GATE Questions & Answers of Applications of Fourier Transforms

What is the Weightage of Applications of Fourier Transforms in GATE Exam?

Total 12 Questions have been asked from Applications of Fourier Transforms topic of Signals and Systems subject in previous GATE papers. Average marks 1.75.

Suppose x1t and x2t have the Fourier transforms as shown below.

Which one of the following statements is TRUE?

Suppose the maximum frequency in a band-limited signal xt is 5 kHz. Then, the maximum frequency in xtcos2000πt, in kHz, is ________.

Let x1tX1ω and x2tX2ω be two signals whose Fourier Transforms are as shown in the figure below. In the figure, ht=e-2t denotes the impulse response.
For the system shown above, the minimum sampling rate required to sample y(t), so that y(t) can be uniquely reconstructed from its samples, is

The value of the integral 2-sin2πtπtdt is equal to

Consider a signal defined by

xt=ej10tfor t10for t>1

Its Fourier Transform is

Let ft be a continuous time signal and let Fω be its Fourier Transform defined by

Define gt by $F\left(\omega\right)=\int\limits_{-\infty}^\infty f\left(t\right)e^{-j\omega t}dt$

$g\left(t\right)=\int\limits_{-\infty}^\infty F\left(u\right)e^{-jut}du$

What is the relationship between ft and gt?

A function f(t) is shown in the figure.

The Fourier transform F(ω) of f(t) is

A signal is represented by


The Fourier transform of the convolved signal yt=x2t*xt/2 is

A differentiable non constant even function x(t) has a derivative y(t), and their respective Fourier Transforms are Xω and Yω. Which of the following statements is TRUE?

The Fourier transform of a signal h(t) is Hjω=2cosωsin2ω/ω. 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 $\int\limits_{-\infty}^\infty\left|X\left(\omega\right)\right|^2d\omega$ {where X(ω) is the Fourier transform of x(t)} is

Let xt=rectt-12 (where rect(x)=1 for -12x12 and zero otherwise). Then if sincx=sinπxπx,, the Fourier Transform of x(t)+x(-t) will be given by