Author_Institution :
Dept. of Electr. Eng., Brooklyn Polytech., NY, USA
Abstract :
The discrete wavelet transform (DWT) is usually carried out by filter bank iteration, however, for a fixed number of zero moments, this does not yield a discrete-time basis that is optimal with respect to time-localization. This paper discusses the implementation and properties of an orthogonal DWT, with two zero moments and with improved time-localization. The basis is not based on filter bank iteration, instead different filters are used for each scale. For coarse scales, the support of the discrete-time basis functions approaches 2/3 that of the corresponding functions obtained by filter bank iteration. This slantlet basis is piecewise linear and retains the octave-band characteristic. Closed form expressions for the filters are given and improvement in a denoising example is shown. This basis, being piecewise linear, is reminiscent of the slant transform, to which it is compared
Keywords :
digital filters; discrete wavelet transforms; interference suppression; piecewise linear techniques; signal representation; closed form expressions; coarse scales; denoising example; discrete wavelet transform; discrete-time basis functions; filters; octave-band characteristic; orthogonal DWT; piecewise linear method; slantlet basis; slantlet transform; time-localization; zero moments; Bandwidth; Character generation; Discrete transforms; Discrete wavelet transforms; Filter bank; Noise reduction; Piecewise linear techniques; Signal design; Smoothing methods;
