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: This study introduces several types of simplified fractional Fourier transform (SFRFT) that are simpler than the original FRFT in terms of digital computation, optical implementation, implementation of gradient-index media, and implementation of radar systems.
Abstract: The fractional Fourier transform (FRFT) has been used for many years, and it is useful in many applications. Most applications of the FRFT are based on the design of fractional filters (such as removal of chirp noise and the fractional Hilbert transform) or on fractional correlation (such as scaled space-variant pattern recognition). In this study we introduce several types of simplified fractional Fourier transform (SFRFT). Such transforms are all special cases of a linear canonical transform (an affine Fourier transform or an ABCD transform). They have the same capabilities as the original FRFT for design of fractional filters or for fractional correlation. But they are simpler than the original FRFT in terms of digital computation, optical implementation, implementation of gradient-index media, and implementation of radar systems. Our goal is to search for the simplest transform that has the same capabilities as the original FRFT. Thus we discuss not only the formulas and properties of the SFRFT’s but also their implementation. Although these SFRFT’s usually have no additivity properties, they are useful for the practical applications. They have great potential for replacing the original FRFT’s in many applications.
41 citations
TL;DR: A new discrete polynomial transform constructed from the rows of Pascal's triangle is introduced, and applications of the transform in digital image processing, such as bump and edge detection are discussed.
Abstract: We introduce a new discrete polynomial transform constructed from the rows of Pascal's triangle. The forward and inverse transforms are computed the same way in both the one- and two-dimensional cases, and the transform matrix can be factored into binary matrices for efficient hardware implementation. We conclude by discussing applications of the transform in digital image processing, such as bump and edge detection.
40 citations
01 Nov 1987
TL;DR: In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.
Abstract: In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.
40 citations
TL;DR: In this paper, the authors derived formulas for the two-dimensional Fourier transform of functions with polygonal support and linear amplitude variation from the corresponding formula for a constant function, valid for all nonzero values of the transform variable k, which fail when k is perpendicular or parallel to any edge of the polygon.
Abstract: New formulas for the two-dimensional Fourier transform of functions with polygonal support and linear amplitude variation are derived from the corresponding formula for a constant function. These expressions, valid for all nonzero values of the transform variable k, are superior to those previously reported, which fail when k is perpendicular or parallel to any edge of the polygon. These transforms have applications in diffraction theory and computational electromagnetics. >
40 citations
TL;DR: The split radix was used to develop a fast Hartley transform algorithm, it is performed ''in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms'' as discussed by the authors.
Abstract: The split radix is used to develop a fast Hartley transform algorithm, it is performed `in-place?, and requires the lowest number of arithmetic operations compared with other related algorithms.
40 citations