Hartley transform

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

Measuring the Wiener kernels of a non-linear system using the fast Fourier transform algorithm†

Abstract: A new method is presented for the measurement of the Wiener kernels of a non-linear system. The method uses the complex exponential functions as a set of orthogonal functions with which to expand the kernels. The fast Fourier transform is then employed in the most efficient measurement of the kernels so far discovered.

The Universality of the Radon Transform

Abstract: PREFACE CHAPTERS I-X I. Introduction I.1 Functions, Geometry and Spaces I.2 Parametric Radon transform I.3 Geometry of the nonparametric Radon transform I.4 Parametrization problems I.5 Differential equations I.6 Lie groups I.7 Fourier transform on varieties: The projection slice theorem and the Poisson summation Formula I.8 Tensor products and direct integrals II. The nonparametric Radon transform II.1 Radon transform and Fourier transform II.2 Tensor products and their topology II.3 Support conditions III. Harmonic functions in Rn III.1 Algebraic theory III.2 Analytic theory III.3 Fourier series expansions on spheres III.4 Fourier expansions on hyperbolas III.5 Deformation theory IV. Harmonic functions and Radon transform on algebraic varieties IV.1 Algebraic theory and finite Cauchy problem IV.2 The compact Watergate problem IV.3 The noncompact Watergate problem V. The nonlinear Radon and Fourier transforms V.1 Nonlinear Radon transform V.2 Nonconvex support and regularity V.3 Wave front set V.4 Microglobal analysis VI. The parametric Radon transform VI.1 The John and invariance equations VI.2 Characterization by John equations VI.3 Non-Fourier analysis approach VI.4 Some other parametric linear Radon transforms VII. Radon transform on groups VII.1 Affine and projection methods VII.2 The nilpotent (horocyclic) Radon transform on G/K VIII. Radon transform as the interrelation of geometry and analysis VIII.1 Integral geometry and differential equations VIII.2 The Poisson summation formula and exotic intertwining VIII.3 The Euler-MacLaurin summation formula IX. Extension of solutions of differential equations IX.1 Formulation of the problem IX.2 Hartogs-Lewy extension IX.3 Wave front sets and the Caucy problem X. Periods of Eisenstein and Poincare series X.1 The Lorentz group, Minowski geometry and a nonlinear projection-slice theorem X.2 Spreads and cylindrical coordinates in Minowski geometry X.3 Eisenstein series and their periods X.4 Poincareseries and their periods X.5 Hyperbolic Eisenstein and Poincare series X.6 The four dimensional representation X.7 Higher dimensional groups BIBILIOGRAPHY OF CHAPTERS I-X XI. Some problems of integral geometry arising in tomography XI.1 Introduction XI.2 X-ray tomography XI.3 Attenuated and exponential Radon transforms XI.4 Hyperbolic integral geometry and electrical impedance tomography INDEX

Discrete fractional Hartley and Fourier transforms

Abstract: This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relationship between DFRHT and DFRFT is described, and numerical examples are illustrated to demonstrate that the proposed DFRFT is a better approximation to the continuous fractional Fourier transform than the conventional defined DFRFT. Finally, a filtering technique in the fractional Fourier transform domain is applied to remove chirp interference.

The multiple-parameter discrete fractional Fourier transform

Abstract: The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points. The proposed multiple-parameter discrete fractional Fourier transform (MPDFRFT) is shown to have all of the desired properties for fractional transforms. In fact, the MPDFRFT reduces to the DFRFT when all of its order parameters are the same. To show an application example of the MPDFRFT, we exploit its multiple-parameter feature and propose the double random phase encoding in the MPDFRFT domain for encrypting digital data. The proposed encoding scheme in the MPDFRFT domain significantly enhances data security.

Fractional Fourier transform: A novel tool for signal processing

Abstract: The fractional Fourier transform (FRFT) is the generalization of the classical Fourier transform. It depends on a parameter ? (= a ?/2) and can be interpreted as a rotation by an angle ? in the time-frequency plane or decomposition of the signal in terms of chirps. This paper discusses discrete FRFT (DFRFT), time-frequency distributions related to FRFT, optimal filter and beamformer in FRFT domain, filtering using window functions and other fractional transforms along with simulation results.