# Applied Mathematics/General Fourier Transform

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## Fourier Transform[edit | edit source]

Fourier Transform is to transform the function which has certain kinds of variables, such as time or spatial coordinate, for example, to the function which has variable of frequency.

## Definition[edit | edit source]

- ...(1)

This integral above is referred to as Fourier integral, while is called **Fourier transform** of . denotes "time". denotes "frequency".

On the other hand, Inverse Fourier transform is defined as follows:

- ...(2)

In the textbooks of universities, the Fourier transform is usually introduced with the variable Angular frequency . In other word, is substituted to (1) and (2) in the books. In that case, the Fourier transform is written in two different ways.

1.

2.