2.1 Speech Production
People are able to identify each other by listening to one another. Each person has a unique voice, but also a unique way of speaking that is not directly related to the actual quality of the voice. This is because speech is produced by a combination of the physiological traits and the learned characteristics such as intonation and language usage [17]. In the following we will examine the physiological aspects of speech production.
Figure 2.1: The human speech production mechanism, taken from [33]
Speech is produced by pushing air up from the lungs (see Figure 2.1) and through the 7
vocal cords (larynx), into the throat and the oral cavity to the lips. Sometimes the air ow is directed through the nasal cavity, too [33]. The vocal tract begins just after the vocal cords and ends at the input to the lips, see Figure 2.1. The nasal tract begins at the soft palate, or velum, which controls whether sounds are emitted through the oral cavity or the nasal cavity or both.
The air that is expelled from the lungs and pushed up through the trachea causes the vocal cords to vibrate. These resultant air pulses are the source of excitation of the vocal tract, and are often referred to as the glottal1 pulses. The nature of the air ow through the glottis denes whether the speech is voiced or unvoiced. Voiced speech is produced by tensing the vocal cords periodically, causing the vibration of the air ow that passes through them and thus resulting in glottal pulses that are quasi-periodic [2]. The vibra-tion rate of these glottal pulses is denoted as the fundamental frequency,F0. The value of F0 is dependent on the physical shape and positioning of the vocal cords. Voiced sounds that are produced by the periodic glottal pulses include all the vowels as well as the nasal consonants such as /m/ and /n/ [8].
The acoustic wave formed by the air ow from the lungs and past the glottis is altered by the resonances of the vocal tract and by the lip radiation. The vocal tract resonances depend on the length and shape of the throat and the position of the jaw, tongue and velum, ie. the physical attributes of the speaker. The vocal tract resonances are called formants [14]. The formant frequencies in voiced speech vary when dierent vowels are produced. This means that in voiced speech, the resulting waveform is not only dependent on the fundamental frequency, but also on the formant frequencies, where the former is a result of the physical attributes of the vocal cords and the latter a representation of the physical characteristics of the vocal tract.
When the vocal cords are relaxed and air is pushed through them, a constriction at some point along the vocal tract results in turbulence and the unvoiced sounds are pro-duced. In this case the sound can be modelled as a stochastic process such as white noise.
As the glottis does not vibrate to create these sounds, they do not contain fundamental frequency information though they do contain information pertaining to the vocal tract characteristics. The unvoiced sounds include virtually all consonants. One group of con-sonants that are produced in this way are the fricatives, produced by a turbulent ow of air which results in such sounds as 'sh' and 'f', while another group contains the stop consonants referred to as plosives, such as 'b' and 'p' [9].
2.2 Speech Modelling
The way that speech is modelled is often referred to as the source-lter model [2]. This is because the speech that is ultimately produced by the process that is described in Sec-tion 2.1 depends on two factors: The source characteristics of the speaker and the system characteristics. The system comprises of the vocal tract and lip radiation, i.e. physical attributes, while the source factors are the pulses produced by the air ow through the vocal cords and include such information as the fundamental frequency. The process by
1Glottis = vocal cords and the space between them
which the vocal tract causes changes to the glottal waveform can be modelled as a ltering of the source (glottal pulse) spectrum by the system (vocal tract) characteristics. This model is represented in Figure 2.2. The resulting speech signal thus has an output energy spectrum that is the product of the source function and the system transfer function. The source function is periodic in the time domain, and therefore has a discrete spectrum in the frequency domain [13]. This spectrum decreases with the square of the frequency, see Figure 2.2. The system lter function is approximately periodic and its peaks indicate the formant frequencies [2]. The resultant output spectrum has peaks that represent these formant frequencies formed by the vocal tract system characteristics. The vocal tract can be modelled as a cylindrical tube and it is the resonant frequencies of this tube that are the formants [39]. By changing the shape of such a tube, f.ex. by movement of the tongue, the positions of the resonant frequencies are shifted, thus allowing dierent sounds to be produced.
Figure 2.2: Source Spectrum, System Filter Function and Output Spectrum, taken from [11]
At the core of the source-system speech model is the fact that the source and lter spectra are independent of one another. The power of this model is therefore that it opens the possibility of separating the spectra and modelling just the lter function which can reliably be found in most speech segments, as will be discussed in Chapter 3. The complete speech production model is shown schematically in Figure 2.3.
The source-system model can be represented mathematically by referring to Figure 2.3.
In discrete time, we letu(n)represent the excitation signal, which can be the glottal wave-form or turbulence or both, depending on the sound being produced. For voiced speech, the excitation signal is quasi-periodic with fundamental period T0. (The corresponding rate of vibration is the fundamental frequency, F0 = T10). For unvoiced speech the excita-tion signal is modelled as noise [2]. The vocal tract is represented by the lter funcexcita-tion H(z)while the eect of lip radiation on the speech signal is denoted asR(z). In the time domain, this leads to the following simplied mathematical model for speech production:
s(n) = u(n)⊗h(n)⊗r(n) (2.1)
In the frequency domain, this can be written as:
S(z) = U(z)·H(z)·R(z) (2.2) U(z) is the excitation spectrum, H(z) is the vocal tract spectrum and the impedance caused by the lips is approximated by R(z) [1]. The transformation to the frequency
Speech
Glottal pulses at F0
White Noise
Vocal Tract Filter
Lip Radiation u(n)
H(z) R(z) s(n)
Figure 2.3: Source-Filter Model of Speech Production, adapted from [38]
domain is dened by the Fourier transform [13], given by:
X(z)≡
NX−1
n=0
x(n)z−n, z =ej2πN (2.3) By using the source-lter model we can derive several dierent types of features, either in the time domain or in the frequency domain. This means that for some features (such as those involving the fundamental frequency), it is possible to analyze the speech signal in the time domain, while it is necessary to transform the signal to the frequency domain in order to enable the extraction of other features, f.ex. the Mel-Frequency cepstral coecients. The choice of feature sets also depends on whether the aim is to model the excitation signal (the source) or the vocal tract lter (the system).