Fourier Analysis is a mathematical method of identifying and describing harmonic patterns in complex oscillating environments, and is used in options pricing among other things.

Fourier Analysis is used to compute the probability that results will be within a certain range. Fourier analysis also has many other applications in physics, engineering, and music, for instance, because it can create a system for identifying patterns and simplifying computations for complex systems which feature oscillations and waves which have frequencies.

In finance, Fourier analysis comes in handy for options pricing in particular but can be applied to many things. It helps to reduce to the noise of the market and to identify how closely a value is sticking to its normal cycle. Also called harmonic analysis.