By Mingsian R. Bai, Jeong?Guon Ih, Jacob Benesty(auth.)
Chapter 1 creation (pages 1–7):
Chapter 2 Theoretical Preliminaries of Acoustics (pages 9–32):
Chapter three Theoretical Preliminaries of Array sign Processing (pages 33–94):
Chapter four Farfield Array sign Processing Algorithms (pages 95–150):
Chapter five Nearfield Array sign Processing Algorithms (pages 151–209):
Chapter 6 functional Implementation (pages 211–285):
Chapter 7 Time?Domain MVDR Array clear out for Speech Enhancement (pages 287–314):
Chapter eight Frequency?Domain Array Beamformers for Noise relief (pages 315–344):
Chapter nine program Examples (pages 345–477):
Chapter 10 Concluding comments and destiny views (pages 479–499):
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Additional resources for Acoustic Array Systems: Theory, Implementation, and Application
On the other hand, the unitary matrix V consists of ON right singular vectors, that is, V ¼ ðv1 v2 . . vq Þ, VH V ¼ VVH ¼ IV . Specifically, 2 s1 0 Á Á Á 0 32 vH 1 3 76 7 6 7 6 0 s 2 Á Á Á 0 76 vH s 76 2 7 X 6 76 7 ¼ G ¼ USVH ¼ ½u1 u2 . . us 6 s i ui vH i : 76 . 7 6 .. 76 .. 7 6. i¼1 } 0 54 5 4 0 0 0 ss ð3:10Þ vH s It follows from this decomposition that the linear transformation represented by G can be regarded as a norm-preserving rotation (V), then scaling (S), and another norm-preserving rotation (U).
4. Courant, R. and Hilbert, D. (1953) Methods of Mathematical Physics, Intersciense Publishers, New York. 5. , and Harris, F. (2005) Mathematical Methods for Physicists, Academic Press, Amsterdam. 6. Abramowitz, M. A. (1965) Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover, Mineola, NY. 7. M. and Feshbach, H. (1953) Methods of Theoretical Physics, McGraw-Hill, Columbus, OH. 8. D. (1953) Foundations of Potential Theory, Dover, Mineola, NY. 9. K. (1994) The Boundary Element Methods in Engineering, McGraw-Hill, Columbus, OH.
The method is based on minimization of the following cost function: J ¼ kp À Gqk22 þ kWqk22 ; ð3:19Þ Acoustic Array Systems 38 where W is a weighting matrix and k k2 denotes vector 2-. Expand J as À Á J ¼ pH À qH GH ðp À GqÞ þ qH WH Wq À Á ¼ pH p À qH GH p À pH Gq þ qH GH G þ WH W q: The minimum of this quadratic form can be found by taking the gradient of the cost function: À Á rq J ¼ À2GH p þ 2 GH G þ WH W q ¼ 0 À H Á À1 ^ ¼ G G þ WH W GH p: )q ð3:20Þ A simple choice of the weighting matrix is W ¼ bI, which results in À ÁÀ1 ^ ¼ GH G þ b2 I GH p: q ð3:21Þ Therefore, the parameter b enables us to regularize the inverse process between two extremes of unregularized inverse (b ¼ 0) and fully regularized inverse (b !
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