Editing Additive synthesis (section)

==Implementation methods==

Modern-day implementations of additive synthesis are mainly digital. (See section ''[[#Discrete-time equations|Discrete-time equations]]'' for the underlying discrete-time theory)

===Oscillator bank synthesis===

Additive synthesis can be implemented using a bank of sinusoidal oscillators, one for each partial.<ref name="JOS_Additive"/><!--
{{cite web      
 | title        = Additive Synthesis (Early Sinusoidal Modeling)
 | author       = Julius O. Smith III
 | url          = https://ccrma.stanford.edu/~jos/sasp/Additive_Synthesis_Early_Sinusoidal.html
 | access-date   = 14 January 2012
}}</ref> -->

===Wavetable synthesis===
{{Main|Wavetable synthesis}}
In the case of harmonic, quasi-periodic musical tones, [[wavetable synthesis]] can be as general as time-varying additive synthesis, but requires less computation during synthesis.<ref name="Wavetable Synthesis 101">
{{cite web
 |author       = Robert Bristow-Johnson
 |date         = November 1996
 |title        = Wavetable Synthesis 101, A Fundamental Perspective
 |url          = http://www.musicdsp.org/files/Wavetable-101.pdf
 |access-date  = 21 May 2005
 |archive-url  = https://web.archive.org/web/20130615202748/http://musicdsp.org/files/Wavetable-101.pdf
 |archive-date = 15 June 2013
 |df           = dmy-all
}}
</ref><ref name="Wavetable Matching Synthesis of Dynamic Instruments with Genetic Algorithms">
{{cite journal  
 | author       = Andrew Horner
 | date         = November 1995
 | title        = Wavetable Matching Synthesis of Dynamic Instruments with Genetic Algorithms
 | journal      = Journal of the Audio Engineering Society
 | volume       = 43 | issue = 11 | pages = 916&ndash;931
 | url          = http://www.aes.org/e-lib/browse.cfm?elib=7923
}}</ref> As a result, an efficient implementation of time-varying additive synthesis of harmonic tones can be accomplished by use of ''wavetable synthesis''.

====Group additive synthesis====
Group additive synthesis<ref>
 {{cite web      
 | author       = Julius O. Smith III
 | title        = Group Additive Synthesis
 | url          = https://ccrma.stanford.edu/~jos/sasp/Group_Additive_Synthesis.html 
 | publisher    = [[CCRMA]], Stanford University 
 | access-date   = 12 May 2011
 | archive-url   = https://web.archive.org/web/20110606200135/https://ccrma.stanford.edu/~jos/sasp/Group_Additive_Synthesis.html
 | archive-date  = 6 June 2011 | url-status= live}}</ref><ref>
{{cite journal  
 | author       = P. Kleczkowski
 | title        = Group additive synthesis
 | journal      = [[Computer Music Journal]]
 | volume       = 13 | issue = 1 | pages = 12&ndash;20
 | year         = 1989
  | doi=10.2307/3679851
| jstor       = 3679851
 }}</ref><ref>
{{cite book     
 | author       = B. Eaglestone and S. Oates
 | chapter      = Analytical tools for group additive synthesis
 | title        = Proceedings of the 1990 International Computer Music Conference, Glasgow
 | publisher    = Computer Music Association
 | year         = 1990
 | chapter-url          = http://quod.lib.umich.edu/cgi/p/pod/dod-idx?c=icmc;idno=bbp2372.1990.015
}}</ref> is a method to group partials into harmonic groups (having different fundamental frequencies) and synthesize each group separately with ''wavetable synthesis'' before mixing the results.

===Inverse FFT synthesis===

An inverse [[fast Fourier transform]] can be used to efficiently synthesize frequencies that evenly divide the transform period or "frame". By careful consideration of the [[Discrete Fourier transform|DFT]] frequency-domain representation it is also possible to efficiently synthesize sinusoids of arbitrary frequencies using a series of overlapping frames and the inverse [[fast Fourier transform]].<ref name="RodetDepalle_FFTm1">
{{cite journal    
 | last1        = Rodet | first1 = X.
 | last2        = Depalle | first2 = P.
 | year         = 1992
 | title        = Spectral Envelopes and Inverse FFT Synthesis
 | citeseerx    = 10.1.1.43.4818
 | journal         = Proceedings of the 93rd Audio Engineering Society Convention
}}
</ref>