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Algebra and Geometry of Wavelet Matrices

In: Wavelet Analysis

Author

Listed:
  • Howard L. Resnikoff

    (Future WAVE Inc.)

  • Raymond O. Wells Jr.

    (Rice University, Department of Mathematics)

Abstract

In this chapter, we introduce and study the properties of wavelet matrices. A wavelet matrix is a generalization of square orthogonal or unitary matrices to a larger class of rectangular matrices. Wavelet matrices correspond to the electrical engineer’s multirate digital filter banks, where each row in the matrix corresponds to one filter in the filter bank. Each wavelet matrix contains the basic information necessary to define an associated wavelet system, which will be studied in the next chapter. Many of the analytic properties of wavelet systems depend on the algebraic properties of wavelet matrices. In particular, the algebraically varying wavelet matrices form a parametrization of the corrresponding wavelet systems.

Suggested Citation

  • Howard L. Resnikoff & Raymond O. Wells Jr., 1998. "Algebra and Geometry of Wavelet Matrices," Springer Books, in: Wavelet Analysis, chapter 4, pages 39-85, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0593-7_4
    DOI: 10.1007/978-1-4612-0593-7_4
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