What is : Source-Filter Theory ??

[alm-alr]

Hi guys,
I need as clear as possible explanation  about Source- Filter theory and if this theory still predominating in phonetics or has it some 'errors" or alternative ??  .....what does it mean "linearity and independence  in this theory , "they say :source and the filter may be considered to be independent of each other  !!!! How can we explain the correlation "in case of voiced fricative consonant like 'z' or 'v'  or even unvoiced fricative like 's' and 'f' .....between the source -which is  always as i understand  ,the glottis-  and   vocal tract cavities filters , according to this theory ?
Thanks in advance !!

[jkpate]

Source-filter theory is a mathematical model for speech production. As with all models, it is incomplete, but very useful. It models glottal vibration as an arbitrary signal (but usually a harmonic train) that does not change over time, and the vocal tract as a linear filter that does not change over time. In a physical sense, we can understand the glottal vibration to be independent of the vocal tract shape because glottal tension can change without the vocal tract changing shape, and vice-versa. I'm not sure I understand your last couple of sentences with exclamation marks and ellipses, so let me know if this is not clear.

It is linear in that it assumes that the filter is a linear filter. A filter [latex]f[/latex] is linear if, for any two signals [latex]x[/latex] and [latex]x^\prime[/latex] and any scaling constant [latex]\lambda[/latex], we have [latex]f( x + x^\prime ) = f( x ) + f( x^\prime ) [/latex] and [latex]f(\lambda x) = \lambda f(x)[/latex]. Concretely, this means that the output of the vocal tract at each frequency is proportional to the input source: the vocal tract doesn't generate any acoustic energy itself.

We can see right away many ways in which the source-filter theory does not account for all of speech. The most obvious is that speech is not time-invariant, because we move our mouths frequently when we talk. Another is that the vocal tract does produce acoustic energy, with all that soggy meat sploshing around. But it is a very useful theory for what it was designed for: relating vocal fold vibration and vocal tract configuration to produced sounds over relatively short time scales, when they will be approximately invariant.

[alm-alr]

Thanks a lot for your reply,
still some points are unclear to me ,let me start with one point
Is it meant by independence of source and filter , that when I produce a consonant like "mmmmmm"' and put it aside as a spectrogram  ,then comparing this waveform  to the source glottal pronation ( or waveform)  i will  find no  correlation between them, or should i see  some common features between them , maybe( with respect to frequencies ) the Fundamental Frequency (F0) will  the only common between them ?

[jkpate]

"independence" here is meant in a mechanical sense, not in a statistical sense. For example, suppose we have a language with two lexical tones, high and low, and the lexicon just happens to have twice as many high tones as low tones on /i/ vowels, but half as many high tones as low tones on /u/ vowels. In a dataset of speech from such a language, there will be a statistical correlation between vowel frontness and f0. Source-filter theory does not attempt to account for these kinds of correlations. The mechanical sense of independence only means that the tongue, lips, velum, and jaw can move around without affecting glottal tension, and glottal tension can change without affecting the tongue, lips, velum, and jaw.