Source–filter model of speech production

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The source–filter model of speech production models speech as a combination of a sound source, such as the vocal cords, and a linear acoustic filter, the vocal tract (and radiation characteristic). An important assumption that is often made in the use of the source-filter model is the independence of source and filter. In such cases, the model should more accurately be referred to as the "independent source-filter model".

While only an approximation, the model is widely used in a number of applications because of its relative simplicity. To varying degrees, different phonemes can be distinguished by the properties of their source(s) and their spectral shape. Voiced sounds (e.g., vowels) have (at least) a source due to (mostly) periodic glottal excitation, which can be approximated by an impulse train in the time domain and by harmonics in the frequency domain, and a filter that depends on, e.g., tongue position and lip protrusion. On the other hand, fricatives have (at least) a source due to turbulent noise produced at a constriction in the oral cavity (e.g., the sounds represented orthographically by "s" and "f"). So called voiced fricatives (such as "z" and "v") have two sources - one at the glottis and one at the supra-glottal constriction.

The source-filter model is used in both speech synthesis and speech analysis, and is related to linear prediction. The development of the model is due, in large part, to the early work of Gunnar Fant, although others, notably Ken Stevens, have also contributed substantially to the models underlying acoustic analysis of speech and speech synthesis.

In implementation of the source-filter model of speech production, the sound source, or excitation signal, is often modelled as a periodic impulse train, for voiced speech, or white noise for unvoiced speech. The vocal tract filter is, in the simplest case, approximated by an all-pole filter, where the coefficients are obtained by performing linear prediction to minimize the mean-squared error in the speech signal to be reproduced. Convolution of the excitation signal with the filter response then produces the synthesised speech.

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