Fourier Transform Help with Mathematica

In summary, the conversation discusses instructions for performing a Fourier Transformation and Inverse Fourier in Mathematica. The correct method involves defining a function of k instead of x and multiplying b by k instead of the absolute value of k.
  • #1
TL;DR Summary
I am attempting to do a problem involving wave functions and imaginary numbers
I am attempting to be able to do this problem with the help of Mathematica and Fourier transform. My professor gave us instructions for Fourier Transformation and Inverse Fourier, but I don't believe that my output in Mathematica is correct.
Problem 1.38 statement.jpeg

My working on paper.jpeg

image of attempt to do it Dr Uys way.jpg
 
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  • #2
You're supposed to define a function of ##k##, not ##x##, and find the inverse Fourier transform to get ##f(x)##. Also, note that ##b## is multiplied by ##k##, not ##\lvert k \rvert##.
 
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  • #3
vela said:
You're supposed to define a function of ##k##, not ##x##, and find the inverse Fourier transform to get ##f(x)##. Also, note that ##b## is multiplied by ##k##, not ##\lvert k \rvert##.
vela said:
You're supposed to define a function of ##k##, not ##x##, and find the inverse Fourier transform to get ##f(x)##. Also, note that ##b## is multiplied by ##k##, not ##\lvert k \rvert##.
thanks so much!
 

What is a Fourier Transform?

A Fourier Transform is a mathematical tool that allows us to decompose a function into its constituent frequencies. It transforms a signal from its original domain (often time or space) to a representation in the frequency domain.

How is a Fourier Transform helpful in Mathematica?

In Mathematica, the Fourier Transform function allows you to easily perform calculations and manipulations on signals and functions in the frequency domain. This can be useful in many scientific and engineering applications, such as signal processing, image analysis, and differential equations.

What is the difference between discrete and continuous Fourier Transforms?

A discrete Fourier Transform (DFT) is used for signals that are sampled at discrete intervals, such as digital signals. A continuous Fourier Transform (CFT) is used for signals that are continuous, such as analog signals. In Mathematica, the Fourier function performs a discrete Fourier Transform by default, but the FourierTransform function can be used for continuous signals.

Can I perform an inverse Fourier Transform in Mathematica?

Yes, Mathematica has a built-in function called InverseFourier that allows you to transform a signal back to its original domain after performing a Fourier Transform. This can be useful for analyzing and processing signals in the time or space domain.

Are there any limitations to using Fourier Transforms in Mathematica?

While Mathematica's Fourier Transform functions are powerful tools, they do have some limitations. For example, they may not work well for signals with sharp discontinuities or for functions that are not well-behaved. It is always important to carefully consider the properties of your signal before using a Fourier Transform in Mathematica or any other software.

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