Browse Definitions:
Definition

Fourier synthesis

Fourier synthesis is a method of electronically constructing a signal with a specific, desired periodic waveform . It works by combining a sine wave signal and sine-wave or cosine-wave harmonics (signals at multiples of the lowest, or fundamental, frequency) in certain proportions. The scheme gets its name from a French mathematician and physicist named Jean Baptiste Joseph, Baron de Fourier, who lived during the 18th and 19th centuries.

Many waveforms represent signal energy at a fundamental frequency and also at harmonic frequencies (whole-number multiples of the fundamental). The relative proportions of energy concentrated at the fundamental and harmonic frequencies determine 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 functions 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 synthesis, it is necessary to know, or to determine, the coefficients a , a 1 , a 2 , a 3 , ..., a n , ... and b 1 , b 2 , b 3 , ..., b n , ... that will produce the waveform desired when "plugged into" the generalized formula for the Fourier series, as defined above. Then, sine and cosine waves with the proper amplitudes (as defined by the coefficients) must be electronically generated and combined, up to the highest possible value of n . The larger the value of n for which sine-wave and cosine-wave signals are generated, the more nearly the synthesized waveform matches the desired waveform.

Fourier synthesis is used in electronic music applications to generate waveforms that mimic the sounds of familiar musical instruments. It is also employed in laboratory instruments known as waveform generators or function generators. These devices are used to test communication systems.

Compare Fourier analysis .

This was last updated in September 2005

Start the conversation

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.

-ADS BY GOOGLE

File Extensions and File Formats

SearchCompliance

  • smart contract

    A smart contract, also known as a cryptocontract, is a computer program that directly controls the transfer of digital currencies...

  • risk map (risk heat map)

    A risk map, also known as a risk heat map, is a data visualization tool for communicating specific risks an organization faces. A...

  • internal audit (IA)

    An internal audit (IA) is an organizational initiative to monitor and analyze its own business operations in order to determine ...

SearchCloudProvider

  • cloud ecosystem

    A cloud ecosystem is a complex system of interdependent components that all work together to enable cloud services.

  • cloud services

    Cloud services is an umbrella term that may refer to a variety of resources provided over the internet, or to professional ...

  • uncloud (de-cloud)

    The term uncloud describes the action or process of removing applications and data from a cloud computing platform.

SearchSecurity

  • cyberextortion

    Cyberextortion is a crime involving an attack or threat of an attack coupled with a demand for money or some other response in ...

  • Cybercrime

    Cybercrime is any criminal activity that involves a computer, networked device or a network.

  • National Security Agency (NSA)

    The National Security Agency is the official U.S. cryptologic organization of the United States Intelligence Community under the ...

SearchHealthIT

  • Practice Fusion

    Practice Fusion Inc. is a San Francisco-based company that developed a free electronic health record (EHR) system available to ...

  • RHIA (Registered Health Information Administrator)

    An RHIA, or registered health information administrator, is a certified professional who oversees the creation and use of patient...

  • 21st Century Cures Act

    The 21st Century Cures Act is a wide-ranging healthcare bill that funds medical research and development, medical device ...

SearchDisasterRecovery

SearchStorage

  • storage medium (storage media)

    In computers, a storage medium is any technology -- including devices and materials -- used to place, keep and retrieve ...

  • Random Access Memory (RAM)

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

  • floating gate transistor (FGT)

    A floating gate transistor (FGT) is a complementary metal-oxide semiconductor (CMOS) technology capable of holding an electrical ...

SearchSolidStateStorage

  • hybrid hard disk drive (HDD)

    A hybrid hard disk drive is an electromechanical spinning hard disk that contains some amount of NAND Flash memory.

Close