f) (c) 4exp(-j4*pi*f) (d) 2exp(j8*pi*f)

Answer: c

35.The impulse response h[n] of a linear time-invariant system is given by

h[n]=u[n+3] + u[n+2]2u[n-7] [GATE-2004]

where u[n] is the unit step response sequence. The above system is

(a) Stable but not causal

(b)Stable and causal

(c) Causal but unstable

(d)Unstable and not causal

Answer: a

36.The Fourier transform of a conjugate symmetric function is always


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(a) Imaginary [GATE-2004]

(b)Conjugate antisymmetric

(c) Real

(d)Conjugate symmetric

Answer: c37.The z-transform of a system is H(z)= z/(z-0.2) [GATE-2004]

If the ROC is IzI


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F. Continuous and periodic signal

G. Discrete and aperiodic signal

H. Discrete and periodic signal

GROUP-2

1. Fourier representation is continuous and aperiodic

2. Fourier representation is discrete and aperiodic

3. Fourier representation is continuous and periodic

4. Fourier representation is discrete and periodic

(a) E-3,F-2,G-4,H-1

(b)E-1,F-3,G-2,H-4

(c) E-1,F-2,G-3,H-4

(d)E-2,F-1,G-4,H-3

Answer: c

40. For a signal x(t) the Fourier transform is X(f). Then the inverse Fourier transform of X(3f+2)

is given by [GATE-2005]

(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)

Answer: b

40.A system with input x[n] and output y[n] is given as y[n]= (sin(5/6)*pi*n) x(n) .

The system is [GATE-2006]

(a) linear, stable and invertible

(b)non-linear, stable and non-invertible

(c) linear, stable and non-invertible(d) linear, unstable and invertible

Answer: c

41. 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 [GATE-2007]


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Answer: d

42. 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 [GATE-2007]

Answer: b

43. The input and output of a continuous time system are respectively denoted by x(t) and y(t).

Which of the following descriptions is corresponds to a causal system? [GATE-2008]

(a) y(t) = x(t-2) + x(t+4)

(b)y(t) = (t-4) x(t+1)

(c) y(t) = (t+4) x(t-1)

(d)y(t) = (t+5) x(t+5)

Answer: c

44. A Discrete time linear shift-invariant system has an impulse response h[n] with h[0]=1,

h[1]= -1, h[2]= 2, and zero otherwise. The system is given an input sequence x[n] with

x[0]=x[2]= 1 and zero otherwise. The number of nonzero samples in the output sequence y[n],

and the value of y[2] are, respectively [GATE-2008]

(a) 5,2 (b) 6,2 (c) 6,1 (d) 5,3

Answer: d

Statement for Linked Answer Questions 20 and 21: [GATE-2008]

45. The frequency response H(w) of this system in terms of angular frequency w,is given by,

H(w)=

(a) 1/(1+j2w) (b) (sinw)/w (c) 1/(2+jw) (d) jw/(2+jw)

Answer: c

46. The output of this system, to the sinusoidal input x(t)=2cos(2t) for all the time t, is

(a) 0

(b)2^(0.25) cos(2t-0.125*pi)

(c) 2^(0.5) cos(2t-0.125*pi)

(d)2^(0.5) cos(2t-0.25*pi)

Answer: d


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47. The Fourier series of a real periodic function has only [GATE-2009]

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

Answer: a

48. A system with transfer function H(z) has impulse response h(.) defined as h(2)=1, h(3)= -1

and h(k)=0 otherwise. Consider the following statements. [GATE-2009]

S1: H(z) is a low pass filter

S2: H(z) is an FIR filter

Which of the following is correct?

(a) Only S2 is true

(b)Both S1 and S2 are false

(c) Both S1 and S2 are true, and S2 is a reason for S1

(d)Both S1 and S2 are true, but S2 is not a reason for S1.Answer: a

49. The 4-point discrete Fourier transform (DFT) of a discrete time sequence {1, 0, 2, 3) is

(a) [0, -2+2j, 2, -2-2j] [GATE-2009]

(b)[2, 2+2j, 6, 2-2j]

(c) [6, 1-3j, 2, 1+3j]

(d)[6, -1+3j, 0, -1-3j]

Answer: d

50. The trigonometric Fourier series of an even function does not even have the

(a) Dc term [GATE-2011]

(b)Cosine terms

(c) Sine terms

(d)Odd terms

Answer: c


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Signals & Systems Gate Complete Question Set

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