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

-ADS BY GOOGLE

File Extensions and File Formats

SearchCompliance

  • risk management

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

  • compliance as a service (CaaS)

    Compliance as a Service (CaaS) is a cloud service service level agreement (SLA) that specified how a managed service provider (...

  • data protection impact assessment (DPIA)

    A data protection impact assessment (DPIA) is a process designed to help organizations determine how data processing systems, ...

SearchSecurity

  • DMZ (networking)

    In computer networks, a DMZ (demilitarized zone), also sometimes known as a perimeter network or a screened subnetwork, is a ...

  • quantum supremacy

    Quantum supremacy is the experimental demonstration of a quantum computer's dominance and advantage over classic computers by ...

  • Australian Assistance and Access Bill

    The Australian Assistance and Access Bill is legislation introduced and passed in 2018 by the Parliament of Australia to support ...

SearchHealthIT

SearchDisasterRecovery

  • business continuity plan (BCP)

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

  • disaster recovery team

    A disaster recovery team is a group of individuals focused on planning, implementing, maintaining, auditing and testing an ...

  • cloud insurance

    Cloud insurance is any type of financial or data protection obtained by a cloud service provider. 

SearchStorage

Close