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

-ADS BY GOOGLE

Dateiendungen und Dateiformate

Gesponsert von:

SearchCompliance

SearchSecurity

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

  • RAID 6 (redundant array of independent disks)

    RAID 6, also known as double-parity RAID, uses two parity stripes on each disk. It allows for two disk failures within the RAID ...

  • hard disk drive (HDD)

    A computer hard disk drive (HDD) is a non-volatile memory hardware device that controls the positioning, reading and writing of ...

  • byte

    In most computer systems, a byte is a unit of data that is eight binary digits long. Bytes are often used to represent a ...

Close