Fourier Transform of Useful Functions (Unit impulse, Unit Step, Signum and Rectangular Function)

In this video, the Fourier Transform of some Useful functions like Unit Impulse Function, Unit Step Function, Sign Function (Signum Function), and Rectangular Function is evaluated.

By watching this video, you will learn the following topics:

0:00 Introduction
0:22 Unit Impulse Function and its Fourier Transform
4:42 Unit Step Function and the Fourier Transform of the exponential Function
7:48 Signum Function Fourier Transform
11:00 Unit Step Function Fourier Transform
12:30 Unit Rectangular Function Fourier Transform

Fourier Transform:
The Fourier Transform is very useful tool for the frequency domain analysis of the signal.
In this video, the Fourier Transform of some useful functions like Unit Step, Unit Impulse, Signum, Rectangular Function, and the exponential function is evaluated.

Here is the Fourier Transform of some useful functions:

Unit Impulse Function:
δ (t) == 1

Exponential Function:
e^(-at) u(t) == 1 / (a + j 2πf) ; where a is greater than 0
e^(at) u(-t) == 1 / (a - j 2πf) ; where a is greater than 0

Signum Function:
sgn(t) == 1 / (jπf )

Unit Step Function:
u(t) == {1/2 δ (f) + (1 / j 2πf)}

Rectangular Function:
Rect (t/ 𝜏) == 𝜏 sinc (πf𝜏)

This video will be helpful to all the students of science and engineering in understanding the Fourier Transform and for evaluating the Fourier Transform of some useful functions.

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#FourierTransform
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