Comparison with formant synthesis

With the series formant synthesiser, we saw that the transfer function for a single formant with specified frequency and bandwidth could be created by a second-order filter. 

Synthesis techniques based on vocal-tract models 

Recall tiiat Equation (13.18) is exactly the same as the LP equation (12.15), where A = [a, 02,. , Op] are the predictor coefficients and jc[n] is the error signal e[n]. This shows that the result of LP gives us the same type of transfer function as the serial formant synthesiser, and hence LP can produce exactly the same range of fi equency responses as the serial formant synthesiser. The sigitificance is of course tiiat we can derive the LP coefficients automatically from speech and don t have to perform manual or potentially errorful automatic formant analysis. This is not, however, a solution to the formant-estimation problem itself reversing the set of Equations (13.14)-(13.18) isnot trivial, meaning that, while we can accurately estimate the all-pole transfer function for arbitrary speech, we can t necessarily decompose this into individual formants. 

Beyond this the formant synthesiser and LP model start to diverge. Firstly, with the LP model, we use a single all-pole transfer function for aU sounds. In the formant model, there are separate transfer functions in the formant synthesiser for the oral and nasal cavities. In addition, a further separate resonator is used in formant synthesis to create a voiced source signal from the impulse train in the LP model the filter that does this is included in the all-pole filter. Hence the formant synthesiser is fundamentally more modular in that it separates these components. This lack of modularity in the LP model adds to the difficulty in providing physical interpretations for the coefficients. 

One of the commonalities with the formant model is that LP synthesis maintains a source-filter separation. This means that, for a sequence of frames, we can resynthesise this with a different fundamental frequency from that of the original. The benefit is that, for a given transition effect that we wish to synthesise, we need analyse only one example of it we can create the full range of fundamental-frequency effects by virtue of the separate control of the source. 

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