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Acoustic Array Systems: T heory, Implementation an d Application Chapter 3. Theoretical Preliminaries

of Array Signal 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 3.1

Linear Algebra Basics 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 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 and Jacob Benesty.

c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 4 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 3.2 Digital Signal Processing Basi cs

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 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 and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd.

8 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 and Jacob Benesty. c 2013 John Wiley & Sons Singapore Pte. Ltd. Published 2013 by John Wiley & Sons Singapore Pte. Ltd. 1 0 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 1 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 2 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 3 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

4 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

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 6

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 7 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 8 3.3

Array Signal Processing Basic s 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 9 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

0 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 1

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 2

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 3 3.4

Optimization 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. 2

4 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 5

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 6

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 7 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 8 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 9 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 0 3.5 Inverse Filtering from a Model Matching Perspective

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 1

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 2 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 3

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