How to Easily Convolve a Function with Itself?

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Discussion Overview

The discussion revolves around the process of convolving a function with itself, exploring whether there is a straightforward method or formula to achieve this. Participants consider both theoretical aspects and practical implications, particularly in relation to specific functions like the squared Bessel function.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about an easy method or formula for convolving a function with itself.
  • Another participant introduces the concept of autocorrelation, referencing the Wiener-Khinchin Theorem and its relation to correlation.
  • A different participant suggests taking the Fourier transform of the function, squaring the transform, and then applying the inverse transform to find the convolution.
  • A later reply expresses concern about the complexity of the method, particularly in relation to the specific function being considered (a squared Bessel function).

Areas of Agreement / Disagreement

Participants do not reach a consensus on a straightforward method for convolution, and multiple approaches are presented without agreement on their efficacy or simplicity.

Contextual Notes

The discussion does not resolve the complexity of the convolution process, particularly for specific functions, and lacks clarity on the assumptions or definitions involved in the proposed methods.

thomitsu
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Hallo there!

I was wondering wether there is an easy way to convolve a function with itself.
For example is ther an easy formula or something that gives directly the result?
thanks in advance
 
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for example, for correlation...

The correlation of a function with itself is called its autocorrelation
In this case the correlation theorem becomes
the transform pair
– This is the Wiener-Khinchin Theorem
Corr(g,g)↔G( f )G*( f ) = G( f )^2

Is there something like that for convolution?
 


I don't know if it helps any, but take the Fourier transform of the function, square the transform, and take the inverse transform of the result.
 


Oh god! This is so complicated( my function is a squared bessel function)! I will try it though.thank you so much!
 

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