Python for Bioinformatics

21 Fourier Transforms

Any periodic signal with a wavelength of λ can be decomposed into a set of frequencies with wavelengths that are integer multiples of λ. In practice any digital signal can be converted to a set of frequencies without loss of information. A common way to compute these frequencies is through the use of the Fourier transform, but it is not the only method.

By converting information into Fourier space, it becomes possible to apply a large host of filters to keep the desired frequencies and dispose of the undesirable ones. Fourier filtering has been used to clean up noisy signals, to isolate targets, and to search for complicated structures in the signal. This chapter will focus on a few aspects of Fourier theory and some applications ...