Editing Superposition principle (section)

==Relation to Fourier analysis and similar methods==
By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific and simple form, often the response becomes easier to compute.

For example, in [[Fourier analysis]], the stimulus is written as the superposition of infinitely many [[Sine wave|sinusoid]]s. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different [[amplitude]] and [[phase (waves)|phase]].) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.

As another common example, in [[Green's function|Green's function analysis]], the stimulus is written as the superposition of infinitely many [[impulse function]]s, and the response is then a superposition of [[impulse response]]s.

Fourier analysis is particularly common for [[wave]]s. For example, in electromagnetic theory, ordinary [[light]] is described as a superposition of [[plane wave]]s (waves of fixed [[frequency]], [[Polarization (waves)|polarization]], and direction). As long as the superposition principle holds (which is often but not always; see [[nonlinear optics]]), the behavior of any light wave can be understood as a superposition of the behavior of these simpler [[plane wave]]s.