The author investigates and summarises some of the computational tasks of discrete transforms in which block diagonal structure plays a dominant role. Walsh-Hadamard transform (WHT) based algorithm designs for various well known discrete transforms are presented; it can be proved that, owing to their block diagonal structure, the WHT based discrete transforms are more efficient than those of th...

basis structure. The design is generic and scalable, which allows better performance when more parallel sub-units are implemented.

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced:...

We investigate the asymptotic behavior of two types of Tukey depth-based multivariate trimmed means. Sufficient conditions for asymptotic normality of these location estimators are given. Two approaches to trimming are distinguished and central limit theorems are derived for each one. Asymptotic normality is proved using Hadamard differentiability of the location functionals. In the one-dimensi...

We show that it is possible to de ne Hartley-like transforms for (generalized) character tables of nite groups. This large class of transforms include Hartley transforms for discrete Fourier transforms over abelian groups and Hartley-like transforms for the discrete cosine transform of type I.

We consider the implementation of multiplication and division operations on one and two dimensional mesh of processors. We develop an O( √ n) step 2-dim mesh algorithm for multiplying two n-bit numbers. The algorithm is simple and does not rely upon discrete fourier transforms. We also develop an O(n) step 1-dim mesh algorithm for dividing a 2n-bit number by an n-bit number. This algorithm appe...

We present much briefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley, and scale transform and other relatives of the Fourier transform. ? 2003 Published by Elsevier B.V.

One of the main requirements in many signal processing applications is to have a “meaningful representation” in which signal’s characteristics are readily apparent. For example, for recognition, the representation should highlight salient features; for denoising, it should efficiently separate signal and noise; and for compression, it should capture a large part of signal using only a few coeff...