Topic
Hartley transform
About: Hartley transform is a research topic. Over the lifetime, 2709 publications have been published within this topic receiving 79944 citations.
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TL;DR: In this paper, the authors present techniques for implementing a fast algorithm for implementing odd-type DCTs and DSTs, which include a mapping between the real-valued data sequence to an intermediate sequence to be used as an input to a DFT.
Abstract: This disclosure presents techniques for implementing a fast algorithm for implementing odd-type DCTs and DSTs. The techniques include the computation of an odd-type transform on any real-valued sequence of data (e.g., residual values in a video coding process or a block of pixel values of an image coding process) by mapping the odd-type transform to a discrete Fourier transform (DFT). The techniques include a mapping between the real-valued data sequence to an intermediate sequence to be used as an input to a DFT. Using this intermediate sequence, an odd-type transform may be achieved by calculating a DFT of odd size. Fast algorithms for a DFT may be then be used, and as such, the odd-type transform may be calculated in a fast manner
53 citations
TL;DR: In this paper, two new algorithms for computing an nth-order Hankel transform are proposed based on characterizing a circularly symmetric function and its two-dimensional Fourier transform by a radial section.
Abstract: In this paper two new algorithms for computing an nth‐order Hankel transform are proposed. The algorithms are based on characterizing a circularly symmetric function and its two‐dimensional Fourier transform by a radial section and interpreting the Hankel transform as the relationship between the radial section in the two domains. By utilizing the property that the projection of a two‐dimensional function in one domain transforms to a radial section in the two‐dimensional Fourier transform or inverse Fourier transform domain, several efficient procedures for computing the Hankel transform exploiting the one‐dimensional FFT algorithm are suggested.
53 citations
TL;DR: A novel asymmetric single-channel color image encryption using Hartley transform and gyrator transform using optoelectronic encryption and decryption systems is proposed.
53 citations
TL;DR: The numerical simulation and experiment have proved the validity of the multiscale windowed Fourier transform for phase extraction of fringe patterns and makes the extracted phase more precise than other methods.
Abstract: A multiscale windowed Fourier transform for phase extraction of fringe patterns is presented. A local stationary length of signal is used to control the window width of a windowed Fourier transform automatically, which is measured by an instantaneous frequency gradient. The instantaneous frequency of the fringe pattern is obtained by detecting the ridge of the wavelet transform. The numerical simulation and experiment have proved the validity of this method. The combination of the windowed Fourier transform and the wavelet transform makes the extracted phase more precise than other methods.
52 citations
TL;DR: This paper structure certain types of non-bandlimited signals based on two ladder-shape filters designed in the LCT domain based on the phase function of the nonlinear Fourier atom which is the boundary value of the Mobius transform.
52 citations