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Acoustic Array Systems: Theory, Implementation and Application Chapter 5. Nearfield Array Signal Processing Algorithms Acoustic Array Systems: Theory, Implementation and Application Chapter 5. Nearfield Array Signal Processing Algorithms 5. 1 Fourier NAH 5. 2 Basis Function Model (BFM)-based NAH 5. 3 BEM-based NAH (IBEM): Direct and Indirect Formulations 5. 4 Equivalent Source Model (ESM)-based NAH 5. 5 Comparison of the Nearfield Algorithms Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 1

5. 1 Fourier NAH Acoustic Array Systems: Theory, Implementation and Application, First Edition. 5. 1 Fourier NAH Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 2

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 3

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 4

5. 2 Basis Function Model (BFM)-based NAH Acoustic Array Systems: Theory, Implementation and 5. 2 Basis Function Model (BFM)-based NAH Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 5

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 6

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 7

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 8

5. 3 BEM-based NAH (IBEM): Direct and Indirect Formulations Acoustic Array Systems: Theory, 5. 3 BEM-based NAH (IBEM): Direct and Indirect Formulations Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 9

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 10

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 11

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 12

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 13

5. 4 Equivalent Source Model (ESM)-based NAH Acoustic Array Systems: Theory, Implementation and 5. 4 Equivalent Source Model (ESM)-based NAH Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 14

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 15

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 16

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 17

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 18

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 19

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 20

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 21

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 22

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 23

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 24

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 25

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 26

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 27

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 28

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 29

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 30

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 31

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 32

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 33

Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih Acoustic Array Systems: Theory, Implementation and Application, First Edition. Mingsian R. Bai, Jeong-Guan Ih and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 34