Formants in the Time Domain FOFs

In prior chapters we looked at subtractive synthesis techniques, such as modal synthesis (Chapter 4) and linear predictive coding (Chapter 8). In these methods a complex source is used to excite resonant fQters. The source usually has a flat spectnun, or exhibits a simple roll-off pattern like f or ip (6 dB or 12 dB per octave). The filters, possibly time-varying, shape the spectrum to model the desired sound. 

Figaie 13.3. Wavetable view of additive formant synthesis. 

In a source/filter vocal model such as LPC or parallel/cascade formant synthesis, periodic impulses are used to excite resonant filters to produce vowels. We could construct a simple alternative model using three, four, or more tables storing the impulse responses of the individual vowel formants. Note that it isn t necessary for the tables to contain pure exponentially decaying sinusoids. We could include aspects of the voice source, etc., as long as those effects are periodic. FOFs (originally introduced as Formant Onde Functions in French, translates to Formant Wave Functions in English) were created for 

So you might now ask, is there a fast version of the wavelet transform, like the FFT allows us to compute the DFT rapidly In feet, there are a number of fest wavelet transform techniques that allow the subband decomposition to be accomplished in essentially Aflogj(Af) time just like the FFT. We won t get into that now, for there are lots of books about wavelets and wavelet transforms. Mostly what we re trying to do here is to develop the idea that bandlimited grains might motivate good soimd synthesis methods. 

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