Fourier cosine/sine transforms

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Homework Help Overview

The discussion revolves around the Fourier cosine and sine transforms, specifically addressing the conditions under which these transforms exist for certain functions, such as e^x.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the conditions for the existence of Fourier transforms, questioning the implications of a function being singular and the requirement for functions to vanish at infinity.

Discussion Status

Some participants have provided clarifications regarding the conditions necessary for the Fourier transform to exist, while others are seeking further understanding of specific terms and concepts related to the topic.

Contextual Notes

There is an emphasis on the behavior of functions as they approach infinity, which is central to the discussion of Fourier transforms.

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why doesn't e^x have Fourier cosine/sine transforms?
 
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It is too singular as x-->infty.
 
could you please explain the meaning of singular?
 
f(x) must vanish as x goes to infinity in order for the the Fourier transform of f(x) to exist
 
i see! thank you very much!
 

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