Elements of Human Voice

The following sections are included:

• Dedication
• Preface
• Contents
• List of Figures
• List of Tables

Acoustic waves in air are the carrier of human voice. The production, transmission, and receiving of human voice follow the laws of acoustics. The theory of acoustic waves is a very mature branch of physics. There are excellent monographs and textbooks on this subject [63, 72]. In this Chapter, we will review the basic theory and facts of acoustic waves in air as the background information for the understanding of human voice.

The science of human voice production involves both physics and physiology. Human voice is produced by a group of human organs. There is a vast amount of literature about the anatomy and physiology of those organs. For a brief overview, see Sataloff’s Scientific American article The Human Voice [74]. More detail can be found in chapter 2 of Sundberg’s Science of the Singing Voice [92], and first four chapters of Titze’s Principles of Voice Production [95]. Even more detail can be found in Clinical Anatomy and Physiology of the Voice [75], a part of Sataloff’s Professional Voice [78]. In this chapter, we make a brief review of the anatomy and physiology of the voice organs as a background for the discussion of human voice production mechanism in the following two chapters.

In this chapter, we present basic experimental facts of human voice, collected by various instruments. Based on those facts, in Chapter 4, the physics of human voice production is expounded, which becomes the foundation of the mathematical representations of human voice in Part II.

In Chapter 3, the basic experimental facts of human voice are presented. In this Chapter, a theory is formulated to explain the experimental observations as completely as possible. The focus is vowels and voiced consonants, especially to explain voice waveforms with simultaneous EGG signals, videokymography information, and in vivo pressure measurements. The production of plosives and fricatives is relatively straightforward, which has been outlined in Section 2.3 in Chapter 2.

According to Part I, especially Chapter 4, voiced sound is a superposition of individual timbrons. Each timbron is triggered by a glottal closure, or for a small percentage of cases, by an incomplete glottal closure. Therefore, the problem of mathematical representation of voice is reduced to the mathematical representation of underlying timbrons. However, in most cases, a timbron starts before the previous timbrons disappear. A great majority of timbrons overlap with others. Consequently, the first step in parameterizing voice signals is to extract individual timbrons from a continuous flow of voice signal. In this chapter, various methods to extract individual timbrons in the voiced sections of speech signals are presented. Plosives can also be represented by the mathematical form of timbrons. The process of identifying and parameterizing plosives is then presented. Finally, the treatment of unvoiced sections, which is rather straightforward, is presented.

As we have presented in Chapter 5, for voiced sections of speech signals, the amplitude spectrum of each pitch period defines the underlying timbron. However, the amplitude spectrum is inconvenient and over-specified. For vowels, the features of the amplitude spectrum concentrate in the lowfrequency range, typically 0.3 kHz to 5 kHz. A high frequency resolution is required only in that frequency range. For fricatives, the amplitude spectrum is mostly in the high-frequency range, but the required frequency resolution is low. In this Chapter, we introduce a mathematical representation of the timbre spectrum, the timbre vector, which follows the human sensitivity of frequency. The timbre vector can be viewed as a vector of unit norm in a Hilbert space, resembling a state vector in quantum mechanics. Thus the mathematical tools in quantum mechanics can be applied.

In Chapter 6, we show that the amplitude spectrum of a timbron can be represented by a timbre vector, which contains a set of normalized Laguerre spectral coefficients, representing the instantaneous timber of the frame. Besides a timbre vector, the feature vector of a frame also contains the type of the frame (through the voicedness index), duration and intensity, constituting a complete mathematical representation of a frame.

Much of the speech and voice technology depends on some type of parameterization of speech and voice. Non-parametric methods, such as the pitchsynchronous overlap add technique (PSOLA) [9, 65, 66], which works in time domain, can only make very limited modifications to the natural speech, with applications confined in, for example, unit-selection TTS systems. To date, the most widely used parameterization methods are linear predictive coding (LPC) [58] and mel-frequency cepstral coefficients (MFCC) [24]. It is known that the vocoders based on LPC and MFCC can only produce reconstructed speech of rather poor quality, for example, see Chapter D24 of Springer Handbook of Speech Processing [6].

A good understanding of human voice production is the starting point of improving voice and developing algorithms for voice and speech technology. In Part I, a theory of human voice production is presented, which also serves as the scientific foundation of Part II, Mathematical Representations and the applications in speech and voice technology.

Through experiments, Michael Faraday found that electromagnetic phenomena are mediated by fields in the space, which can be visualized by using magnetic or electrical powders. James Clerk Maxwell, using partial differential equations (the mathematical tools for the theory of mechanics of continuous media) to represent the electrical and magnetic fields envisioned by Michael Faraday, resulted in a set of equations as the basis of electromagnetism as we know it.

The following sections are included:

• Appendix A: Kramers-Kronig Relations
• Appendix B: Laguerre Functions
• Bibliography
• Index