Editing Additive synthesis (section)

===Time-dependent amplitudes===
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| [[File:Harmonic additive synthesis spectrum.png|280px]]
| <span style="font-size:85%;line-height:130%;">Example of harmonic additive synthesis in which each harmonic has a time-dependent amplitude. The fundamental frequency is 440&nbsp;Hz.</span>
[[File:Harmonic additive synthesis.ogg|noicon|150px]]
<span style="font-size:70%;line-height:130%;font-style:italic;">Problems listening to this file? See [[Media help]]</span>
|}
More generally, the amplitude of each harmonic can be prescribed as a function of time, <math>r_k(t)</math>, in which case the synthesis output is

{{NumBlk|:|<math>y(t) = \sum_{k=1}^{K} r_k(t) \cos\left(2 \pi k f_0 t + \phi_k \right)</math>.|{{EquationRef|2}}}}

Each [[Envelope (waves)|envelope]] <math>r_k(t)\,</math> should vary slowly relative to the frequency spacing between adjacent sinusoids.  The [[bandwidth (signal processing)|bandwidth]] of <math>r_k(t)</math> should be significantly less than <math>f_0</math>.