Electronics and Communication GATE 2023 Questions with Answer

Ques 53 Network Theory

The switch S₁ was closed and S₂ was open for a long time. At t=0, switch S₁ is opened and S₂ is closed, simultaneously. The value of i_c(0⁺), in amperes, is

Ques 54 Signal and Systems

Consider a system with input x(t) and output y(t) = x(e^t). The system is

Ques 55 Signal and Systems

Let m(t) be a strictly band-limited signal with bandwidth B and energy E. Assuming ω_o = 10B, the energy in the signal m(t)cos ω_ot is

Ques 56 Signal and Systems

The Fourier transform X(ω) of x(t) = e^-t2 is Note: ∫^∞_-∞e^-y2dy = √π

Ques 57 Signal and Systems

In the table shown below, match the signal type with its spectral characteristics.

Ques 58 Signal and Systems

For a real signal, which of the following is/are valid power spectral density/densities?

C

D

Ques 59 Signal and Systems

Consider a discrete-time periodic signal with period N = 5. Let the discrete-time Fourier series (DTFS) representation be x[n] = Σ⁴_k=0a_ke^pk2πn/5, where a₀ = 1, a₁ = 3j, a₂ = 2j, a₃ = -2j and a₄ = -3j. The value of the sum Σ⁴_n=0x[n]sin4πn/5

Ques 60 Signal and Systems

Let an input x[n] having discrete time Fourier transform
X(ejΩ) = 1 - e^-jΩ + 2e^-3jΩ be passed through an LTI system. The frequency response of the LTI system is H(e^jΩ) = 1 - 1/2 e^-j2Ω. The output y[n] of the system is

Ques 61 Signal and Systems

Let x(t) = 10 cos(10.5Wt) be passed through an LTI system having impulse response h(t) = π(sin Wt/πt)²cos 10Wt. The output of the system is

Ques 62 Signal and Systems

Let x₁(t) and x₂(t) be two band-limited signals having bandwidth B = 4π × 10³ rad/s each. In the figure below, the Nyquist sampling frequency, in rad/s, required to sample y(t), is

Ques 63 Signal and Systems

Let x₁(t) = u(t + 1.5) - u(t - 1.5) and x₂(t) is shown in the figure below. For y(t) = x₁(t) * x₂(t), the ∫^∞_-∞y(t)dt is ____ (rounded off to the nearest integer).

Ques 64 Signal and Systems

Let X(t) be a white Gaussian noise with power spectral density 1/2 W/Hz. If X(t) is input to an LTI system with impulse response e^-tu(t), the average power of the system output is ____ W (rounded off to two decimal places).