Vocal-tract filter

We have informally observed that the vocal tract filter acts as a resonator that is, it amplifies certain fi equencies and attenuates others. How does this behaviour arise ... 

That said formant s5mthesis does share much in common with the all-pole vocal tract model. As with the tube model, the formant synthesiser is modular with respect to the source and vocal tract filter. The oral cavity component is formed from the connection of between 3 and 6 individual formant resonators in series, as predicted by the vocal tract model, and each formant resonator is a second order filter of the t5q)c discussed in Section 10.5.3. 

MFCC synthesis is a technique which attempts to S3mthesise from a representation that we use because of its statistical modelling properties. A completely accurate S3mthesis from this is not possible, but it is possible to perform fairly accurate vocal tract filter reconstruction. Basic techniques use an impulse/noise excitation method, while more advanced techniques attempt a complex parameterisation of the source. 

At integer multiples of the fundamental frequency we have the harmonics. Speech with a low fundamental frequency (say 100 Hz) will have closely spaced harmonics (occurring at 200 Hz, 300 Hz, 400 Hz,...), whereas speech with a higher fundamental frequency (e g. 200 Hz) will have widely spaced harmonics (400 Hz, 600 Hz, 800 Hz etc.). The tongue, jaw and tip positions create differently shaped cavities, the effect of which is to amplify certain harmoiucs while attenuating others. This gives some clue as to why we call this a vocal-tract filter here the vocal tract filters the harmonics by changing the amplitude of each harmonic. 

The above demonstrates some of the fundamental properties of travelling waves. First, note that some of the behaviour is determined by the motion of the hand, while some is determined by the properties of the rope itself For example, the fiequency of the waves is determined purely by the rate of movement of the hand the rope itself has no influence on this at all. In contrast, the rate at which the wave travels along the rope is not influenced by the hand at all no matter how quickly or slowly the hand moves, the wave always travels at the same speed, and this speed is determined by the properties of the rope. This shows why it is appropriate to use the theory of signals and filters where an initial source (the wave created by the moving hand) has its behaviour modified 1 a filter (the rope). Furthermore, we should also clearly see the parallels between this and the behaviour of the glottis source and vocal-tract filter in speech production. 

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