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

   Christopher Heil

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Correspondence toChristopher Heil.

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