Showing papers on "Harmonic wavelet transform published in 1977"
TL;DR: A new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency is outlined.
Abstract: We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using fast Fourier transforms. The new algorithm offers advantages in speed and substantial advantages in storage requirements over conventional methods for evaluating Hankel transforms with large numbers of points.
293 citations
TL;DR: The Walsh-Hadamard transform has recently received increasing attention in engineering applications due to the simplicity of its implementation and to its properties which are similar to the familiar Fourier transform.
Abstract: The Walsh-Hadamard transform has recently received increasing attention in engineering applications due to the simplicity of its implementation and to its properties which are similar to the familiar Fourier transform. The transform matrices found so far to possess fast algorithms are the naturally ordered and dyadically ordered matrices, whose algorithms are similar to the Cooley-Tukey algorithm, and to the machine-oriented algorithm of Corinthios [2], respectively.
65 citations
IBM1
TL;DR: These transforms, which under certain conditions can be computed via fast transform algorithms allow the implementation of digital filters with better efficiency and accuracy than the fast Fourier transform (FFT).
Abstract: In this paper pseudo Fermat number transforms (FNT's) are discussed. These transforms are defined in a ring of integers modulo an integer submultiple of a pseudo Fermat number, and can be computed without multiplications while allowing a great flexibility in word length selection. Complex pseudo FNT's are then introduced and are shown to relieve some of the length limitations of conventional Fermat number transforms (FNT's). These transforms, which under certain conditions can be computed via fast transform algorithms allow the implementation of digital filters with better efficiency and accuracy than the fast Fourier transform (FFT).
44 citations
TL;DR: The fast Fourier transform andd the fast Walsh transform are too slow for some real-time applications, so these are replaced by simple, modular logic solutions.
Abstract: The fast Fourier transform andd the fast Walsh transform are too slow for some real-time applications. For binary data, an 'instant' Fourier transform is based on harmonic analysis in a space of 2 n -tuples of 0s and 1s. Simple, modular logic finishes transforming 2n real-time serial binary data one clock pulse after the last datum arrives.
17 citations
IBM1
TL;DR: One "General-N" (i.e. many allowable DFT sizes (N) but certainly not any vector size) complex WFTA programming technique is described.
Abstract: The Winograd Fourier Transform Algorithm (WFTA) requires about 20% of the multiplications used in an optimized FFT, while the number of additions remains unchanged. This paper describes one "General-N" (i.e. many allowable DFT sizes (N) but certainly not any vector size) complex WFTA programming technique.
12 citations
Patent•
18 Mar 1977TL;DR: In this paper, a series of stored images representing sine and cosine components of the Fourier transform is generated to obtain a fast, two-dimensional transform of the image.
Abstract: Two dimensional optical or electrical images are processed through a storage tube designed to yield the correlation function between the input images and stored images. By generating a series of stored images representing sine and cosine components of the Fourier transform, a fast, two-dimensional transform of the image is obtained.
12 citations
10 citations
IBM1
TL;DR: The sinc and cosinc transform (SCT) as mentioned in this paper uses Walsh functions to obtain the Fourier transform, which converts a staircase approximation of a function to a set of sinc terms in the frequency domain.
Abstract: A new transform, the sinc and cosinc transform, uses Walsh functions to obtain the Fourier transform. This technique converts a staircase approximation of a function to a set of sinc and cosinc terms in the frequency domain that is equivalent to the Fourier transform. The calculation is slower than the fast Fourier transform (FFT) but is devoid of aliasing. The interpolation and scaling in the frequency domain are built in, and any frequency point may be chosen without changing the number or spacing of the samples in the time domain. The intervening set of coefficients is computed more rapidly than those obtained using the fast Hadamard transform.
9 citations
TL;DR: In this article, a program for the calculation of one-to-three-dimensional Fourier transforms from flexible models is described and the intensity distributions of both oriented and unoriented models is possible.
Abstract: A program for the calculation of one- to three-dimensional Fourier transforms from flexible models is described. The calculation of the intensity distributions of both oriented and unoriented models is possible.
6 citations
TL;DR: In this paper, a numerical method of holographic reconstruction of 2D fields is presented, where the 2D Fourier transform of the field is generated by using the slowness curve of the medium.
Abstract: A numerical method of holographic reconstruction of 2-dimensional fields is presented. Reconstructions are obtained indirectly, by generating the 2-dimensional Fourier transform of the field by using the slowness curve of the medium. Wideband data can be handled efficiently by this method, which also works in dispersive and anisotropic space. Examples of monochromatic and multifrequency holographic reconstructions are shown.
