Browse Definitions :
Definition

Fourier series

A Fourier (pronounced foor-YAY) series is a specific type of infinite mathematical series involving trigonometric functions. The series 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 series are used in applied mathematics, and especially in physics and electronics, to express periodic functions such as those that comprise communications signal waveform s.

Let { a , a 1 , a 2 , a 3 , ..., a n , ...} and { b 1 , b 2 , b 3 , ..., b n , ...} be infinite sets of constant s. These constants are called the Fourier coefficient s. Let x be a variable. The general Fourier series is given by:

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 + ...

Some waveforms are simple, such as the pure sine wave , but these are theoretical ideals. In the real world, most waveforms contain energy at harmonic frequencies (whole-number multiples of the lowest, or fundamental, frequency). The proportion of energy at harmonic frequencies, compared with the energy at the fundamental, depends on the waveform. Fourier series mathematically define such waveforms as functions of displacement (usually amplitude , frequency , or phase ) versus time .

As the number of calculated terms in a Fourier series increases, the series more and more closely approximates the exact function that defines a complex signal waveform. Computers can calculate Fourier series out to hundreds, thousands, or millions of terms.

This was last updated in September 2005

Join the conversation

2 comments

Send me notifications when other members comment.

Please create a username to comment.

This explanation is very lacking. The Fourier series is by no means intuitive, but this explanation serves no purpose to anyone first reading on the Fourier series.
Cancel
I agree;when explaining something one has to start with first principles,even if someone has prerequisite knowledge.If you don't you come across as a teaching "parrot,"with little confidence that the "teacher" actually understands it themselves.
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

  • tokenization

    Tokenization is the process of replacing sensitive data with unique identification symbols that retain all the essential ...

  • incident response

    Incident response is an organized approach to addressing and managing the aftermath of a security breach or cyberattack, also ...

  • Federal Information Security Management Act (FISMA)

    The Federal Information Security Management Act (FISMA) is United States legislation that defines a framework of guidelines and ...

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

Close