Browse Definitions :
Definition

Fourier analysis

Fourier analysis is a method of defining periodic waveform s in terms of trigonometric function s. The method gets its name from a French mathematician and physicist named Jean Baptiste Joseph, Baron de Fourier, who lived during the 18th and 19th centuries. Fourier analysis is used in electronics, acoustics, and communications.

Many waveforms consist of energy at a fundamental frequency and also at harmonic frequencies (multiples of the fundamental). The relative proportions of energy in the fundamental and the harmonics determines the shape of the wave. The wave function (usually amplitude , frequency, or phase versus time ) can be expressed as of a sum of sine and cosine function s called a Fourier series , uniquely defined by constants known as Fourier coefficient s. If these coefficients are represented by a , a 1 , a 2 , a 3 , ..., a n , ... and b 1 , b 2 , b 3 , ..., b n , ..., then the Fourier series F ( x ), where x is an independent variable (usually time), has the following form:

F ( x ) = a /2 + a 1 cos x + b 1 sin x + a 2 cos 2 x + b 2 sin 2 x + ...
+ a n cos nx + b n sin nx + ...

In Fourier analysis, the objective is to calculate coefficients a , a 1 , a 2 , a 3 , ..., a n and b 1 , b 2 , b 3 , ..., b n up to the largest possible value of n . The greater the value of n (that is, the more terms in the series whose coefficients can be determined), the more accurate is the Fourier-series representation of the waveform.

Compare Fourier synthesis .

This was last updated in September 2005
SearchNetworking
SearchSecurity
  • man in the browser (MitB)

    Man in the browser (MitB) is a security attack where the perpetrator installs a Trojan horse on the victim's computer that is ...

  • Patch Tuesday

    Patch Tuesday is the unofficial name of Microsoft's monthly scheduled release of security fixes for the Windows operating system ...

  • parameter tampering

    Parameter tampering is a type of web-based cyber attack in which certain parameters in a URL are changed without a user's ...

SearchCIO
  • e-business (electronic business)

    E-business (electronic business) is the conduct of business processes on the internet.

  • business resilience

    Business resilience is the ability an organization has to quickly adapt to disruptions while maintaining continuous business ...

  • chief procurement officer (CPO)

    The chief procurement officer, or CPO, leads an organization's procurement department and oversees the acquisitions of goods and ...

SearchHRSoftware
SearchCustomerExperience
  • clickstream data (clickstream analytics)

    Clickstream data and clickstream analytics are the processes involved in collecting, analyzing and reporting aggregate data about...

  • neuromarketing

    Neuromarketing is the study of how people's brains respond to advertising and other brand-related messages by scientifically ...

  • contextual marketing

    Contextual marketing is an online marketing strategy model in which people are served with targeted advertising based on their ...

Close