Questions & Answers of Applications of Fourier Transforms

Question No. 44

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

Which one of the following statements is TRUE?

Question No. 115

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

Question No. 138

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

Question No. 139

The value of the integral 2-sin2πtπtdt is equal to

Question No. 139

Consider a signal defined by
xt=ej10tfor t10for t>1
Its Fourier Transform is

Question No. 45

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?

Question No. 215

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

The Fourier transform F(ω) of f(t) is

Question No. 219

A signal is represented by

xt=1t<10t>1

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

Question No. 245

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?

Question No. 42

The Fourier transform of a signal h(t) is Hjω=2cosωsin2ω/ω. The value of h(0) is

Question No. 31

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

Question No. 39

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