Browse Definitions:

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

Start the conversation

Send me notifications when other members comment.

By submitting you agree to receive email from TechTarget and its partners. If you reside outside of the United States, you consent to having your personal data transferred to and processed in the United States. Privacy

Please create a username to comment.


File Extensions and File Formats

Powered by:


  • risk map (risk heat map)

    A risk map, also known as a risk heat map, is a data visualization tool for communicating specific risks an organization faces.

  • internal audit (IA)

    An internal audit (IA) is an organizational initiative to monitor and analyze its own business operations in order to determine ...

  • pure risk (absolute risk)

    Pure risk, also called absolute risk, is a category of threat that is beyond human control and has only one possible outcome if ...


  • federated identity management (FIM)

    Federated identity management (FIM) is an arrangement that can be made among multiple enterprises to let subscribers use the same...

  • cross-site scripting (XSS)

    Cross-site scripting (XSS) is a type of injection security attack in which an attacker injects data, such as a malicious script, ...

  • firewall

    In computing, a firewall is software or firmware that enforces a set of rules about what data packets will be allowed to enter or...



  • business continuity and disaster recovery (BCDR)

    Business continuity and disaster recovery (BCDR) are closely related practices that describe an organization's preparation for ...

  • business continuity plan (BCP)

    A business continuity plan (BCP) is a document that consists of the critical information an organization needs to continue ...

  • call tree

    A call tree -- sometimes referred to as a phone tree -- is a telecommunications chain for notifying specific individuals of an ...


  • volume manager

    A volume manager is software within an operating system (OS) that controls capacity allocation for storage arrays.

  • external storage device

    An external storage device, also referred to as auxiliary storage and secondary storage, is a device that contains all the ...

  • NetApp SolidFire

    NetApp SolidFire is a business division of NetApp Inc. that specializes in all-flash storage systems.


  • hybrid hard disk drive (HDD)

    A hybrid hard disk drive is an electromechanical spinning hard disk that contains some amount of NAND Flash memory.