GATE EC || SIGNALS & SYSTEMS ||LAPLACE & Z TRANSFORM ||PYQS(2000-2025)

Given that

A linear time invariant system has an impulse response e^2t, for t > 0. If initial conditions are 0 and the input is e^3t, the output for t > 0 is

(GATE 2000 || EC || MCQ || 2 MARKS)

Let u(t) be the step function. Which of the waveforms in the figure corresponds to the convolution of u(t) – u(t – 1) with u(t) – u (t – 2)?

(GATE 2000 || EC || MCQ || 2 MARKS)

The transfer function of a system is given by [Tex]H(s)=\frac{1}{s^2(s-2)}[/Tex]. The impulse response of the system is ? (* denotes convolution, and u(t) is unit step function)

(GATE 2001 || EC || MCQ || 1 MARKS)

The Laplace transform of a continuous-time signal x(t) is

If the Fourier transform of this signal exists, then x(t) is

(GATE 2001 || EC || MCQ || 2 MARKS)

The Laplace transform of i(t) is given by:

[Tex]I(s)=\frac{2}{s(1+s)}[/Tex]

[Tex]\text{As } t\to\infty,\ \text{the value of } i(t)\ \text{tends to}[/Tex]

(GATE 2003 || EC || MCQ || 1 MARKS)

Consider the function f(t) having Laplace transform [Tex]F(s)=\frac{\omega_0}{s^2+\omega_0^2}, \quad \operatorname{Re}(s)>0[/Tex]. The final value of f(t) would be:

(GATE 2006 || EC || MCQ || 2 MARKS)

The 3-dB band width of the low-pass signal e^–tu(t), where u(t) is the unit step function, is given by

(GATE 2007 || EC || MCQ || 2 MARKS)

A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s = –2 and s = –4, and one simple zero at s = –1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is

(GATE 2008 || EC || MCQ || 2 MARKS)