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Wavelet Bases and Frames

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A Basis Theory Primer

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

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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.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Christopher Heil

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  1. Christopher Heil
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Correspondence to Christopher Heil .

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© 2011 Birkhäuser Boston

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Heil, C. (2011). Wavelet Bases and Frames. In: A Basis Theory Primer. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4687-5_12

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