FOURIER TRANSFORMATION Meaning and
Definition
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Fourier transformation is a mathematical technique used to decompose a complex function into simpler trigonometric components. It is named after the French mathematician Jean-Baptiste Joseph Fourier, who introduced the concept in the early 19th century. The main purpose of a Fourier transformation is to convert a time-domain signal or function into its frequency-domain representation.
In simpler terms, Fourier transformation allows us to analyze a complex waveform and break it down into its individual frequency components. This transformation provides valuable insights into the frequency content and characteristics of a signal. By revealing the amplitude and phase of different frequencies present in a signal, Fourier transformation enables the identification and study of specific phenomena that may not be easily observable in the time domain.
The mathematical operation of Fourier transformation involves integrating the product of the function being transformed and a complex exponential function over the entire domain. The output of the transformation is a representation of the original function in terms of the frequency domain, consisting of a series of complex numbers known as coefficients or spectrum.
Applications of Fourier transformation span across various fields, including signal processing, image analysis, audio processing, data compression, and quantum mechanics. The Fourier transformation is a fundamental tool in understanding and manipulating signals and functions, enabling the derivation of important properties and enabling their analysis across different domains.
Etymology of FOURIER TRANSFORMATION
The word "Fourier transformation" is named after Jean-Baptiste Joseph Fourier, a French mathematician and physicist who lived from 1768 to 1830. Fourier made significant contributions to the mathematical analysis of periodic phenomena and heat conduction. The Fourier transformation, also known as the Fourier series, was developed by Fourier as a method to represent a periodic function as a sum of sine and cosine functions.
Fourier's work on the analysis of periodic functions and the representation of signals using trigonometric functions laid the foundation for the field of signal processing and has become widely used in various disciplines, including mathematics, physics, engineering, and computer science.
