29/12/2024
300/1000 | Fourier Transform of e^(-atĀ²) | Step-by-Step Solution & Inverse Transform
Timestamps:
00:00 FOURIER TRANSFORM of e^-atĀ² where a is greater than 0
00:28 What is Fourier Transform ?
01:22 Solution
01:55 How to make a perfect square
05:48 Result from Error Function
06:22 Inverse FOURIER TRANSFORM of e^-atĀ² where a is greater than 0
06:36 Inverse & FOURIER TRANSFORM of e^-atĀ² where a is 1/2
_Description_
In this video, we'll find the Fourier Transform of the function e^(-atĀ²) where a is greater than 0. We'll start with the definition of the Fourier Transform, then solve the integral step-by-step. We'll also discuss how to make a perfect square and use the error function to simplify the result. Finally, we'll find the Inverse Fourier Transform of the same function.
_Hashtags_
_Keywords_
Fourier Transform, Inverse Fourier Transform, e^(-atĀ²), Error Function, Calculus, Mathematics, Engineering Mathematics, Signal Processing, Image Processing, Integral Transforms.
