GATE→2026→Signals and Systems→Continuous/Discrete Signals & Transforms
Q1
MCQ[1 Mark]
Consider the discrete-time sequence x[n] = 0.9^{|n|}. The region of convergence of its Z-transform X(z) is
GATE→2026→Signals and Systems→Continuous/Discrete Signals & Transforms
Q2
MCQ[1 Mark]
Let x_c(t) be a continuous-time periodic signal with period T, sampled at T_s (T_s != T) to yield x[n]. Which statement is correct?
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q3
MCQ[1 Mark]
For a discrete-time LTI system with impulse response h[n] = 1 for n in {0, 1, 2}, find the output y[n] for input x[n].
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q4
MCQ[1 Mark]
Evaluate the integral of x(t) delta(t+3) dt from -inf to inf for x(t) = -t^2 {u(t+4) - u(t-4)}.
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q5
NAT[1 Mark]
For the periodic signal x(t) = 1 + 2 cos(2 pi t) + 2 cos(4 pi t) + 2 cos(6 pi t), find the mean squared value over its period T.
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q6
MCQ[2 Marks]
For y(t) = x_1(t) * x_2(t) (convolution of given trapezoidal/triangular signals), find the integral of y(t) from -inf to inf.
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q7
MCQ[2 Marks]
If impulse response of LTI system S is u(t), which statement is true about BIBO stability?
GATE→2025→Signals and Systems→Continuous/Discrete Signals & Transforms
Q8
NAT[2 Marks]
For an ideal low-pass filter with cutoff frequency 200 pi rad/s, find h(0) in the time domain.
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q9
MCQ[1 Mark]
If y(t) = x(-t), which statement is always true for the convolution of x(t) and y(t)?
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q10
MCQ[1 Mark]
Find the ROC of the Laplace transform for the finite-duration signal x(t) = e^{t^2} [u(t-1) - u(t-10)].
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q11
NAT[1 Mark]
Find the value of the derivative of X(omega) at omega = 0 for x(t) = e^{-t^4} cos(t).
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q12
MCQ[2 Marks]
For the system with relation y(t) = e^{-t} integral_{-inf}^t e^tau x(tau) dtau, the system is
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q13
MCQ[2 Marks]
Consider discrete-time systems T1 and T2 defined by partial sums. Which statement is true regarding BIBO stability?
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q14
MCQ[2 Marks]
If X(z) is the Z-transform of x[n], what is the Z-transform of y[n] = x[2n]?
GATE→2024→Signals and Systems→Continuous/Discrete Signals & Transforms
Q15
NAT[2 Marks]
If energy of x(t) is E, and energy of y(t) = 2x(2t-1) is cE, find the value of c.
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q16
MCQ[1 Mark]
Find the impulse response of the LTI system described by dy/dt + 3y(t) = 2x(t) starting from rest.
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q17
MCQ[1 Mark]
For X(omega) = rect(omega / 2W_0), which statement is true about x(t)?
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q18
MCQ[1 Mark]
For X(z) = 4z / ((z - 1/5)(z - 2/3)(z - 3)), which statement regarding ROC and DTFT convergence is true?
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q19
MSQ[1 Mark]
Which of the following statements regarding discrete-time LTI systems are true?
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q20
NAT[1 Mark]
For the given signals x(t) and y(t), their convolution z(t) = x(t) * y(t) is maximum at t = T_1. Find T_1 in seconds.
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q21
NAT[2 Marks]
Find the fundamental period N of the discrete-time signal x[n] = 1 + 3 sin(15*pi*n/8 + 3*pi/4) - 5 sin(pi*n/3 - pi/4).
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q22
NAT[2 Marks]
For the periodic signal x_p[n] of period N=5 formed from x[n] with DTFT X(Omega) = (1 + cos Omega)e^{-j Omega}, find the magnitude of Fourier series coefficient |a_3|.
GATE→2023→Signals and Systems→Continuous/Discrete Signals & Transforms
Q23
NAT[2 Marks]
A signal x(t) = 2 cos(180 pi t) cos(60 pi t) is sampled at 200 Hz and filtered by a 100 Hz low-pass filter. Find the maximum frequency in Hz in the filtered signal.
GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms
Q24
MCQ[2 Marks]
For a causal LTI system governed by y(t) + 0.25 (dy/dt) = 2 x(t), find its impulse response h(t).
GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms
Q25
MCQ[2 Marks]
An input x(t) is passed through an LTI bandpass filter with impulse response h(t). What is the system output?
GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms
Q26
MCQ[2 Marks]
For the continuous-time system defined by y(t) = x(e^t), the system is
GATE→2022→Signals and Systems→Continuous/Discrete Signals & Transforms
Q27
MCQ[2 Marks]
A periodic signal x[n] with period N=3 has non-zero Fourier coefficients a_{-3} = 2 and a_4 = 1. Which option represents the signal?