5 citations
01 Feb 1977
01 May 1977
TL;DR: An elegant method of obtaining the Arcsine transform and its application to several important signal processing problems are discussed, among them computation of discrete Fourier transforms and correlation functions, realization of digital filters, modulation and detection of signals, and construction of frequency synthesizers.
Abstract: By initially transforming a signal into its Arcsine value, the multiplications required in the subsequent processing of the signal can be replaced by additions and table look-ups. With the advent of large read-only memories, this may be an attractive method to reduce computation time and simplify hardware in signal processing systems. An elegant method of obtaining the Arcsine transform and its application to several important signal processing problems are discussed. Among these are computation of discrete Fourier transforms and correlation functions, realization of digital filters, modulation and detection of signals, and construction of frequency synthesizers.
TL;DR: In this article, a statistical model is used to predict the output signal-to-noise ratio (SNR) when a two-pass fast Fourier transform (FFT) is computed using fixed-point arithmetic.
Abstract: A statistical model is used to predict the output signal-to-noise ratio (SNR) when a two-pass fast Fourier transform (FFT) is computed using fixed-point arithmetic. The results show that the ratio varies essentially as the square root of the number of points in the transform. Also included are the results of the simulation of a fixed-point machine and the variation of the error as a function of the length of the coefficients.
01 Jan 1977
Proceedings Article•
22 Aug 1977TL;DR: This paper presents an efficient method to calculate two-dimensional discrete Fourier transforms over windowed regions of the light intensity matrix based on the fast Fourier transform algorithm, which can be beaten by any nonparallel algorithm.
Abstract: Computer vision systems based on general purpose computers often need efficient texture description algorithms. One common method is to calculate two-dimensional discrete Fourier transforms over windowed regions of the light intensity matrix. Although these methods described in the literature are based on the fast Fourier transform algorithm, the computation time is still too high to permit the description of texture for as many windows as are needed for good segmentation. When a set of transforms over a window at every position of the matrix is needed, an efficient method can be used. It saves information computed for previous windows and uses it to reduce the effort expended on the current window. For a window N × N and an image matrix M × M, the time complexity is reduced from O(N2M2logN) to O(N2M2). This complexity cannot be beaten by any nonparallel algorithm.
01 Jan 1977
TL;DR: In this paper, the Fourier Transform of the image at points lying on a circle in Fourier space is sampled by transmitting the image through a rotating grating, and a system using two rotating gratings is proposed to improve the performance for continuous images.
Abstract: We describe an image scanning method which samples the Fourier Transform of the image at points lying on a circle in Fourier space. It works by transmitting the image through a rotating grating. Reconstructions of point and continuous images are illustrated. A system using two rotating gratings is proposed to improve the performance for continuous images.
20 Jun 1977
TL;DR: It is shown here how the Fourier Transformation can be transformed into Fourier-like transformations using just a single agent.
Abstract: 確率 過程y(t)は 周波 数 ωlに対 して振幅 αlと確率 変数 である位相角 φlの余弦関数 との積 の重 ね合せ によ って与 えられ る. この調和関数型 のモデルは,任 意 の波形 がフー リエ級 数 に展 開可能であることか ら,重 ね合 わせの総 数.Mが 十分大 きければ,多 くの不規則変動 を適確 にモデル化 で きよ う. さらに,式(1)の 確率過程y(t)は フー リエの逆変換 に類似 であることか ら,高 速 フー リエ変換(Fast Fourier Transformation.以 下FFTと 呼ぶ)を 用 いてコ ン ピューターによ りきわめて効率 よ く作成 可能 である2). 本 報告 は,コ ンピューターによ り確率 過程y (t)を 効 率 よ く作成 するべ くFFTへ の使用方 法を整理 し,そ の 適用性 を検討 したものである.な お,式(1)の モデルの 中で も α1が時 間の関数 としても変動する非定常確率過 程の作成方法が,こ の報告の主題 とな っている.
TL;DR: The most important result of this study has been the demonstration that an apparently complex behaviour pattern can be simulated by making simple decision based on hologram image.
Abstract: A brief overview of the orb-web construction is presented. Computer situation, in combination with 2-D Fourier transform of the hologram image, is a method of discriminating between realistic and unrealistic hypotheses about which cues are used in orb-web construction. The potential applications of coherent spatial filtering were particularly evident in the field of orb-web transformation, and this method stimulated additional interest in these techniques. The most important result of this study has been the demonstration that an apparently complex behaviour pattern can be simulated by making simple decision based on hologram image.