Editing Additive synthesis (section)

==Additive analysis/resynthesis==
[[Image:Sinusoidal Analysis & Synthesis (McAulay-Quatieri 1988).svg|thumb|350px|Sinusoidal analysis/synthesis system for Sinusoidal Modeling (based on {{harvnb|McAulay|Quatieri|1988|p=161}})<ref name=MQ1988>{{cite journal
 |last1        = McAulay
 |first1       = R. J.
 |last2        = Quatieri
 |first2       = T. F.
 |author-link2  = Thomas F. Quatieri
 |year         = 1988
 |title        = Speech Processing Based on a Sinusoidal Model
 |url          = http://www.ll.mit.edu/publications/journal/pdf/vol01_no2/1.2.3.speechprocessing.pdf
 |journal      = The Lincoln Laboratory Journal
 |volume       = 1
 |issue        = 2
 |pages        = 153&ndash;167
 |access-date  = 9 December 2013
 |archive-url  = https://web.archive.org/web/20120521071601/http://www.ll.mit.edu/publications/journal/pdf/vol01_no2/1.2.3.speechprocessing.pdf
 |archive-date = 21 May 2012
 |df           = dmy-all
}}</ref>]]

It is possible to analyze the frequency components of a recorded sound giving a "sum of sinusoids" representation. This representation can be re-synthesized using additive synthesis. One method of decomposing a sound into time varying sinusoidal partials is [[short-time Fourier transform|short-time Fourier transform (STFT)]]-based McAulay-[[Thomas F. Quatieri|Quatieri]] Analysis.<ref name=MQ1986>
{{cite journal    
 | last1        = McAulay | first1 = R. J.
 | last2        = Quatieri| first2 = T. F.
 | date         = Aug 1986
 | title        = Speech analysis/synthesis based on a sinusoidal representation
 | journal      =  IEEE Transactions on Acoustics, Speech, and Signal Processing
 | volume = 34 | issue = 4 | pages        = 744–754
| doi = 10.1109/TASSP.1986.1164910 }}</ref><ref>
{{cite web      
 | title        = McAulay-Quatieri Method
 | url          = http://www.clear.rice.edu/elec301/Projects02/lorisFor/mqmethod2.html
}}</ref>

By modifying the sum of sinusoids representation, timbral alterations can be made prior to resynthesis. For example, a harmonic sound could be restructured to sound inharmonic, and vice versa. Sound hybridisation or "morphing" has been implemented by additive resynthesis.<ref name="XSerraPhD">
{{cite thesis   
 | degree       = PhD
 | last         = Serra | first = Xavier
 | date         = 1989
 | title        = A System for Sound Analysis/Transformation/Synthesis based on a Deterministic plus Stochastic Decomposition
 | url          = http://mtg.upf.edu/node/304
 | publisher    = Stanford University
 | access-date   = 13 January 2012
}}</ref>

Additive analysis/resynthesis has been employed in a number of techniques including Sinusoidal Modelling,<ref>
{{cite web      
 | last1        = Smith III | first1 = Julius O.
 | last2        = Serra     | first2 = Xavier
 | title        = PARSHL: An Analysis/Synthesis Program for Non-Harmonic Sounds Based on a Sinusoidal Representation
 | url          = https://ccrma.stanford.edu/~jos/parshl/Additive_Synthesis.html
 | access-date   = 9 January 2012
}}</ref> [[Spectral modeling synthesis|Spectral Modelling Synthesis]] (SMS),<ref name="XSerraPhD"/> and the Reassigned Bandwidth-Enhanced Additive Sound Model.<ref>
{{cite thesis   
 | degree       = PhD
 | last         = Fitz | first = Kelly
 | date         = 1999
 | title        = The Reassigned Bandwidth-Enhanced Method of Additive Synthesis
 | publisher    = Dept. of Electrical and Computer Engineering, University of Illinois Urbana-Champaign
 | citeseerx    = 10.1.1.10.1130
}}</ref> Software that implements additive analysis/resynthesis includes: SPEAR,<ref>[http://www.klingbeil.com/spear/ SPEAR Sinusoidal Partial Editing Analysis and Resynthesis for Mac OS X, MacOS 9 and Windows]</ref> LEMUR, LORIS,<ref>{{Cite web |url=http://www.hakenaudio.com/Loris/ |title=Loris Software for Sound Modeling, Morphing, and Manipulation |access-date=13 January 2012 |archive-url=https://web.archive.org/web/20120730195624/http://www.hakenaudio.com/Loris/ |archive-date=30 July 2012 |df=dmy-all }}</ref> SMSTools,<ref>[http://mtg.upf.edu/technologies/sms SMSTools application for Windows]</ref> ARSS.<ref>[http://arss.sourceforge.net/ ARSS: The Analysis & Resynthesis Sound Spectrograph]</ref>

