Bent functions f : F2 → F2 achieve largest distance to all linear functions. Equivalently, their spectrum with respect to the Hadamard-Walsh transform is flat (i.e. all spectral values have the same absolute value). That is equivalent to saying that the function f has optimum periodic autocorrelation properties. Negaperiodic correlation properties of f are related to another unitary transform c...

The paper deals with the F-transform technique which was introduced as a method for an approximate representation of continuous functions which is appropriate for many applications. In the terminology of neural networks, the F-transform uses so called off-line (batch) learning. However, for certain applications an on-line (incremental) learning algorithm has to be implemented. We study the F-tr...

The structure and the properties of the eigenfunctions of the canonical integral transform are investigated. It is shown that a signal can be decomposed into a set of the orthogonal eigenfunctions of the generalized Fresnel transform. The property that the set contains a finite number of functions is obtained. The canonical integral transform, also known as the generalized Fresnel transform (GF...

This paper investigates the relations between the least-squares approximation techniques and the Fuzzy Transform. Assuming that the function f : R → R underlying a discrete data set D := {(xi, f(xi))}i=1 has been computed with interpolating or least-squares constraints, we prove that the Discrete Fuzzy Transform of the sets {f(xi)}i=1 and {f(xi)}i=1 is the same. This result shows that the Discr...

Given a formal power series f(z) ∈ C[[z]] we define, for any positive integer r, its rth Witt transform, W (r) f , by W (r) f (z) = 1 r ∑ d|r μ(d)f(z d)r/d, where μ denotes the Möbius function. The Witt transform generalizes the necklace polynomials, M(α;n), that occur in the cyclotomic identity 1 1− αy = ∞

This article investigates the application of swarm and evolutionary algorithms, namely SOMA, DE, GA, for optimizing F-transform-based image compression. To do this, we introduce cost function, evaluating approximation decompressed to original image, concerning parameters that control quality F-transform. function is then minimized by selected algorithms find optimal settings compression decompr...