The slantlet transform-a discrete wavelet transform of approximation order 2 with improved time-localization

The discrete wavelet transform is usually carried out by filter bank iteration; however, for a fixed approximation order, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper describes new orthogonal discrete wavelet transform with approximation order two and improved time-localization. It is not based on filter bank iteration; instead, new filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches two-thirds that of the corresponding functions obtained by filter bank iteration. The new basis retains the octave-band characteristic and leads cleanly to a DWT for finite-length signals. Closed-form expressions for the filters are given, an efficient implementation of the transform is described, and improvement in a denoising example is shown. The basis, being piecewise linear, is reminiscent of the slant transform with which it is compared.