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
  • pure risk

    Pure risk refers to risks that are beyond human control and result in a loss or no loss with no possibility of financial gain.

  • risk reporting

    Risk reporting is a method of identifying risks tied to or potentially impacting an organization's business processes.

  • chief risk officer (CRO)

    The chief risk officer (CRO) is the corporate executive tasked with assessing and mitigating significant competitive, regulatory ...

  • encryption key

    In cryptography, an encryption key is a variable value that is applied using an algorithm to a string or block of unencrypted ...

  • payload (computing)

    In computing, a payload is the carrying capacity of a packet or other transmission data unit.

  • script kiddie

    Script kiddie is a derogative term that computer hackers coined to refer to immature, but often just as dangerous, exploiters of ...

  • What is risk mitigation?

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

  • fault-tolerant

    Fault-tolerant technology is a capability of a computer system, electronic system or network to deliver uninterrupted service, ...

  • synchronous replication

    Synchronous replication is the process of copying data over a storage area network, local area network or wide area network so ...