Python Programming for Biology: Bioinformatics and Beyond

19

Signal processing

Contents

Signals

Simulating a signal

Displaying a signal

Fast Fourier transform

The theory of FFT

FFT using NumPy

Peaks

A ‘

Peak

’ class

Peak picking

Peak fitting

2D gel peak-picking example

Signals

In science many different kinds of experiment involve the recording of signals: series of

measurements  that  represent  the  variation  in  some  kind  of  underlying  physical  property.

The  signal  can  then  be  interpreted,  based  on  some  theoretical  model  of  the  experiment.

Commonly the recorded signal is one that varies over time, such as sound or radio waves,

but it could also represent a variation in space, or indeed along any other kind of axis. In

general  a  signal  is  represented  by  values  that  are  directly  recorded  by  instruments  at

specific,  usually  regular,  intervals;  although  in  some  situations  derived  data,  like  a  DNA

sequence, can also be thought of in terms of signals.

If a signal varies in a regular manner, i.e. oscillates, then it is often the frequencies that

occur  within  the  signal  that  are  of  interest,  rather  than  the  original  signal  itself.  This  is

because  the  underlying  frequencies  are  generally  characteristic  of  what  made  the  signal.

To take a toy example, if we have a peal of bells, where each bell has a different tone, we

can  record  the  variation  of  the  overall  sound  signal  over  time.  Then,  by  looking  at  the

component  frequencies  we  can  discern  the  tones  of  the  individual  bells  that  made  the

sound. As we will illustrate, it is possible to convert the time signal into a spectrum of its

component frequencies using what is known as a Fourier transform.