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.

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.

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

-ADS BY GOOGLE

File Extensions and File Formats

Powered by:

SearchCompliance

SearchSecurity

  • copyright

    Copyright is a legal term describing ownership of control of the rights to the use and distribution of certain works of creative ...

  • keylogger (keystroke logger or system monitor)

    A keylogger, sometimes called a keystroke logger or system monitor, is a type of surveillance technology used to monitor and ...

  • password

    A password is an unspaced sequence of characters used to determine that a computer user requesting access to a computer system is...

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 ...

  • call tree

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

  • mass notification system (MNS)

    A mass notification system is a platform that sends one-way messages to inform employees and the public of an emergency.

SearchStorage

  • RAID (redundant array of independent disks)

    RAID (redundant array of independent disks) is a way of storing the same data in different places on multiple hard disks to ...

  • data migration

    Data migration is the process of transferring data between data storage systems, data formats or computer systems.

  • compact disc (CD)

    A compact disc is a portable storage medium that can be used for recording, storing and playing back audio, video and other data ...

SearchSolidStateStorage

  • NVMe (non-volatile memory express)

    NVMe (non-volatile memory express) is a host controller interface and storage protocol to enable a solid-state drive to use the ...

  • SSD RAID (solid-state drive RAID)

    SSD RAID (solid-state drive RAID) is a methodology commonly used to protect data by distributing redundant data blocks across ...

  • Tier 0

    Tier 0 (tier zero) is a level of data storage that is faster, and perhaps more expensive, than any other level in the storage ...

SearchCloudStorage

  • RESTful API

    A RESTful application program interface breaks down a transaction to create a series of small modules, each of which addresses an...

  • cloud storage infrastructure

    Cloud storage infrastructure is the hardware and software framework that supports the computing requirements of a private or ...

  • Zadara VPSA and ZIOS

    Zadara Storage provides block, file or object storage with varying levels of compute and capacity through its ZIOS and VPSA ...

Close