===Products===
{{multiple image |direction=vertical |align=right |width=165
 | header   = Additive re-synthesis using timbre-frame concatenation:
 | image1   = Wavesequence.svg
 | caption1 = Concatenation with crossfades (on Synclavier)
 | image2   = Vocaloid's phonemes crossfading - en.jpg
 | caption2 = Concatenation with spectral envelope interpolation (on Vocaloid)
}}

New England Digital [[Synclavier]] had a resynthesis feature where samples could be analyzed and converted into "timbre frames" which were part of its additive synthesis engine. [[Technos acxel]], launched in 1987, utilized the additive analysis/resynthesis model, in an [[Additive synthesis#Inverse FFT synthesis|FFT]] implementation.

Also a vocal synthesizer, [[Vocaloid]] have been implemented on the basis of additive analysis/resynthesis: its spectral voice model called [[Excitation plus Resonances]] (EpR) model<ref name=BonadaICMC01>
{{cite journal    
 | last1        = Bonada | first1 = J.
 | last2        = Celma  | first2 = O.
 | last3        = Loscos | first3 = A.
 | last4        = Ortola | first4 = J.|first5=X. |last5=Serra |first6=Y. |last6=Yoshioka |first7=H. |last7=Kayama |first8=Y. |last8=Hisaminato |first9=H. |last9=Kenmochi
 | year         = 2001
 | title        = Singing voice synthesis combining Excitation plus Resonance and Sinusoidal plus Residual Models
 | periodical   = Proc. Of ICMC
 | citeseerx    = 10.1.1.18.6258
}} ([http://mtg.upf.edu/files/publications/icmc2001-celma.pdf PDF])</ref><ref>
{{cite thesis   
 | degree       = PhD
 | last         = Loscos | first = A.
 | year         = 2007
 | title        = Spectral processing of the singing voice
 | location     = Barcelona, Spain
 | publisher    = Pompeu Fabra University
| hdl= 10803/7542
 }} ([http://www.tdx.cat/bitstream/handle/10803/7542/talm.pdf?sequence=1 PDF]).<br/>
See "''<!-- 2.4.2.5 -->Excitation plus resonances voice model''" (p. 51)
</ref> is extended based on Spectral Modeling Synthesis (SMS),
and its [[Diphone synthesis|diphone]] [[concatenative synthesis]] is processed using
''spectral peak processing'' (SPP)<ref>{{harvnb|Loscos|2007|p=44}}, "''<!-- 2.4.2.2 -->Spectral peak processing"''</ref> technique similar to modified [[phase-locked vocoder]]<ref>{{harvnb|Loscos|2007|p=44}}, "''<!-- 2.4.2.1.2 -->Phase locked vocoder''"</ref> (an improved [[phase vocoder]] for formant processing).<ref name=BonadaSMAC03>
{{cite journal    
 | last1        = Bonada | first1 = Jordi
 | last2        = Loscos | first2 = Alex
 | year         = 2003
 | title        = Sample-based singing voice synthesizer by spectral concatenation: 6. Concatenating Samples
 | url          = http://mtg.upf.edu/node/322
 | periodical   = Proc. of <!-- the Stockholm Music Acoustics Conference --> SMAC 03
 | pages        = 439&ndash;442
}}</ref> Using these techniques, spectral components (''[[formant]]s'') consisting of purely harmonic partials can be appropriately transformed into desired form for sound modeling, and sequence of short samples (''diphones'' or ''[[phoneme]]s'') constituting desired phrase, can be smoothly connected by interpolating matched partials and formant peaks, respectively, in the inserted transition region between different samples. (See also [[Dynamic timbres]])