Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis. Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation. If you want to find out more, look up fourier synthesis and the fourier transform.
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
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Fourier analysis shows that the saw wave is constructed through manipulation of a sine wave, I can't remember the maths behind it but it's definitely a sine wave.
Physics would be one of a few examples of fourier transform. One would also use it when they are using engineering so, yeah that is basically it as far as the fourier transform is concerned.
Fourier analysis Frequency-domain graphs
Fourier analysis began with trying to understand when it was possible to represent general functions by sums of simpler trigonometric functions. The attempt to understand functions (or other objects) by breaking them into basic pieces that are easier to understand is one of the central themes in Fourier analysis. Fourier analysis is named after Joseph Fourier who showed that representing a function by a trigonometric series greatly simplified the study of heat propagation. If you want to find out more, look up fourier synthesis and the fourier transform.
Tatsuo Kawata has written: 'Fourier analysis in probability theory' -- subject(s): Fourier series, Fourier transformations, Probabilities
Randall J. LeVeque has written: 'Fourier analysis of the SOR iteration' -- subject- s -: Iterative solution, SOR iteration, Fourier analysis
B. T. Grothaus has written: 'Fourier grain shape analysis' -- subject(s): Alluvial fans, Fourier analysis, Correlation (Statistics)
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
The general field of Fourier analysis is often known as harmonic analysis. The Fourier analysis it occurs in the modeling time-dependent phenomena such as speech, EKGs, EEGs, earthquakes and tides. Examples also include the study of vibrations and circular, physical and rectangular pictures. It also involves the transmission of pictures including the weather or pictures of remote planets taken by space probes.
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Fourier Analysis Frequency-domain graphs
Using Fourier Analysis -which is too difficult to explain in this forum.
Fourier analysis shows that the saw wave is constructed through manipulation of a sine wave, I can't remember the maths behind it but it's definitely a sine wave.
Fourier time series analysis helps in decomposing a complex signal into its constituent frequencies, allowing for better understanding of the signal's frequency content. This analysis is fundamental in areas like signal filtering, spectral analysis, and noise reduction in signal processing. It also aids in identifying and isolating specific frequency components within a signal.