Abstract The linear canonical transform (LCT) plays an important role in signal and image processing from both theoretical practical points of view. Various sampling representations for band-limited non-band-limited signals the LCT domain have been established. We focus this paper on derivative reconstruction, where reconstruction procedure utilizes samples its first derivative. Our major aim w...

The discrete wavelet transform (DWT) is usually carried out by filterbank 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 filterbank i...

This paper describes the implementation of a Quantized Discrete Transform algorithm (QDCT) for an H.26L test model. The QDCT is used for both MPEG and H.263 video coding [1]. The MPEG and H.263 coding are based on fractional 8x8 blocks. The new H.26L video standard uses a residue transform that is based on a 4x4 block and an integer transform. Several implementations of the QDCT are proposed in...

An exact, one-to-one transform is presented that not only allows digital circular convolutions, but is free from multiplications and quantisation errors for transform lengths of arbitrary powers of two. The transform is analogous to the Discrete Fourier Transform, with the canonical harmonics replaced by a set of cyclic integers computed using only bit-shifts and additions modulo a prime number...

Using the operational matrix of an orthogonal function to perform integration for solving, identifying and optimizing a linear dynamic system has several advantages: (1) the method is computer oriented, thus solving higher order differential equation becomes a matter of dimension increasing; (2) the solution is a multiresolution type; (3) the answer is convergent, even the size of increment is ...

This paper deals with the numerical continuation of invariant manifolds regardless of the restricted dynamics. Common examples of such manifolds include limit sets, codimension 1 manifolds separating basins of attraction (separatrices), stable/unstable/centre manifolds, nested hierarchies of attracting manifolds in dissipative systems and manifolds appearing in bifurcations. The approach is bas...

Prolate spheroidal wave functions (PSWFs) possess many remarkable properties. They are orthogonal basis of both square integrable space of finite interval and the Paley-Wiener space of bandlimited functions on the real line. No other system of classical orthogonal functions is known to obey this unique property. This raises the question of whether they possess these properties in Clifford analy...

The multirate digital signal processing (DSP) is required in digital system where more than one sampling rate is required. In this paper, we propose the two channel (2dimensional) perfect reconstruction multirate filter bank, which is based on the linear canonical transform. The main motivation is the fact that Linear Canonical Transform (LCT) provides a general mathematical tool with very broa...