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 aid (pages 315–344):
Chapter nine program Examples (pages 345–477):
Chapter 10 Concluding comments and destiny views (pages 479–499):
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Extra resources for Acoustic Array Systems: Theory, Implementation, and Application
N ð2:44Þ where Pm n ðcos uÞ is the associated Legendre functions of order m and degree n. Spherical harmonics, as functions of the azimuth angle u and the zenith angle f, are frequently encountered in separation of variables of the wave equation in spherical coordinates. The condition that U is finite on the sphere Acoustic Array Systems 18 requires that n is an integer, Àn m n. Therefore, there are 2n þ 1 values corresponding to the order m for each degree n. The spherical harmonics satisfy the following orthonormality condition ð m0 Ã ð2:45Þ Ym n ðu; fÞY n0 ðu; fÞ dV ¼ dnn0 dmm0 ; where Ã denotes the complex conjugate, dV sin ududf, 0 pleteness condition 1 n X X Ã m 0 0 Ym n ðu; fÞY n ðu ; f Þ ¼ n¼0 m¼Àn u p and 0 f 2p and the com- 1 dðu À u0 Þdðf À f0 Þ; sin u ð2:46Þ for azimuth angles u and u0 and zenith angles f and f0 .
2VN . In this case, it is possible to perfectly reconstruct the continuous-time signal by using an ideal low-pass filter with cutoff frequency Vs =2. More precisely, let xc ðtÞ be continuous and band-limited signal with X c ðjVÞ ¼ 0 for jVj ! VN ; ð3:42Þ where VN is the cutoff frequency, also referred to as the Nyquist frequency. xc ðtÞ is uniquely determined by its samples x½n ¼ xc ðnT Þ if Vs ¼ 2p ! 2VN ; T ð3:43Þ where Vs is the sampling frequency and T is the sampling period. Linear time-invariant (LTI) systems are completely characterized by their impulse response function (IRF) h½n defined as the output of the system subject to a unit pulse input d½n.
0 with singular values s 1 ! s 2 ! Á Á Á ! s s ; where s ¼ minfp; qg: The singular values and the singular vectors can be shown to be the positive square roots and the corresponding eigenvectors of the eigenvalue problems, GGH u ¼ lu and GH Gv ¼ lv, respectively. The unitary matrix U consists of orthonormal (ON) left singular vectors, that is, Acoustic Array Systems 36 U ¼ ðu1 u2 . . up Þ; UH U ¼ UUH ¼ IU . On the other hand, the unitary matrix V consists of ON right singular vectors, that is, V ¼ ðv1 v2 .
Acoustic Array Systems: Theory, Implementation, and Application by Mingsian R. Bai, Jeong?Guon Ih, Jacob Benesty(auth.)