GATE EE

Signals and Systems

Continuous and Discrete Time Signals

Previous Years Questions

## Marks 1

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 ...

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 corre...

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

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 frequen...

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 ra...

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 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 __________.

The value of the integral $$\int_{-5}^{+6}e^{-2t}\delta\left(t-1\right)dt$$ is equal to ________.

## Marks 2

The function shown in the figure can be represented as
...

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