Maple question: defining functions as inverse Fourier transforms

In summary, the conversation discusses a Fourier transformed variable and an attempt to inverse Fourier transform it using Maple. The speaker suggests adding a syntax at the beginning and end of the code to get an implicit expression with integral. They also recommend seeking help on mapleprimes.com for further questions.
  • #1
hunt_mat
Homework Helper
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Hi,

I have a a Fourier transformed variable [itex]\hat{\eta}(k)[/itex] defined as the following:

[tex]
\hat{\eta}(k)=\frac{e^{-k^{2}}\tanh k}{kU^{2}+(-B+\Omega U+E_{b}|k|-k^{2})\tanh k}
[/tex]

The parameters [itex]U,B,\Omega,E_{b}[/itex] have all been defined previously. I have naively tried the following:

[tex]
\eta :=\textrm{invfourier}(ETA,k,x)
[/tex]

This doesn't work. What am I doing wrong?

Cheers
 
  • #3
First thing what is ETA?, you should write ##\hat{\eta}## in this place.
Second, if you read the help in maple then you should add at the beginning of the code: "
upload_2016-6-27_23-4-42.png
"
I assume there's no easy term for the inverse Fourier transform of this expression, but you can get an implicit expression with integral by adding in the last place the syntax: "NO_INT".

I also assume that you read already the help so I don't really no where you get it wrong, perhaps show us your code?

BTW, I find mapleprimes.com as the best place for my questions regarding maple (I am not advertising it's just my experience).
 

1. What is an inverse Fourier transform?

An inverse Fourier transform is a mathematical operation that takes a function in the frequency domain and converts it back to the time domain. It is the opposite of a Fourier transform, which converts a function from the time domain to the frequency domain.

2. How do you define a function as an inverse Fourier transform in Maple?

To define a function as an inverse Fourier transform in Maple, you can use the command ifourier followed by the function you want to convert from the frequency domain to the time domain. For example, ifourier(FrequencyFunction).

3. What is the purpose of using inverse Fourier transforms in Maple?

Inverse Fourier transforms are commonly used in Maple for signal processing and analysis. They allow you to convert a signal from the frequency domain to the time domain, making it easier to analyze and manipulate.

4. Can you use inverse Fourier transforms to solve differential equations in Maple?

Yes, inverse Fourier transforms can be used to solve differential equations in Maple. They can be used to transform a differential equation from the time domain to the frequency domain, solve it, and then transform the solution back to the time domain.

5. Are there any limitations to using inverse Fourier transforms in Maple?

One limitation of using inverse Fourier transforms in Maple is that the function being transformed must be square integrable. This means that the integral of the function squared must converge. Additionally, the function must also have a continuous first derivative.

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