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.
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
B. T. Grothaus has written: 'Fourier grain shape analysis' -- subject(s): Alluvial fans, Fourier analysis, Correlation (Statistics)
Randall J. LeVeque has written: 'Fourier analysis of the SOR iteration' -- subject- s -: Iterative solution, SOR iteration, Fourier analysis
It is to convert a function into a sum of sine (or cosine) functions so as to simplify its analysis.
Using Fourier Analysis -which is too difficult to explain in this forum.
Fourier Analysis Frequency-domain graphs
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.
It is difficult to describe how Fourier time series analysis helps with signal processing without going into deep detail. Basically, it helps to manipulate the data to be understood in a simpler way. For the complete detailed explanation one can view Wikipedia "Fourier Analysis".
F. Roddier has written: 'Distributions et transformation de Fourier' -- subject- s -: Fourier transformations, Theory of distributions - Functional analysis -
Cepstrum -The Fourier transform of the logarithm of the mean square density, i.e. simply speaking, the spectrum analysis of a spectrum analysis.