What Is the Physical Meaning of the Fourier Transform and FFT?

[haiha]

Hi all,

I just know the Fourier series can be applied in differential equation solving, and that's all. Can anyone tell me the physical meaning of the Fourier transform, and fast Fourier transform too.

Thank you very much.

 

[Hurkyl]

What do you mean by "physical meaning", and why do you think there is one?

The typical uses of the Fourier transform are just to obtain a different representation of the object under study. e.g. some questions about real-valued functions are easier to answer in terms of their frequency spectrum. Some questions about polynomials are easier to answer by knowing point-value pairs than it is by knowing the coefficients.

The fast Fourier transform is just a computationally efficient way of computing a Fourier transform.