What are the limitations/ disadvantages of the Fourier Tran

[ramdas]

I am fond of Fourier series &
Fourier transform. In Fourier
domain, we can come to know
what frequency components are
present and the contribution of
each component in forming the
given signal.But every approach has some
advantages and
disadvantages.Here, I want to
know what are the limitations/
disadvantages of the Fourier
Transform and Fourier Series? It
would be better for me if you
explain them with the help of
example(or links or any relevant
information) to understand
them easily.

 

[Simon Bridge]

Well, if you have a time domain function and you need a position domain function, the Fourier transform is unlikely to be a lot of help.
i.e. it is no good in any situation where you don't need the Fourier transform.

Tools are useful in their contexts - and most limitations for a tool in context are not about the context. i.e. a hammer is good for hammering nails, but it can be slow and tiring, especially if you want to attach wood to concrete, so ramset. But that is not a limit of the hammer, it is a limit of the user and the job (time constraint not inherent to hammer).

So to understand the limits of the Fourier transform - whose usefulness is not limited to just finding the frequency domain function from a time domain function - you need to understand the types of jobs you may want it to do and what sorts of constraints those jobs have to work under. i.e. numerical analysis of a discrete time-series as a real-time inverse problem.

 

[DrClaude]

If the original data is already discrete and finite, then there is no loss of information when doing a discrete Fourier transform. It is therefore just a different way to look at the same information content, and as Simon said, whether to look at something in time (or position) or in frequency it's a matter of what you are trying to accomplish.

 

[ramdas]

Why my question is deleted.If it is duplicate ,where is the original one?

 

[Drakkith]

Why my question is deleted.If it is duplicate ,where is the original one?

This is the original thread. I deleted the duplicate thread last night. If you have any questions about this, please message me.