#### In-depth

## The Fourier transform

#### The Fourier transform is widely used for converting any mathematical description of a time domain waveform into the frequency domain equivalent. As such it can be viewed as a generalization of the Fourier series expansion. There is also an inverse Fourier transform which will convert from the frequency domain to the time domain. The Fourier transform X(f) of a time function x(t) is defined as: and the inverse Fourier transform is given by: A more detailed analyis of Fourier transforms can be found in Haykin (1989).