Hough Transform (H.T.) is a classical tool for multiple alignment detection in image processing, based on the property that Aligned Points are transformed into Intersecting Curves (APIC). Among the alternative transforms which possess the APIC property, one of the most interesting is Polar Transform (P.T.) which exchanges a point (a,b) and the straight line with equation ax + by = 1. This trans...

A new family of probability distributions βM,N , M = 0 · · ·N, N ∈ N on the unit interval (0, 1] is defined by the Mellin transform. The Mellin transform of βM,N is characterized in terms of products of ratios of Barnes multiple gamma functions, shown to satisfy a functional equation, and a Shintani-type infinite product factorization. The distribution log βM,N is infinitely divisible. If M < N...

The fast Fourier transform (FFT) autoindexing routines written by the Rossmann group at Purdue University have been incorporated in MOSFLM, providing a rapid and reliable method of indexing oscillation images. This is a procedure which extracts direct-space information about the unit cell from the FFT. The method and its implementation in MOSFLM are discussed.

Szegö quadrature formulas represent the analogue on the unit circle of the well-known Gauss–Christoffel quadratures for intervals of the real line. In the present work, Szegö formulas are revised and an application to the computation of the Fourier transform given. 2006 Elsevier Inc. All rights reserved.

This paper introduces a new transform known as HARWHT. It results from the Kronecker product of the discrete Hartley transform (DHT) and discrete Walsh-Hadamard transform (WHT). The eigenvectors and eigenvalues of the HARWHT transform matrices are presented using Kronecker product. Then, the results of the eigen decomposition of the transform matrices are used to define discrete fractional HARW...

The Fast Hartley Transform (FHT), a discrete version of the Hartley Transform (HT), has been studied in various papers and shown to be faster and more convenient to implement and handle than the corresponding Fast Fourier Transform (FFT). As the HT is not as nicely separable as the Fourier Transform (FT), a multidimensional version of the HT needs to perform a final correction step to convert t...

This paper presents a real-valued discrete multicamer modulation approach that is based on the use of the discrete Hartley transform (DHT) and its inverse (IDHT) to perform the modulation and demodulation operations. Since the DHT and IDHT definitions are identical, we can use the same hardware or program to implement the modulator and demodulator of the proposed multicarrier method. As compare...

We prove that a bounded operator S on La for p > 1 is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disk if S satisfies some integrable conditions. Some estimates about the norm and essential norm of Toeplitz operators with symbols in BT are obtained.

We study the completeness properties of the set of wavelets in L2(R). It is well-known that this set is not closed in the unit ball of L2(R). However, if one considers the metric inherited as a subspace (in the Fourier transform side) of L2(R, dξ) ∩ L(R∗, dξ |ξ| ), we do obtain a complete metric space.

In this paper, a relation for finding type-II discrete sine transform (DST) from type-I discrete Hartley transform (DHT) has been derived. The transform length N is taken as even. Using this relation, the (N 1) output components of DST can be realized from DHT. The DHT is one of the transforms used for converting data in time domain into frequency domain using only real values.