By Mingsian R. Bai, Jeong?Guon Ih, Jacob Benesty(auth.)
Chapter 1 advent (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 useful 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 feedback and destiny views (pages 479–499):
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Additional info for Acoustic Array Systems: Theory, Implementation, and Application
Mathematically, pðxÞ ¼ Agðx; xs þ d=2Þ À Agðx; xs À d=2Þ Dgðx; xs Þ ¼ Ajdj ; jdj where d is the vector pointing from one monopole to another, gðx; xs Þ ¼ eÀjkr ; 4pr r ¼ jx À xs j is the free-space Green’s function defined previously. As jdj ! 9 Dipole and quadrupole sources. (a) Vector definition of a dipole, (b) dipole with d aligned with y-axis, (c) directivity pattern of the dipole source, (d) general structure of a quadrupole where rs and r denote the gradients evaluated at xs and x, respectively, D ¼ Ad is termed the dipole moment and er ¼ ðx À xs Þ=r.
Up form an ON basis for NðGH Þ Right singular vectors v1 ; v2 ; . . ; vr form an ON basis for RðGH Þ Right singular vectors vrþ1 ; vrþ2 ; . . ; vq form an ON basis for NðGÞ SVD finds application in many diverse areas of engineering problems. 1) when it has no exact solution and we wish to find an approximate solution that minimizes the error norm kp À Gqk. Let ( 1=s i for 1 i r þ S ii ¼ : ð3:13Þ 0 for r þ 1 i s We may define the pseudoinverse of G as Gþ ¼ VSþ UH ¼ s X i¼1 H s À1 i vi ui ; ð3:14Þ Theoretical Preliminaries of Array Signal Processing 37 It can be shown that the least-squares solution of q can be expressed as q ¼ Gþ p ¼ VSþ UH p ¼ r H X ui p vi : si i¼1 ð3:15Þ The solution obtained using SVD gives the optimal solution in least-squares sense for overdetermined and square problems (p3q), or the solution with minimum norm (energy) for underdetermined problems (p < q).
72 is one such example. Forward propagation per se is a convolution or mixing process, which tends to “smooth out” the field radiated by a complex source. The inverse of the forward problem seeks to recover the source details based on the already-smoothed data. It follows that inverse problems are generally ill-conditioned or ill-posed, to some extent. Ill-conditioning or the so-called ill-posedness will arise in one way or another in all inverse problems. This can be easily appreciated by matrix formalism.
Acoustic Array Systems: Theory, Implementation, and Application by Mingsian R. Bai, Jeong?Guon Ih, Jacob Benesty(auth.)