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
SearchCompliance
  • compliance risk

    Compliance risk is an organization's potential exposure to legal penalties, financial forfeiture and material loss, resulting ...

  • information governance

    Information governance is a holistic approach to managing corporate information by implementing processes, roles, controls and ...

  • enterprise document management (EDM)

    Enterprise document management (EDM) is a strategy for overseeing an organization's paper and electronic documents so they can be...

SearchSecurity
  • Extensible Authentication Protocol (EAP)

    The Extensible Authentication Protocol (EAP) is a protocol for wireless networks that expands the authentication methods used by ...

  • session key

    A session key is an encryption and decryption key that is randomly generated to ensure the security of a communications session ...

  • data breach

    A data breach is a cyber attack in which sensitive, confidential or otherwise protected data has been accessed and/or disclosed ...

SearchHealthIT
SearchDisasterRecovery
  • risk mitigation

    Risk mitigation is a strategy to prepare for and lessen the effects of threats faced by a business.

  • call tree

    A call tree is a layered hierarchical communication model that is used to notify specific individuals of an event and coordinate ...

  • Disaster Recovery as a Service (DRaaS)

    Disaster recovery as a service (DRaaS) is the replication and hosting of physical or virtual servers by a third party to provide ...

SearchStorage
  • cloud storage

    Cloud storage is a service model in which data is transmitted and stored on remote storage systems, where it is maintained, ...

  • cloud testing

    Cloud testing is the process of using the cloud computing resources of a third-party service provider to test software ...

  • storage virtualization

    Storage virtualization is the pooling of physical storage from multiple storage devices into what appears to be a single storage ...

Close