GATE EE

Signals and Systems

Continuous Time Signal Fourier Transform

Previous Years Questions

## Marks 1

Let an input x(t) = 2 sin(10$$\pi$$t) + 5 cos(15$$\pi$$t) + 7 sin(42$$\pi$$t) + 4 cos(45$$\pi$$t) is passed through an LTI system having an impulse re...

A function f(t) is shown in the figure.
The Fourier transform F($$\mathrm\omega$$) of f(t) is
...

A signal is represented by $$$x\left(t\right)=\left\{\begin{array}{l}1\;\;\;\left|t\right|\;<\;1\\0\;\;\;\left|t\right|\;>\;1\end{array}\right.$...

## Marks 2

Suppose x1(t) and x2(t) have the Fourier transforms as shown below.
Which one of the following statements is TRUE?...

Consider a signal defined by $$$x\left(t\right)=\left\{\begin{array}{l}e^{j10t}\;\;\;for\;\left|t\right|\leq1\\0\;\;\;\;\;\;\;for\;\;\left|t\right|>...

A differentiable non constant even function x(t) has a derivative y(t), and their respective
Fourier Transforms are X($$\omega$$) and Y($$\omega$$). W...

A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre
frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output ...

Let f(t) be a continuous time signal and let F($$\omega$$) be its Fourier Transform defined by $$F\left(\omega\right)=\int_{-\infty}^\infty f\left(t\r...

The Fourier transform of a signal h(t) is $$H\left(j\omega\right)=\left(2\cos\omega\right)\left(\sin2\omega\right)/\omega$$. The value of h(0) is

x(t) is a positive rectangular pulse from t = -1 to t = +1 with unit height as shown
in the figure. The value of $$\int_{-\infty}^\infty\left|X\left(\...