Description of the Fourier Transform

The original data are labeled h(t) as a function of time t, or else in the frequency domain, where the process is specified by giving its amplitude H(f) as a function of frequency f.

We can consider h(t) and H(f) as two different representations of the same function, linked by the Fourier Transform equations:

If t is measured in seconds, then f is measured in cycles per second, or Hertz. However, the equations work with other units too. Note that the angular frequency w is also widely used. The relationship between f and w is:

This convolution function is continuous and is applied to infinite time and frequency domains. Its numerical equivalent is the Discrete Fourier Transform (DFT).