Expansions which give arbitrarily orthonormal tilings of the time-frequency plane are considered. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. It is shown how orthonormal tilings can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. One method is based on lapped orthogonal transforms, which makes it possible to change the number of channels in the transform. A second method is based on the construction of boundary filters and gives arbitrary tilings. An algorithm is presented which for a given signal decides on the best binary segmentation and which tree split to use for each segment. It is optimal in a rate-distortion sense. The results of experiments on test signals are presented.
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