Marks 1
1
A continuous-time system that is initially at rest is described by
$${{dy(t)} \over {dt}} + 3y(t) = 2x(t)$$,
where $$x(t)$$ is the input voltage and $$y(t)$$ is the output voltage. The impulse response of the system is
GATE EE 2023
2
Consider the system with following input-output relation $$y\left[n\right]=\left(1+\left(-1\right)^n\right)x\left[n\right]$$
where, x[n] is the input and y[n] is the output. The system is
GATE EE 2017 Set 1
3
Let $$z\left(t\right)=x\left(t\right)\ast y\left(t\right)$$, where "*" denotes convolution. Let C be a positive real-valued
constant. Choose the correct expression for z(ct).
GATE EE 2017 Set 1
4
The value of $$\int_{-\infty}^{+\infty}e^{-t}\partial\left(2t-2\right)dt$$. where $$\partial\left(t\right)$$ is the Dirac delta function, is
GATE EE 2016 Set 1
5
A moving average function is given by $$y\left(t\right)=\frac1T\int_{t-T}^tu\left(\tau\right)d\tau$$. If the input u is a sinusoidal
signal of frequency
$$\frac1{2T}Hz$$,
then in steady state, the output y will lag u (in degree) by
________.
GATE EE 2015 Set 1
6
For a periodic signal the $$v\left(t\right)=30\sin100t\;+\;10\cos300t\;+\;6\sin\left(500t\;+\;\frac{\mathrm\pi}4\right)$$
fundamental frequency in radians/s is
GATE EE 2013
7
A point Z has been plotted in the complex plane, as shown in figure below.
The plot of the complex number $$y=\frac1z$$ is
The plot of the complex number $$y=\frac1z$$ isGATE EE 2011
8
The convolution of the function $$f_1\left(t\right)=e^{-2t}\;u\left(t\right)$$ and $$f_2\left(t\right)=e^t\;u\left(t\right)$$ is equal to __________.
GATE EE 1995
9
The value of the integral $$\int_{-5}^{+6}e^{-2t}\delta\left(t-1\right)dt$$ is equal to ________.
GATE EE 1994
Marks 2
1
If the energy of a continuous-time signal $x(t)$ is $E$ and the energy of the signal $2x(2t - 1)$ is $cE$, then $c$ is _____ (rounded off to 1 decimal place).
GATE EE 2024
2
The period of the discrete-time signal $$x[n]$$ described by the equation below is $$N=$$ __________ (Round off to the nearest integer).
$$x[n] = 1 + 3\sin \left( {{{15\pi } \over 8}n + {{3\pi } \over 4}} \right) - 5\sin \left( {{\pi \over 3}n - {\pi \over 4}} \right)$$
GATE EE 2023
3
The function shown in the figure can be represented as
GATE EE 2014 Set 1
4
If u(t), r(t) denote the unit step and unit ramp functions respectively and u(t)*r(t) their convolution, then the function u(t+1)*r(t-2) is given by
GATE EE 2007