DocumentCode :
3795818
Title :
Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms
Author :
C. Herley;J. Kovacevic;K. Ramchandran;M. Vetterli
Author_Institution :
Dept. of Electr. Eng., Columbia Univ., New York, NY, USA
Volume :
41
Issue :
12
fYear :
1993
Firstpage :
3341
Lastpage :
3359
Abstract :
The authors consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. They show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. The method is based on the construction of boundary and transition filters; these allow us to construct essentially arbitrary tilings. Time-varying modulated lapped transforms are a special case, where both boundary and overlapping solutions are possible with filters obtained by modulation. They present a double-tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g., rate-distortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented.
Keywords :
"Time frequency analysis","Fourier transforms","Wavelet packets","Wavelet transforms","Filters","Tiles","Tree data structures","Cost function","Testing","Sampling methods"
Journal_Title :
IEEE Transactions on Signal Processing
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/78.258078
Filename :
258078
Link To Document :
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