Sinusoidal models techniques

The family of techniques known as sinusoidal models use this as their basic building block and performs speech modification by finding the sinusoidal components for a waveform and performing modification by altering the parameters of the above equation, namely the amplitudes, phases and frequencies. It has some advantages over models such as TD-PSOLA in is that it allows adjustments in the frequency domain. While frequency domain adjustments are possible in the linear prediction techniques, the sinusoidal techniques facilitate this with far fewer assumptions about the nature of the signal and in particular don t assume a source and all-pole filter model. 

Given the parameters of the model, we can reconstruct a time domain waveform for each frame by use of the synthesis Equation 14.3. Figure 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 conjunction with sinusoidal models). 

MBROLA is a PSOLA like technique which uses sinusoidal modelling to decompose each frame and from this resynthesise the database at a constant pitch and phase, thus alleviating many problems in inaccurate epoch detection. 

While in second-generation synthesis signal processing is used mainly to modify pitch and timing, it can also be used in concatenation. If we are using a technique tiiat gives us some sort of spectral representation, such as residual-excited LP or sinusoidal modelling, then we can smooth or interpolate the spectral parameters at the join. This is possible only in models with a spectral representation, and is one of the reasons why residual-excited LP and sinusoidal models are chosen over PSOLA. 

Spectral modelling techniques are the legacy of the Fourier analysis theory. Originally developed in the nineteenth century, Fourier analysis considers that a pitched sound is made up of various sinusoidal components, where the frequencies of higher components are integral multiples of the frequency of the lowest component. The pitch of a musical note is then assumed to be determined by the lowest component, normally referred to as the fundamental frequency. In this case, timbre is the result of the presence of specific components and their relative amplitudes, as if it were the result of a chord over a prominently loud fundamental with notes played at different volumes. Despite the fact that not all interesting musical sounds have a clear pitch and the pitch of a sound may not necessarily correspond to the lower component of its spectrum, Fourier analysis still constitutes one of the pillars of acoustics and music. 

We can illustrate this latter technique with the simple thermokinetic model with the Arrhenius temperature dependence discussed above. This will also allow us to see that the two approaches are not separate, but that oscillations change smoothly from the basically sinusoidal waveform at the Hopf bifurcation to the relaxation form in other parts of the parameter plane. 

As an alternative to the chromatographic pulse technique a method based on a steady-state sinusoidal varying input concentration can be used. This method, first proposed by Deisler and Wilhelm [26], is an improvement over pulse input chromatography in certain systems because simpler, less accurate measurements are required and the modeling process is mathematically less complicated [27]. 

Equation (20) was also used to compute the acoustic response of fluid cylinders immersed in water and insonified normal to their axis with a sinusoidal wavepacket. The examples shown here can be considered by other techniques ( 5 ) but serve as appropriate tests for the accuracy of the model which can then be used to compute the acoustic responses of systems which cannot be readily treated by other methods. The material properties of the cylinder are shown in Table 1 and were chosen to enable the calculated echo structure of the cylinders to be compared with previously published analytical work ( 5 ). ... 

Informed by the technique of sines plus noise spectral modeling, we can now improve our sinusoidal additive synthesis model significantly by simply adding a filtered noise source as shown in Figure 6.13. 

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