What Is a Fourier Analysis?
Fourier analysis is a research method that mainly studies the Fourier transform of functions and its properties.
Fourier analysis
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- Fourier analysis is a research method that mainly studies the Fourier transform of functions and its properties.
- Fourier analysis
- An important branch of analysis that has gradually formed since the 18th century, mainly studying the Fourier transform of functions and its properties. Also called reconciliation analysis. After nearly two centuries of development, the field of research has expanded from linear groups and circular groups to general abstract groups. The research on the latter is also called the Fourier analysis on the group to distinguish it from the classical Fourier analysis of the former. Fourier analysis, as a branch of mathematics, has broadly influenced the development of other branches of mathematics, both conceptually and methodically. The formation of many important ideas in mathematics is closely related to the development of Fourier analysis.
- French scientist J.-B.-J. Fourier was engaged in the study of heat flow due to the needs of industrial processing of metals at that time. In the article titled "Analytical Theory of Heat", he developed the heat flow equation and pointed out how to solve it. In the process of solving, he proposed the idea that any periodic function can be represented by a triangular series. Although his thoughts lacked strict arguments, they had a profound impact on modern mathematics, physics, and engineering technology, and became the origin of Fourier analysis.
- The Fourier analysis method is a mathematical method for analyzing periodic non-sinusoidal signals. It is used to analyze the DC component, the fundamental frequency component, and the harmonic component of the time domain signal to find out the time domain variation law. The analysis method is actually converting a periodic non-sinusoidal signal into a series of sine and cosine waves.