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Wavelet Bases and Frames

  • Christopher Heil
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

The Gabor systems that we studied in the preceding chapter are generated from time-frequency shifts of a single function. A time-frequency shift is a composition of the two simple operations of translation and modulation. Wavelets are likewise generated by two simple operations, this time translation and dilation. A composition of translation and dilation is called a time-scale shift (see the illustration in Figure 12.1), and so a wavelet system is a collection of time-scale shifts of a single function.

Keywords

Orthonormal Basis Scaling Function Wavelet Base Wavelet Frame Gabor Frame 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 2011

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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