What Fourier transform be called? Correlation or convolution?

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The discussion centers on the classification of the Fourier transform as either a correlation or convolution formula. It highlights that the Fourier transform involves two main components: a function f(t) and a complex exponential term. Participants clarify that Fourier transforms, convolutions, and correlations are distinct concepts, although they are interconnected. Specifically, the Fourier transform of a product of functions results in the convolution of their individual transforms. Understanding these relationships is crucial for accurately describing the Fourier transform's nature.
ramdas
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We know that in the Fourier transform formula ,there are mainly two terms function f(t) and complex exponential term ( function).


But I am confused that what should i call Fourier transform formula as a correlation or convolution formula? So can anybody help regarding it?
 
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You need to describe what you are looking for. Fourier transform, convolution, and correlation are all different concepts.

There is a connection between the Fourier transforms and convolutions - the Fourier transform of a product of two functions is the convolution of the individual transforms, and vice versa.
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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