Chapter 1

Fourier Transforms & Special Functions

1.1 Introduction

At the heart of Fourier acoustics is the Fourier transform which includes the concepts of the Fourier series and the Hankel transform. We present in this chapter much of the prerequisite mathematics needed to understand the concepts presented in this book. Special functions, like the Dirac delta function are crucial and provide an elegant shorthand in the mathematics. The rectangle and comb functions are invaluable in understanding the formulation of nearfield acoustical holography, especially in regard to discretization of the formulation for coding on a computer. Essential in this discretization is the relationship between the DFT (discrete Fourier transform) and the integral ...

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