TY - JOUR
T1 - Tilings of the Time-Frequency Plane
T2 - Construction of Arbitrary Orthogonal Bases and Fast Tiling Algorithms
AU - Herley, Cormac
AU - Kovacevic, Jelena
N1 - Funding Information:
Manuscript received September 8, 1992; revised June 8, 1993. The Guest Editor coordinating the review of this paper and approving it for publication was Dr. Pierre Duhamel. This work was supported in part by the National Science Foundation under Grants ECD-88-111 I1 and MIP-90-14189, and in part by the New York State Science and Technology Foundation's CAT. The authors were with the Department of Electrical Engineering and the Center for Telecommunications Research, Columbia University, New York, NY 10027-6699. C. Herley and J. Kovacevic are now with AT&T Bell Laboratories, Murray Hill, NJ 07974-0636. K. Ramchandran is now with the Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801. M. Vetterli is now with the Electrical Engineering and Computer Science Department, University of California at Berkeley, Berkeley. CA 94720. IEEE Log Number 9212171.
PY - 1993/12
Y1 - 1993/12
N2 - We 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. We 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. We 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-dis-tortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented.
AB - We 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. We 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. We 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-dis-tortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented.
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U2 - 10.1109/78.258078
DO - 10.1109/78.258078
M3 - Article
AN - SCOPUS:0027806249
SN - 1053-587X
VL - 41
SP - 3341
EP - 3359
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 12
ER -