What is Fourier's analysis?
Fourier analysis is a mathematical method used to decay and transform the periodic function - ie the mathematical relationship between quantity and variables or variables, whose relative values are constantly repeated after a regular period of time - on a set of simpler functions that can then be summarized and transformed into the original form. At the beginning of the 19th century, a French physicist and mathematician Jean Baptiste Joseph Fourier, transformed the equation of partial differentiation representing the spread of heat into a number of simpler trigonometric wave functions - ie Sines and Kosina - that could be exceeded to reconstruct the original function.
Today, Fourier analysis is used to analyze and better understand a wide range of natural and artificial processes and phenomena. This has been applied to a wider range of problems in physical and natural scientists and in engineering, including quantum mechanics, acoustics, electrical engineering, image processing and signal, neurolOgie, optics and oceanography.
Fourier analysis begins with a fourier transformation that extends or decomposes, the only, more complicated feature of the periodic wave on a set of simpler elements called the Fourier series, which takes the form of Sinus and Kosin's waves or complex exponential equations. These can then be resolved by means of simpler mathematics and overlapping or recombricted to provide the original function through a linear combination. Fourier analysis closely defined refers to the process of decomposing the original function into a number of simpler components. More generally, it may also include Fourier's synthesis, a process by which the original function is reconstructed by the implementation of an inverse transformation, which essentially performs Fourier's in reverse analysis.
Fourier's analysis has evolved and proceeded to improve, spread and core of what became known as an areaHarmonic analyzes, and proceeded to include the study of more abstract and general phenomena. Fourier analysis is now used actively, regularly and widely in the theory of econometrics and financial markets by scientists and experts who have forecasts, as well as analyze and better understand, the nature and behavior of a wide range of data and parameters of time series that show non -linear relations and repeating wave patterns over time. Its many applications are used to model long -term economic cycles, the relationship between inflation and demand for money and formulas and trends in stocks, foreign exchange and markets with housing and cycles in semiconductor industry, as well as to measure the efficacy of the national economy.