Chapter 6: Timbre Vectors

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.