Showing papers on "Hartley transform published in 1978"
TL;DR: A digital method for solving the phase-retrieval problem of optical-coherence theory: the reconstruction of a general object from the modulus of its Fourier transform, which should be useful for obtaining high-resolution imagery from interferometer data.
Abstract: We present a digital method for solving the phase-retrieval problem of optical-coherence theory: the reconstruction of a general object from the modulus of its Fourier transform. This technique should be useful for obtaining high-resolution imagery from interferometer data.
1,762 citations
TL;DR: In this paper, a method for the numerical calculation of Fourier transforms in variables that are the logarithms of the original variable and transform variable is described, which can also be applied to Bessel and spherical Bessel transforms.
234 citations
TL;DR: A combined Fourier–Mellin transform yields a representation of a signal that is independent ofdelay and scale change, which should be useful for speech analysis, where delay and scale differences degrade the performance of correlation operations or other similarity measures.
Abstract: A combined Fourier–Mellin transform yields a representation of a signal that is independent of delay and scale change. Such a representation should be useful for speech analysis, where delay and scale differences degrade the performance of correlation operations or other similarity measures. At least two different versions of a combined Fourier–Mellin transform can be implemented. The simplest version (the ‖F‖2−‖M‖2 transform) completely eliminates spectral phase information, while a slightly more complicated version (the ?−? transform) preserves some phase information. Both versions can be synthesized with a Fourier transform and an exponential‐sampling algorithm. Exponential sampling produces a frequency scale distortion that is similar to the effect of the cochlea. The ‖F‖2−‖M‖2 transform can also be implemented with a bank of proportional bandwidth filters. If the relative phase between spectral components is preserved, then a Fourier–Mellin transformer can perform compression of linear‐period modulat...
74 citations
01 Feb 1978
TL;DR: In this article, a procedure for numerical evaluation of the Hankel (Fourier-Bessel) transform of any integer order using the FFT algorithm is proposed. The basis for the procedure is the projection-slice theorem associated with the two-dimensional Fourirer transform.
Abstract: A procedure is proposed for the numerical evaluation of the Hankel (Fourier-Bessel) transform of any integer order using the FFT algorithm The basis for the procedure is the "projection-slice" theorem associated with the two-dimensional Fourirer transform
57 citations
TL;DR: In this paper, an expression for the Fourier transform of two-centre Gaussian orbital products is obtained which is identical in form with expressions for overlap integrals, and explicit expressions of the transform for all combinations up to ff products are given.
Abstract: An expression for the Fourier transform of two-centre Gaussian orbital products is obtained which is identical in form with expressions for overlap integrals. The one-centre transform is a special case, and is obtained in a trivial way from the two-centre expression. Explicit expressions of the transform for all combinations up to ff products are given.
23 citations
01 Jan 1978
TL;DR: A general class of even/odd transforms, including the Karhunen-Loeve transform, the discrete cosine transform, and the Walsh-Hadamard transform, is presented in this paper.
Abstract: A general class of even/odd transforms is presented that includes the Karhunen-Loeve transform, the discrete cosine transform, the Walsh-Hadamard transform, and other familiar transforms. The more complex even/odd transforms can be computed by combining a simpler even/odd transform with a sparse matrix multiplication. A theoretical performance measure is computed for some even/odd transforms, and two image compression experiments are reported.
21 citations
TL;DR: This new hybrid algorithm requires fewer multiplications than any previously known algorithm and is a combination of a Winograd algorithm and a fast complex integer transform developed previously by the authors.
Abstract: In this paper it is shown that the cyclic convolution of complex values can be performed by a hybrid transform. This transform is a combination of a Winograd algorithm and a fast complex integer transform developed previously by the authors. This new hybrid algorithm requires fewer multiplications than any previously known algorithm.
9 citations
9 citations
TL;DR: In this paper, a comparative study of frame rate limitations, windowing, time and frequency resolution, spectral correlation, complexity, and inverse structures for the conventional chirp-z-transform (CZT) and the sliding CZT realization of the discrete sliding Fourier transform is presented.
Abstract: Two sequential short-time spectral analysis techniques, amenable to nonrecursive filter implementation, are the conventional chirp-z-transform (CZT) realization of the discrete Fourier transform and the sliding CZT realization of the discrete sliding Fourier transform. This paper presents a comparative study of frame rate limitations, windowing, time and frequency resolution, spectral correlation, complexity, and inverse structures for these methods, with particular emphasis on the recently proposed sliding transform. The sliding transform and its CZT realization are viewed as skewed output samples of a filter bank, an approach which aids in understanding the relationship between the conventional and sliding schemes. Numerous forward and inverse CZT formulations are presented to improve resolution, frame rates, and compactness.
8 citations
TL;DR: This correspondence points out some inconsistencies between definitions and algorithms presented in the paper by H. F. Silverman.
Abstract: This correspondence points out some inconsistencies between definitions and algorithms presented in the paper by H. F. Silverman.
