Abstract
The complex discrete wavelet transform having perfect translation invariance has already been proposed. However, its frequency density is fixed by octave filter banks and its time density is fixed by constant intervals between wavelets. In this paper, a novel complex discrete wavelet transform based on perfect translation invariance is designed to create variable time-frequency density. This transform can divide an octave frequency band into an arbitrary number of filter banks, and its wavelets can be arrayed on the time base with variable intervals, and its frame forms perfect translation invariance.
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