**Fourier analysis, **

### Definition of Fourier analysis:

Data series analysis based on the concept that any graph (representation of a function) can be regarded as composed of an (almost) infinite series of sine and cosine functions. Thus, the response of a system to complex changes (stimuli) can be computed on the basis of its known response to simple changes. Fourier analysis is an important tool in disparate fields such as physical sciences and sales forecasting. Based on the work of the French mathematician Jean Baptiste Joseph Fourier (1768-1830) on heat flow in 1807. Also called harmonic analysis.

The analysis of a complex waveform expressed as a series of sinusoidal functions, the frequencies of which form a harmonic series.

Fourier analysis is a type of mathematical analysis that attempts to identify patterns or cycles in a time series data set which has already been normalized. In particular, it seeks to simplify complex or noisy data by decomposing it into a series of trigonometric or exponential functions, such as sine waves. Each of these sine waves would have a specific cycle length, amplitude, and phase relationship with the other sine waves, which then could be added back together to reconstruct the observed data.

By first identifying and removing any effects of spurious trends or other complicating factors from the data set, the effects of periodic cycles or patterns can be identified more accurately, leaving the analyst with a better estimate of the direction that the data under analysis will take in the future.

### How to use Fourier analysis in a sentence?

- Fourier analysis is a mathematical technique that decomposes complex time series data into components that are simpler trigonometric functions.
- Fourier analysis has been applied to stock trading, but research examining the technique has found little to no evidence that it is useful in practice.
- The idea is to be able to remove noise or confounding factors from the data set in order to identify true patterns or trends.
- His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.

Meaning of Fourier analysis & Fourier analysis Definition