Real Time Basis Function Synthesis

Basis Functions and Genetic Algorithms

Time-varying harmonic spectra can be synthesized by summing the fixed spectra of several basis functions. In our algorithm, all the basis functions are phase locked; each one has its own amplitude envelope, but they all share the same frequency envelope. Our algorithm includes an efficient time-domain method for timbre morphing. The advantage of this synthesis technique over sinusoidal synthesis is that it requires much less processing power in real time; the disadvantage is that some timbres cannot be accurately synthesized. In particular, non-harmonic timbres will not be well suited to basis function synthesis.

The basis function synthesis is implemented in Symbolic Sound's Kyma environment. To prepare a Lemur file for real-time synthesis, you must export a Harmonic Envelopes file from Lemur, and then run a genetic algorithm on the Harmonic Envelopes file to search for the basis functions and envelopes.

Exporting Harmonic Envelopes Files

Prepare the analysis file by exporting a Harmonic Envelopes file from Lemur:

Use the mouse to select the track(s) which represent the fundamental of the Lemur file. If the file is non-harmonic, it will not be well suited to this technique.
Select the Label Tracks from the Edit menu and label the selected tracks "1."
Use Select Tracks By Threshold from the Select menu to select tracks which exceed the analysis threshold by some amount (try 6 dB). Tracks which barely exceed the threshold will not be selected.
Use Label Tracks from the Edit menu to label tracks with the nearest harmonic number.
Use Export from the File menu to export the Harmonic Envelope file.

Use Kyma's options to do the Genetic Search for basis functions and their envelopes.

Use Kyma's GASynthesis Sound Object for real-time synthesis and morphing.

More Information

For more information on genetic searches and basis function synthesis, please see:

Andrew Horner, James Beauchamp, and Lippold Haken, "Methods for Multiple Wavetable Synthesis of Musical Instrument Tones," Journal of the Audio Engineering Society, Vol. 41, No 5, pp. 336-356, May 1993.
Andrew Horner, James Beauchamp, and Lippold Haken, "Machine Tongues XVI: Genetic Algorithms and their Application to FM Matching Synthesis," Computer Music Journal, 17:4, pp. 17-29, Winter 1993.

For more information about a real-time timbre morphing technique, which differs from the techniques discussed in the above papers, please contact L-Haken@uiuc.edu.

For more information about using Lemur for Real Time Sinusoidal Synthesis see Haken 1992 and 1995.

For more information about Kyma, please contact symsound@shout.net.

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