This paper presents a new cost-efficient realization scheme of pattern matching circuits in FPGA structures with embedded memory blocks (EMB). The general idea behind the proposed method is to implement combinational circuits using a net of finite state machines (FSM) instead. The application of functional decomposition method reduces the utilization of resources by implementing FSMs using both EMBs and LUT-based programmable logic blocks available in contemporary FPGAs. Experimental results for the proposed method are also shown. A comparison with another dedicated method yields extremely encouraging results: with a comparable number of EMBs, the number of logic cells has been reduced by 95%.

The paper presents a logic synthesis method oriented towards FPGA architectures with specialized embedded memory blocks. Existing methods do not ensure effective utilization of possibilities provided by these specialized embedded modules. The presented method, based on balanced decomposition, leads to much more effective implementations of digital systems in modern FPGA structures.

High dynamic range (HDR) images require a higher number of bits per color channel than traditional images. This brings about problems to storage and transmission, especially in distributed wireless sensor networks in which transmission capability and energy consumption are critical issues. The paper proposes a structure of compressing multiple dynamic range images, which is called multiple dynamic range (MDR) coding. MDR imaging system is attractive due to the capability of reconstructing lower dynamic range images from partial bitstream. MDR coding shows its advantages in terms of energy efficiency in distributed wireless sensor networks. The efficacy of MDR coding is also illustrated by presenting the results of encoding a series of synthetic and natural MDR images

An efficient algorithm for generating fixed polarity arithmetic expansions for ternary functions is presented. It calculates the required spectral coefficients in a recursive manner based on a developed definition of the polarity matrix. The application of the algorithm for generating both complete polarity matrix and selected fixed polarity arithmetic expansion is given. Computational cost of the algorithm in terms of required number of additions and multiplications is also derived and it is shown to be more efficient than the calculation by matrix multiplication. Fast flow diagrams for implementation of the algorithm on hardware are also shown.

Two different algorithms for generating the complete fixed polarity arithmetic transform polarity matrix of a quaternary function are presented. The first approach utilizes relations between coefficient vectors whereas the second one is using relations between the column coefficient vectors to reduce the computational cost. Both algorithms are described and their computational costs are derived and compared.

Hardware calculation of generalized fastest linearly independent arithmetic (LIA) expansions using systolic processor is presented in this paper. The relation between the forward flow graph of a particular LIA transform and the systolic processor structure for its spectra calculation is given. In general, a particular systolic hardware structure can be used for more than one fastest LIA transforms with appropriate reordering of inputs and/or outputs

The generalization of multi-polarity arithmetic-Walsh transform in the form of layered Kronecker matrices and its corresponding representations is proposed. As the new hybrid arithmetic-Walsh transform has a structure similar to that of the Walsh and arithmetic transform matrices, similar spectral transform decision diagrams are held in the expanded transform as well. The new kind of spectral transform decision diagram has terminals corresponding to the multi-polarity arithmetic-Walsh transform to represent the arithmetic-Walsh spectra of discrete functions

In this paper, the family of fastest ternary linearly independent arithmetic transforms, which possesses forward and inverse butterfly diagrams with lowest computational complexity have been identified. This family is recursively defined and has consistent formulas relating forward and inverse transform matrices. Computational costs of the calculation for presented transforms are also discussed.

This comment relates to two published articles by Tsai et al. (ibid. vol.45(1), 1996 and vol.46(2), 1997) that used four types of two-variable Boolean symmetries and explained their transitivity conditions and relations with Reed-Muller transform. We show that some research in this area had been done earlier about which the authors are unaware.

A method has been developed to find disjoint bi-decomposition of Boolean functions. From the knowledge of a subset of Walsh spectrum for a Boolean function and by checking some preliminary conditions, the new algorithm is applied to identify the type of bi-decomposition and its existence. All three types of bi-decomposition are considered including OR, AND and EXOR type. The new method is very efficient by using a filtering procedure that establishes quickly the lack of bi-decomposition from the knowledge of just a few Walsh spectral coefficients. The type of bi-decomposition and affirmation/negation of variables in its logic sub-functions are directly identified by manipulation on the reduced cubical representation of Boolean functions and their corresponding Walsh spectra.

