The discrete Pascal transform and its applications

We introduce a new discrete polynomial transform constructed from the rows of Pascal’s triangle. The forward and inverse transforms are computed the same way in both the oneand two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in

A circuit-breaker restrike diagnostic algorithm using ATP and wavelet transforms

Circuit breaker restrikes are unwanted occurrence, which can ultimately lead to breaker. Before 2008, there was little evidence in the literature of monitoring techniques based on restrike measurement and interpretation produced during switching of capacitor banks and shunt reactor banks. In 2008 a non-intrusive radiometric restrike measurement method, as well a restrike hardware detection algorithm was developed. The limitations of the radiometric measurement method are a band limited frequency response as well as limitations in amplitude determination. Current detection methods and algorithms required the use of wide bandwidth current transformers and voltage dividers. A novel non-intrusive restrike diagnostic algorithm using ATP (Alternative Transient Program) and wavelet transforms is proposed. Wavelet transforms are the most common use in signal processing, which is divided into two tests, i.e. restrike detection and energy level based on deteriorated waveforms in different types of restrike. A ‘db5’ wavelet was selected in the tests as it gave a 97% correct diagnostic rate evaluated using a database of diagnostic signatures. This was also tested using restrike waveforms simulated under different network parameters which gave a 92% correct diagnostic responses. The diagnostic technique and methodology developed in this research can be applied to any power monitoring system with slight modification for restrike detection.

Frame-rate stereopsis using non-parametric transforms and programmable logic

A frame-rate stereo vision system, based on non-parametric matching metrics, is described. Traditional metrics, such as normalized cross-correlation, are expensive in terms of logic. Non-parametric measures require only simple, parallelizable, functions such as comparators, counters and exclusive-or, and are thus very well suited to implementation in reprogrammable logic.

Möbius transforms, coincident Boolean functions and non-coincidence property of Boolean functions

Boolean functions and their Möbius transforms are involved in logical calculation, digital communications, coding theory and modern cryptography. So far, little is known about the relations of Boolean functions and their Möbius transforms. This work is composed of three parts. In the first part, we present relations between a Boolean function and its Möbius transform so as to convert the truth table/algebraic normal form (ANF) to the ANF/truth table of a function in different conditions. In the second part, we focus on the special case when a Boolean function is identical to its Möbius transform. We call such functions coincident. In the third part, we generalize the concept of coincident functions and indicate that any Boolean function has the coincidence property even it is not coincident.

Simplified algorithms based on Haar transforms for signal recognition in protective relays

This letter presents the development of simplified algorithms based on Haar functions for signal extraction in relaying signals. These algorithms, being computationally simple, are better suited for microprocessor-based power system protection relaying. They provide accurate estimates of the signal amplitude and phase.

A cryptographic system based on finite field transforms

In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.

Block- and strand-multiplexing for fast computation of a class of transforms

The transforms dealt with in this paper are defined in terms of the transform kernels which are Kroneeker products of the two or more component kernels. The signal flow-graph for the computation of such a transform is obtained with the flow-graphs for the component transforms as building blocks.

Block Convolution Using Discrete Trigonometric Transforms and Discrete Fourier Transform

We derive expressions for convolution multiplication properties of discrete cosine transform II (DCT II) starting from equivalent discrete Fourier transform (DFT) representations. Using these expressions, a method for implementing linear filtering through block convolution in the DCT II domain is presented. For the case of nonsymmetric impulse response, additional discrete sine transform II (DST II) is required for implementing the filter in DCT II domain, where as for a symmetric impulse response, the additional transform is not required. Comparison with recently proposed circular convolution technique in DCT II domain shows that the proposed new method is computationally more efficient.

Application of D transforms in the analysis of nonlinear distributed parameter systems

The scope of application of Laplace transforms presently limited to the study of linear partial differential equations, is extended to the nonlinear domain by this study. This has been achieved by modifying the definition of D transforms, put forth recently for the study of classes of nonlinear lumped parameter systems. The appropriate properties of the new D transforms are presented to bring out their applicability in the analysis of nonlinear distributed parameter systems.

Discrete Wiener¿Lee transforms

The use of Wiener–Lee transforms to construct one of the frequency characteristics, magnitude or phase of a network function, when the other characteristic is given graphically, is indicated. This application is useful in finding a realisable network function whose magnitude or phase curve is given. A discrete version of the transform is presented, so that a digital computer can be employed for the computation.

Revisiting Riesz transforms on Heisenberg groups

We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre expansions.

Compressive sensing for music signals: comparison of transforms with coherent dictionaries

Compressive Sensing (CS) is a new sensing paradigm which permits sampling of a signal at its intrinsic information rate which could be much lower than Nyquist rate, while guaranteeing good quality reconstruction for signals sparse in a linear transform domain. We explore the application of CS formulation to music signals. Since music signals comprise of both tonal and transient nature, we examine several transforms such as discrete cosine transform (DCT), discrete wavelet transform (DWT), Fourier basis and also non-orthogonal warped transforms to explore the effectiveness of CS theory and the reconstruction algorithms. We show that for a given sparsity level, DCT, overcomplete, and warped Fourier dictionaries result in better reconstruction, and warped Fourier dictionary gives perceptually better reconstruction. “MUSHRA” test results show that a moderate quality reconstruction is possible with about half the Nyquist sampling.

Riesz transforms and multipliers for the Grushin operator

We show that Riesz transforms associated to the Grushin operator G = -Delta - |x|(2 similar to) (t) (2) are bounded on L (p) (a''e (n+1)). We also establish an analogue of the Hormander-Mihlin Multiplier Theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator-valued Fourier multiplier theorem due to L. Weis.