We define a notion of Radon Transform for data in an n by n grid. It is based on summation along lines of absolute slope less than 1 (as a function either of x or of y), with values at non-Cartesian locations defined using trigonometric interpolation on a zero-padded grid. The definition is geometrically faithful: the lines exhibit no 'wraparound effects'. For a special set of lines equispaced ...

It is shown in this paper that the discrete equivalent of a chirp filter is needed to implement the computation of the discrete Fourier transform (DFT) as a linear filtering process. We show further that the chirp filter should not be realized as a transversal filter in a wide range of cases; use instead of the conventional FFT permits the computation of the DFT in a time proportional to N logz...

There are many motivations for the discrete Fourier transform. Those of you in computer science have probably encountered them first in signal processing and perhaps further in cool theory results like switching lemmas. Those of you in physics have definitely encountered the continuous fourier transform, most likely first in quantum theory where we learn that the fourier transform goes between ...

For the computational model where only additions are allowed, the Ω(n log n) lower bound on operations count with respect to image size n × n is obtained for two types of the discrete Radon transform implementations: the fast Hough transform and a generic strip pattern class which includes the classical Hough transform, implying the fast Hough transform algorithm asymptotic optimality. The proo...

Introduction: The discrete Hartley transform (DHT) is an attractive alternative to the discrete Fourier transform (DFT) because of its real-valued computation and properties similar to those of the DFT [1]. Another interesting property of the DHT is that the same kernel is used for both the transform and its inverse transform. Consequently, since its introduction the DHT has found its way to ma...

The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence ϕ ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of...

We compare several algorithms for computing the discrete Fourier transform of n numbers. The number of “operations” of the original Cooley-Tukey algorithm is approximately 2n A(n), where A(n) is the sum of the prime divisors of n. We show that the average number of operations satisfies (l/x)Z,,,2n A(n) (n2/9)(x2/log x). The average is not a good indication of the number of operations. For examp...

A computational algorithm for numerically evaluating the z-transform of a sequence of N samples is discussed. This algorithm has been named the chirp z-transform (CZT) algorithm. Using the CZT algorithm one can efficiently evaluate the z-transform at M points in the z-plane which lie on circular or spiral contours beginning at any arbitrary point in the z-plane. The angular spacing of the point...

Chrestenson generalized Walsh transform factorizations for parallel processing imbedded implementations on field programmable gate arrays are presented. This general base transform, sometimes referred to as the Discrete Chrestenson transform, has received special attention in recent years. In fact, the Discrete Fourier transform and Walsh-Hadamard transform are but special cases of the Chresten...

In this paper, we used tetranuclear copper (II) Schiff base complexes, [Cu4 (μ-sal2hn) (μ-N3)2(N3)2] (1) and [Cu4 (μ-salophen) (μ1, 1-N3)2(N3)2] (2), as new precursor in solid-state thermal decomposition for the synthesis of CuO ...