# Fourier transform meaning

1. Jun 14, 2007

### 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.

2. Jun 14, 2007

### Hurkyl

Staff Emeritus
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.