Resonance formants

Speech spectra have important features called formants which are the three five gross peaks in the spectral shape located between 200 and 4000 Hz. These correspond to the resonances of the acoustic tube of the vocal tract. We will discuss formants further in Chapter 8 (Subtractive Synthesis). For now, we will note that the formant locations for the ahh vowel are radically different from those for the eee vowel, even though the harmonic spacing (and thus, the perceived pitch) is the same for the two vowels. We know this, because a singer can sing the same pitch on many vowels (different spectral shapes, but same harmonic spacings), or the same vowel on many pitches (same spectral shape and formant locations, but different harmonic spacings). 

In a source/filter vocal model such as LPC or parallel/cascade formant synthesis, periodic impulses are used to excite resonant filters to produce vowels. We could construct a simple alternative model using three, four, or more tables storing the impulse responses of the individual vowel formants. Note that it isn t necessary for the tables to contain pure exponentially decaying sinusoids. We could include aspects of the voice source, etc., as long as those effects are periodic. FOFs (originally introduced as Formant Onde Functions in French, translates to Formant Wave Functions in English) were created for... 

Resonate Four formants excited by noise/pulse... 

An amplification caused by a filter is called a resonance, and in speech these resonances are known as formants. The frequencies at which resonances occur are determined solely by the position of the vocal tract they are independent of the glottis. So no matter how the harmonics are spaced, for a certain vocal tract position the resonances will always occur at the same frequencies. Different mouth shapes give rise to different patterns of formants, and in this way, the production mechanisms of height and loudness give rise to different characteristic acoustic patterns. As each vowel has a different vocal tract shape, it will have different formant pattern, and it is these that the listener uses as the main cue to vowel identity. The relationship between mouth shapes and formant patterns is complicated, and is fully examined in Chapter 11. 

Other speech sounds have characteristic spectrogram patterns also. Nasals are generally weak and have a wide formant at around about 300Hz, caused by resonance in the nasal cavity. As the nasal cavity is fixed, the resonance will always occur at the same position. Each nasal has... 

The resonances of the vocal tract are called formants, and these are thought to be the primary means by which listeners differentiate between different vowel sounds. 

This type of filter is commonly called a resonator because it accurately models the types of resonances commonly found in nature. The peak in the the frequeney response is known as a resonance because signals at or near that frequency will be amplified by the filter. For our purposes, it provides a good model of a single vocal tract formant. Resonances are normally described by three properties amplitude - the height of the peak, frequency - where the peak lies in the spectrum, and bandwidth - a measure of the width or sharpness of the peak. 

The first order filter creates a resonance pattern that already has a similar shape to a speech formant the main difference of course is that its resonant frequency is at zero on the frequency axis. The resonance can easily be shifted from d) = 0 by moving its pole off the real-axis, and this... 

Poles have an easy to imderstand interpretation, and in many cases, formant frequency and bandwidth can be directly related to pole values. By suitable choice of pole, a frequency response with appropriate resonances can usually be constructed. 

The backwards waves interfere with the forwards waves, so that they reinforce at certain frequencies. This causes resonances and hence creates formants. 

We know, Ifom Section 10.5.4, that such transfer functions naturally produce resonance patterns and hence formants. 

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. 

Beyond this the similarities between the formant s mthesiser and LP model start to diverge. Firstly, with the LP model, we use a single all-pole transfer function for all sounds. In the formant model, there are separate transfer functions in the formant synthesiser for the oral and nasal cavity. 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 to the coefficients. 

Other speech sounds have characteristic spectrogram patterns also. Nasals are generally weak and have a wide formant at about 300 Hz, which is caused by resonance in the nasal cavity. Since the nasal cavity is fixed, the resonance will always occur at the same position. Each nasal has its own oral-cavity shape, however, and the resonances in this are the main distinguishing feature between [m] and [n]. In stops, it is often possible to see the distinct phases of closure and the subsequent bmst. Although the differences are subtle, it is possible to tell one stop from another from the resonance patterns in the burst and in the immediately neighbouring vowel. Approximants look like weak vowels, which is what we would expect. 

Figure 12.14 shows spectral envelopes for a range of soimds. Here we can see a much-noted weakness of LP envelope estimation, which is that the spectrum can appear very peaky . This arises because, in many speech soimds, particularly vowels, the poles lie close to, but not on, the unit circle. At such locations, even a very small difference in their distance from the unit circle can result in much-sharper formant peaks. For example, for a sampling rate of 10 000 Hz, a pole with radius 0.96 will produce a formant bandwidth of 130 Hz, whereas a pole of 0.98 produces a formant of bandwidth 65 Hz, so any slight error in determining the radius of the pole can produce a spectrum with exaggerated formants. This problem does not occur with pole frequencies, so the LP envelope can normally be relied upon to find the positions of resonances quite accurately. 

Figure 13.3 The complete Klatt synthesiser. The boxes Rl, R2 etc. correspond to resonators generating formants. The A boxes control amplitudes at those points. The diagram shows both the serial and the parallel configurations of the formants.

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