8 citations
01 Jan 1978
01 Jan 1978
TL;DR: The Fourier Transform is one of the most common transformations occurring in nature as discussed by the authors, and it is used in a variety of applications such as encephalography, X-ray crystallography, radar, network design, and chemical Fourier transform spectroscopy.
Abstract: The Fourier Transform is one of the most common transformations occurring in nature. Certain features associated with this transform are found used by man in a variety of occupations and applications. For example, Fourier transforms are used in encephalography, X-ray crystallography, radar, network design, and chemical Fourier transform spectroscopy in both nuclear magnetic resonance and infrared analysis. One example of a physical Fourier transform is far-field or Fraunhofer diffraction; this optical phenomenon occurs with narrow slits in dispersive spectroscopy.
08 Dec 1978
TL;DR: In this article, a coherent optical method capable of performing arbitrary two-dimensional linear transformations has been studied, in which transform coefficients are given by two dimensional inner products of the input image and a set of basis functions.
Abstract: A coherent optical method capable of performing arbitrary two-dimensional linear transformations has recently been studied, in which transform coefficients are given by two-dimensional inner products of the input image and a set of basis functions. Since the inner product of two functions is equal to the value of their correlation when there is zero shift between the functions, it is possible to use an optical correlator to solve for the coefficients of the transform. By using random phase masks in the input and the filter planes of the correlator, we have been able to pack many coefficients close together in the output plane, and thus take better advantage of the space-bandwidth product of the optical system. Both the input random phase mask and the spatial filter are computer-generated holographic elements, created by a computer-controlled laser beam scanner. The system can be "programmed" to perform arbitrary two-dimensional linear transformations. For demonstration, the set of two-dimensional Walsh functions was chosen as a transform basis. When the resolution of the Walsh functions was limited to 128 x 128, up to 256 transform coefficients were obtained in parallel. The signal-to-noise and accuracy of the transform coefficients were compared to the theory.© (1978) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
IBM1
01 Jan 1978
TL;DR: Fourier analysis has been widely used in communication theory and electrical engineering for many, many years and is very well treated in text books covering these fields, but Fourier analysis is also very -useful in many other aspects and it is increasingly being used in all branches of the physical science.
Abstract: Fourier analysis has been widely used in communication theory and electrical engineering for many, many years and is very well treated in text books covering these fields, but Fourier analysis is also very -useful in many other aspects and it is increasingly being used in all branches of the physical science.
TL;DR: In this paper, a two-stage approach to the computation of the discrete Fourier transform is described, which can offer a number of distinct advantages: fewer inherent multiplications over a given range, no complex arithmetic for real data, and flexibility of output.
Abstract: A new two-stage approach to the computation of the discrete Fourier transform is described, which, relative to the fast Fourier transform (f.f.t.), can offer a number of distinct advantages: fewer inherent multiplications over a given range, no complex arithmetic for real data, and flexibility of output. The mathematical foundations and related algorithms are discussed in detail and a guide to the advantages over both the f.f.t. and the recently reported Winograd Fourier transform are included.
01 Jan 1978
TL;DR: The technique that is described by Lanzl and Heitmann in "Direct coherent optical Fourier transform of curves,"1 is shown to be a form of area modulation.
Abstract: The technique that is described by Lanzl and Heitmann in "Direct coherent optical Fourier transform of curves,"1 is shown to be a form of area modulation Simpler and equally useful techniques have already been described
07 Dec 1978
TL;DR: The product separable model for the transform coefficient variances forms the basis of a transform coding algorithm and is described and tested on real sampled images.
Abstract: Image transform coding is a technique whereby a sampled image is divided into blocks. A two-dimensional discrete transform of each block is taken, and the resulting transform coefficients are coded. Coding of the transform coefficients requires their quantization and, consequently, a model for the transform coefficient variances that is based in turn on a correlation model for the image blocks. In the proposed correlation model each block of image data is formed by an arbitrary left and right matrix multiplication of a stationary white matrix. One consequence of this correlation model is that the transform coefficient variances are product separable in row and column indexes. The product separable model for the transform coefficient variances forms the basis of a transform coding algorithm. The algorithm is described and tested on real sampled images.© (1978) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Apr 1978
TL;DR: It has been shown that by employing Fermat Number Transforms a hardware butterfly unit becomes relatively simple to implement and significantly increases the speed of the calculation.
Abstract: Two dimensional convolution computed using minicomputers is very time-consuming using Fourier Transform techniques because of the number of complex multiplications required. It has been shown that by employing Fermat Number Transforms a hardware butterfly unit becomes relatively simple to implement and significantly increases the speed of the calculation. Such a hardware unit, suitable for interfacing to a minicomputer, is briefly described. An algorithm is given which removes the need for a matrix transposition. This algorithm is useful on small disc based computers which cannot store the complete input matrix in main memory since a matrix transposition is a time-consuming operation.