Hartley transform

About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.

FPGA implementation of discrete fractional Fourier transform

Abstract: Since decades, fractional Fourier transform has taken a considerable attention for various applications in signal and image processing domain. On the evolution of fractional Fourier transform and its discrete form, the real time computation of discrete fractional Fourier transform is essential in those applications. On this context, we have proposed new hardware architecture for implementing a Discrete Fractional Fourier Transform (DFrFT) which requires hardware complexity of O(4N), where N is transform order. This proposed architecture has been simulated and synthesized using verilogHDL, targeting a FPGA device (XLV5LX110T). The simulation results are very close to the results obtained by using MATLAB. The result shows that, this architecture can be operated on a maximum frequency of 217MHz.

Representation of the Fourier Transform by Fourier Series

Abstract: The analysis of the mathematical structure of the integral Fourier transform shows that the transform can be split and represented by certain sets of frequencies as coefficients of Fourier series of periodic functions in the interval $$[0,2\pi)$$ . In this paper we describe such periodic functions for the one- and two-dimensional Fourier transforms. The approximation of the inverse Fourier transform by periodic functions is described. The application of the new representation is considered for the discrete Fourier transform, when the transform is split into a set of short and separable 1-D transforms, and the discrete signal is represented as a set of short signals. Properties of such representation, which is called the paired representation, are considered and the basis paired functions are described. An effective application of new forms of representation of a two-dimensional image by splitting-signals is described for image enhancement. It is shown that by processing only one splitting-signal, one can achieve an enhancement that may exceed results of traditional methods of image enhancement.

Spectrum Analysis Tutorial, Part 1: The Discrete Fourier Transform

Abstract: This tutorial is an outgrowth of a course in signal processing given by Julius O. Smith at Stanford University in the fall of 1984 (see Smith 1981, as well). It provides an elementary mathematical introduction to spectrum analysis. This is the first of two parts. In part one, the discrete Fourier transform is introduced and analyzed in depth. In part two, some fundamental spectrum analysis theorems and applications are discussed. The only mathematical background assumed is high school trigonometry, algebra, and geometry. No calculus is required. Familiarity with summation formulae, complex numbers, and vectors is helpful, although not essential.