In this paper, we present a new method to detect skew equivalent and skew non equivalent symmetric variables in Boolean functions. The method uses the Walsh spectrum of Boolean functions and is extremely fast in detecting assymetries to avoid more spectrum calculation. When the symmetry, exists, the method needs half of the spectral coefficients to detect it. Experimental results on a large number of functions show that our approach is very efficient.

In this paper, we review some techniques for embedding watermarks in grey scale digital images and propose a novel method based on multi-resolution and complex Hadamard transforms. The experimental results show that our scheme is robust to JPEG compression, image resizing, cropping, dithering distortion and successive watermarking.

This paper relates to a recently published partly tutorial article that presents some discussion of the polynomial form of Boolean functions and its applications based on the literature published in English and German. We show that a lot of the research in this area has also been done in Eastern Europe, and this note aims to present these unknown developments. The most recent work in this area is also described.

The concept of Linearly Independent arithmetic (LIA) transforms and expansions is introduced in this paper. The recursive ways of generating forward and inverse fast transforms for LIA are presented. The paper describes basic properties and lists those LIA transforms which have convenient fast forward algorithms and easily defined inverse transforms. In addition, those transforms which require horizontal or vertical permutations to have fast transform are also discussed. The computational advantages and usefulness of new expansions based on LIA logic in comparison to known arithmetic expansions are discussed.

Unnormalized Haar spectra and Ordered Binary Decision Diagrams (OBDDs) are two standard representations of Boolean functions used in logic design. In this article, mutual relationships between those two representations have been derived. The method of calculating the Haar spectrum from OBDD has been presented. The decomposition of the Haar spectrum, in terms of the cofactors of Boolean functions, has been introduced. Based on the above decomposition, another method to synthesize OBDD directly from the Haar spectrum has been presented.

No abstract available.

The ways of generation of forward and inverse fast transforms for recently introduced orthogonal logic have been presented. The list of all fast transforms is thoroughly discussed. The paper summarizes those orthogonal transforms which have fast algorithms and easily defined recursive equations. In addition, those transforms which require one or more permutations to have fast transform are also discussed.

Fast forward and inverse transforms for recently introduced Generalized Walsh Transform have been presented. The way of recursive generation of transform matrices by using Kronecker products of elementary matrices have been given. Mutual relations among transform matrices and spectra for arbitrary polarities have been investigated.>

An algorithm has been developed to calculate the arithmetic transform of Boolean functions from their Ordered Binary Decision Diagram (OBDD) representation. The method of decomposition of arithmetic spectral coefficients in terms of the cofactors of Boolean functions that resembles known Shannon decomposition of such functions has been introduced for the first time. Based on the above decomposition, a second new algorithm is presented to synthesize Ordered Binary Decision Diagrams directly from the arithmetic spectrum of Boolean functions.>

A non-linear transform, called "Sign Haar Transform" has been introduced. The transform is unique and converts binary/ternary vectors into ternary spectral domain. Recursive definitions and Fast Transforms for the calculation of Sign Haar Transform have been developed. The new transform is extremely computationally effective both in terms of memory requirements and processing time.>

A theory has been developed to calculate the Rademacher-Walsh transform from a cube array specification of incompletely specified Boolean functions. The importance of representing Boolean functions as arrays of disjoint ON- and DC-cubes has been pointed out, and an efficient new algorithm to generate disjoint cubes from nondisjoint ones has been designed. The transform algorithm makes use of the properties of an array of disjoint cubes and allows the determination of the spectral coefficients in an independent way. The programs for both algorithms use advantages of C language to speed up the execution. The comparison of different versions of the algorithm has been carried out. The algorithm and its implementation provide the fastest and most comprehensive program (having many options) known to the authors for the calculation of the Rademacher-Walsh transform. It successfully overcomes all drawbacks in the calculation of the transform from the design automation system based on spectral method-the SPECSYS system from Drexel University, which uses fast Walsh transform.>