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 functional Implementation (pages 211–285):
Chapter 7 Time?Domain MVDR Array filter 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
Orthonomality results naturally from the Sturm– Liouville theory and is the heart of partial differential equations [4,5]. It is an important and useful property that frequently appears in the context of boundary value problems, eigenvalue problems, special functions, numerical analysis and computations, and so on, in many areas of mathematical physics. Solution processes of simultaneous equations can be simplified by taking advantage of the fact that the inner product in the function space of two orthogonal functions is zero.
It can be shown that the eigenvalues li ; i ¼ 1; 2; Á Á Á must be real and the associated eigenfunctions denoted by fi ðxÞ; i ¼ 1; 2; Á Á Á are orthogonal, provided the differential operator L in the eigenvalue problem LfðxÞ ¼ lfðxÞ is self-adjoint. It follows that any function UðxÞ satisfying the same boundary conditions as fi ðxÞ may be expanded in a series on the basis of fi ðxÞ UðxÞ ¼ 1 X i¼1 ai fi ðxÞ; ð2:38Þ Theoretical Preliminaries of Acoustics 17 where the coefficients ai signify the “contribution” of the function fi ðxÞ in the expansion and can be determined by the orthonomality condition.
Adapted from Oppenheim et al. 4. Let xc ðtÞ FT ! X c ð jVÞ DTFT x½n ! 4 Illustration of spectral aliasing due to sampling. ” Nyquist has shown that the sampling rate must exceed two-times the cutoff frequency VN of the continuous-time signal in order to prevent from aliasing, that is, Vs ! 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 !
Acoustic Array Systems: Theory, Implementation, and Application by Mingsian R. Bai, Jeong?Guon Ih, Jacob Benesty(auth.)