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GATE-2017
Q:
Q:
- A: (2-t)e-t
- B: (1+2t)e-t
- C: (2+t)e-t
- D: (1-2t)e-t
GATE-2013
Q: Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
- A: product of h1(t) and h2(t)
- B: sum of h1(t) and h2(t)
- C: convolution of h1(t) and h2(t)
- D: subtraction of h2(t) from h1(t)
GATE-2013
Q: For a periodic signal v(t) = 30 sin100t + 10 cos 300t + 6 sin(500t + π/4), the fundamental frequency in rad/s
- A: 100
- B: 300
- C: 500
- D: 1500
GATE-2013
Q: Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
- A: All the poles of the system must lie on the left side of the jw axis
- B: Zeros of the system can lie anywhere in the s-plane
- C: All the poles must lie within |s| = 1
- D: All the roots of the characteristic equation must be located on the left side of the jw axis.
GATE-2012
Q: The Fourier transform of a signal h(t) is H(jw) = (2 cosw)(sin2w)/w. The value of h(0) is
- A: 1/4
- B: 1/2
- C: 1
- D: 2
GATE-2011
Q: The trigonometric Fourier series of an even function does not have the
- A: dc term
- B: cosine terms
- C: sine terms
- D: odd harmonic terms
GATE-2010
Q: The system is neither stable nor causal for ROC: 1/4 < |z| < 1/2 Which one of the following statements is valid ?
- A: Both S1 and S2 are true
- B: Both S2 and S3 are true
- C: Both S1 and S3 are true
- D: S1, S2 and S3 are all true
GATE-2009
Q: The Fourier series of a real periodic function has only
Q: The 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
GATE-2009
Q: 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.
Q: 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.
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
GATE-2004
Q: The impulse response h[n] of a linear time-invariant system is given by h[n] = u[n + 3] + u[n - 2) - 2n[n - 7] where u[n] is the unit step sequence. The above system is
- A: stable but not causal
- B: stable and causal
- C: causal but unstable
- D: unstable and not causal