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Fourier analysis

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A visual representation of a fourier transform, the time axis is shown in red, thefrequency axis is shown in blue. Since the time signal is periodic, it only shows certain parts of thespectrum
Fourier transforms

Fourier analysis is a branch ofanalysis that looks at how more complexfunctions can be built with simpler ones. It is also known asclassical harmonic analysis. It is named afterJoseph Fourier who first used it in the 19th century. The process itself is calledFourier transform. Fourier analysis is widely used in fields such asphysics,partial differential equations,number theory,combinatorics,signal processing, imaging,probability theory,statistics,option pricing,cryptography,numerical analysis,acoustics,oceanography,sonar,optics,diffraction,geometry andprotein structure analysis.

Continuous data
Center
Dispersion
Shape
Count data
Summary tables
Dependence
Graphics
Study design
Survey methodology
Controlled experiments
Adaptive Designs
Observational Studies
Statistical theory
Frequentist inference
Point estimation
Interval estimation
Testing hypotheses
Parametric tests
Specific tests
Goodness of fit
Rank statistics
Bayesian inference
Correlation
Regression analysis
Linear regression
Non-standard predictors
Generalized linear model
Partition of variance
Categorical
Multivariate
Time-series
General
Specific tests
Time domain
Frequency domain
Survival
Survival function
Hazard function
Test
Biostatistics
Engineering statistics
Social statistics
Spatial statistics


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