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

Join the conversation

1 comment

Send me notifications when other members comment.

Please create a username to comment.


Fourier analysis is not a method of defining...It's a consequence of the specific propriety of an ortonormal set of functions.

Many waveforms consist of 
energy at a fundamental frequency
ALL the physical waveforms consist of energy for ALL frequency modes 
Cancel

SearchCompliance

  • risk assessment

    Risk assessment is the identification of hazards that could negatively impact an organization's ability to conduct business.

  • PCI DSS (Payment Card Industry Data Security Standard)

    The Payment Card Industry Data Security Standard (PCI DSS) is a widely accepted set of policies and procedures intended to ...

  • risk management

    Risk management is the process of identifying, assessing and controlling threats to an organization's capital and earnings.

SearchSecurity

SearchHealthIT

SearchDisasterRecovery

  • 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 ...

  • cloud disaster recovery (cloud DR)

    Cloud disaster recovery (cloud DR) is a combination of strategies and services intended to back up data, applications and other ...

SearchStorage

  • RAM (Random Access Memory)

    RAM (Random Access Memory) is the hardware in a computing device where the operating system (OS), application programs and data ...

  • business impact analysis (BIA)

    Business impact analysis (BIA) is a systematic process to determine and evaluate the potential effects of an interruption to ...

  • M.2 SSD

    An M.2 SSD is a solid-state drive that is used in internally mounted storage expansion cards of a small form factor.

Close