Python Programming for Biology: Bioinformatics and Beyond

Fast Fourier transform

The Fourier transform is one mathematical technique for determining the frequencies that

exist  in  a  signal.

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 In  essence,  what  the  Fourier  transform  does  is  to  work  out  what

combination  of  pure  sinusoidal  oscillations  the  signal  is  composed  of,  in  terms  of  both

frequency and intensity, so that we can see how much of each frequency is present. The

‘transformation’  is  from  the  original  signal  axis,  which  is  typically  time,  to  a  frequency

axis.  Sometimes  the  signal  oscillates  in  more  than  one  direction,

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 and  so  is  recorded  on

two  orthogonal  axes  and  is  represented  by  complex  numbers,  rather  than  plain  (real)

numbers. Effectively this means that the signal values are two-dimensional, but this can all

be  dealt  with  by  the  Fourier  transform.  Although  time  is  a  continuous  variable,  the

measurement of the signal is usually made at discrete times, and so the relevant technique

to use is the discrete Fourier transform.

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