Fouriersarja
Fouriersarja, or Fourier series, is a method for expressing a periodic function as an infinite sum of trigonometric terms (sines and cosines) or, equivalently, as a sum of complex exponentials. The idea is to decompose a signal into its harmonics, with frequencies that are integer multiples of a fundamental frequency.
Historically, the theory was developed by Jean-Baptiste Joseph Fourier in the early 19th century to solve problems
For a real-valued function f with period 2π that is integrable, its Fourier series is f(x) ~ a0/2
Convergence depends on conditions on f. Under Dirichlet conditions, the series converges to the value between
Applications include analyzing periodic signals, solving partial differential equations such as the heat and wave equations,