Pure sinusoidal models

In principle we could perform Fourier analysis to find the model parameters, but, for reasons explained below, it is in fact advantageous to follow a different procedure that is geared towards our synthesis goals. For purposes of modifying pitch, it is useM to perform the analysis in a pitch-synchronous maimer and in fact one of the main advantages of sinusoidal modelling is that the accuracy of this does not have to be as high as that for PSOLA [293], [420], [519]. 

For a frame of speech, basic sinusoidal analysis can be found by a means similar to LP (Section 12.4), whereby we use the model to create an artificial signal i(n)  

We then attempt to find file set of values for 4/, coo and cpi and choose the best artificial signal as the one that has the lowest error between it and the original s n). So in the 

Given the parameters of the model, we can reconstruct a time-domain waveform for each frame by use of the synthesis equation (14.3). Figiue 14.6 shows a real and resynthesised frame of speech. An entire waveform can be resynthesised by overlapping and adding the frames just as with the PSOLA method (in fact the use of overlap-add techniques was first developed for conjimction with sinusoidal models). 

Modification is performed by separating the harmonics from the spectral envelope, but this is achieved in a way that doesn t perform explicit soiuce-filter separation as with LP analysis. The spectral envelope can be found by a number of niunerical techniques. For example, Kain [244] transforms the spectra into a power spectnun and then uses an inverse Fourier transform to find the time-domain autocorrelation function. The LP analysis is performed on this to give an all-pole representation of the spectral envelope. 

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Since the model is stable, all the roots of P(s), whether they be real or complex, have negative real parts and their corresponding time domain terms will decay away exponentially. Thus if we are only interested in the time domain response at sufficiently large times, we only need to consider the partial fraction expansion of the two purely sinusoidal terms associated with the input ... 

The notion that some components of soimds are well-modeled by sinusoids, while other components are better modeled by spectrally shaped noise, further motivates the residual-excited refinement to the purely sinusoidal additive synthesis model presented in Chapter 4 (Figure 4.4). Using the Fourier transform, we ean inspect the spectrum of a sound and determine whieh... 

Indeed, viscoelasticity has been observed and measured in diastole through both organ-level and molecular-based studies. For example, Templeton et al. [73] applied a sinusoidal volume variation to an isolated LV chamber and measured its viscoelastic response via the phase delay of the resulting pressure response. Additionally, Rankin et al. [51] found that to fit the diastatic stress-strain relationship, a viscoelastic, rather than purely elastic model is needed. Similar results have been reported by Hess et al. [23] in humans, and other investigators have observed viscoelastic chamber properties in a variety of experimental settings [14,30,44,69,80]. 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

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... 

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