Fourier analysis
Quick Summary
Using Fourier analysis, a step function is modeled, or decomposed, as the sum of various sine functions. This striking example demonstrates how even an obviously discontinuous and piecewise linear graph (a step function) can be reproduced to any desired level of accuracy by combining enough sine functions, each of which is continuous and nonlinear.
Fourier analysis is a mathematical technique used to represent periodic functions as an infinite sum of sines and cosines, known as a Fourier series. This method is particularly useful for solving certain differential equations and analyzing phenomena that repeat over fixed intervals.12
The concept was explored by mathematicians like Leonhard Euler but was fully developed and named after Joseph Fourier, a French mathematician who applied it to the study of heat conduction. Fourier analysis has broad applications in fields such as engineering, physics, and the analysis of sound waves, electric currents, and tides. The process involves determining the coefficients for the sine and cosine terms that best approximate the periodic data.1345
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