Bases for time-frequency analysis
Birkhäuser Boston eBooks · 2007
In the first part of this chapter we construct various bases having good time-frequency localization. The construction of wavelet packets, for example, is presented in Section 4.3. Wavelets are, at least metaphorically, localized in the upper time-frequency plane on rectangles whose heights are inversely proportional to the lengths of their time intervals. Wavelet packets arise when a pair of wavelets living on adjacent time intervals is replaced by a pair of packets whose time interval is the union of the wavelet time intervals and whose frequency intervals are the lower and upper halves of the wavelet frequency intervals. Further wavelet packets can be obtained by repeating this type of recombination. When suitably defined, such packets give rise to a general class of basis functions associated with certain rectangles in the plane. 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.