Wavevector-frequency analysis with applications to acoustics

Abstract : The first chapter is introductory, and includes a brief history of the subject. Chapter 2 defines and interprets the parameters that describe harmonic waves, and illustrates how an arbitrary wave field is described in terms of these parameters. The third chapter introduces linear systems and their classifications. The fourth chapter describes the wavevector-frequency characteristics of space-varying, but time-invariant, linear systems, and the fifth chapter treats those characteristics of coupled linear systems. This monograph presents an approach to the description and analysis of acoustic fields and systems that parallels the approach developed in signal processing and linear systems theories to describe and analyze electrical and communications signals and systems. Wavevector-frequency analysis is simply the description of a space-time field or system in terms of the Fourier conjugates of the independent spatial and temporal variables of the field or system. The wavevector is the Fourier conjugate of the spatial vector variable and the frequency is the conjugate of the time variable. The primary advantage of expressing the acoustic field in terms of wavevector and frequency, rather than space and time, is that the Fourier transformation often simplifies the mathematical description of the field or acoustic system, thereby facilitating mathematical analysis and physical interpretation.