The paper presents a new half-cycle adaptive phasor estimation algorithm for digital protective relaying. The algorithm is immune to an exponentially decaying dc component regardless of its initial magnitude and time constant. The algorithm is intended for current signals and improves both the magnitude and impedance measurements. The new measuring technique is based on the recursive half-cycle...

Two-dimensional (2-D) block processing technique for linear filtering of digital images is introduced. New 2-D block structures are derived for 2-D recursive digital filters realized by difference equations and state-space formulations. Several special cases have also been considered and the relevant 2-D block structures are given. The computational costs of different implementation techniques ...

Many applications invoke the Fast Fourier Transform (FFT) on sparse inputs, with most of their Fourier coefficients being very small or equal to zero. Compared with the “dense” FFT algorithms, the input sparsity makes it easier to parallelize the sparse counterparts. In general, sparse FFT algorithms filter input into different frequency bins, and then process the bins separately. Clearly, the ...

In [10], Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms. In particular, Misra showed how powerlists could be used to give simple descriptions to very complex algorithms, such as the Fast Fourier Transform (FFT). Such simplicity in presentation facilitates reasoning about the resulting algorithms, and in fact Misra was able to g...

In this paper, we derive a family of fast and stable algorithms for multiplying and inverting n × n Pascal matrices that run in O(n log n) time and are closely related to De Casteljau’s algorithm for Bézier curve evaluation. These algorithms use a recursive factorization of the triangular Pascal matrices and improve upon the cripplingly unstable O(n log n) fast Fourier transform-based algorithm...

In this paper, we address the issue of automatic generation of disk-based algorithms from tensor product formulas. Disk-based algorithms are required in scientiic applications which work with large data sets that do not t entirely into main memory. Tensor products have been used for designing and implementing block recursive algorithms on shared-memory, vector and distributed-memory multiproces...

Box splines are a multivariate extension of uniform univariate B-splines. Direct evaluation of a box spline basis function can be difficult , but they have a relatively simple Fourier transform and can therefore be evaluated with an inverse FFT. Symmetry, recursive evaluation of the coefficients, and parallelization can be used to optimize performance. A windowing function can also be used to r...

This paper presents a design methodology for developing efficient distributed-memory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and bitonic sort. This design methodology is specifically suited for most modern supercomputers having a distributed-memory architecture with a circuit-switched or wormhole routed mesh or a hypercube interconnection networ...

Recent results by Van Buskirk et al. have broken the record set by Yavne in 1968 for the lowest arithmetic complexity (exact count of real additions and multiplications) to compute a power-of-two discrete Fourier transform. Here, we present a simple recursive modification of the split-radix algorithm that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the co...

We study the classes of computable functions that can be proved to be total by means of parameter free C, and 4 induction schemata, ZC; and ZlI;, over Kalmar elementary arithmetic. We give a positive answer to a question, whether the provably total computable functions of Zq are exactly the primitive recursive ones, and show that the class of such functions for ICI + I% coincides with the class...