Showing papers on "Harmonic wavelet transform published in 1985"
263 citations
TL;DR: In this paper, it was shown that the Fourier transform belongs to Lq(r, da) for a certain natural measure on the su.rface of a circular cone in R3.
Abstract: Let r be the su.rface of a circular cone in R3. We show that if 1 < p < 4/3, 1/q = 3(1-1/p) and f E LP(R3), then the Fourier transform of f belongs to Lq(r, da) for a certain natural measure a on r. Following P. Tomas we also establish bounds for restrictions of Fourier transforms to conic annuli at the endpoint p = 4/3, with logarithmic growth of the bound as the thickness of the annulus tends to zero.
77 citations
TL;DR: The discrete Hartley transform as mentioned in this paper is a new tool for the analysis, design and implementation of digital signal processing algorithms and systems, which is strictly symmetric concerning the transformation and its inverse.
Abstract: The discrete Hartley transform is a new tool for the analysis, design and implementation of digital signal processing algorithms and systems. It is strictly symmetrical concerning the transformation and its inverse. A new fast Hartley transform algorithm has been developed. Applied to real signals, it is faster than a real fast Fourier transform, especially in the case of the inverse transformation. The speed of operation for a fast convolution can thus be increased.
46 citations
01 Dec 1985
TL;DR: In this paper, it was shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than using a complex Fast Fourier Transform.
Abstract: It is shown that the DFT of a real sequence, formed via the Fast Hartley Transform, can be computed at most only 2 times faster than by using a complex Fast Fourier Transform. However, more sophisticated FFT algorithms exist which give the same speedup factor. A simple FHT subroutine is presented to illustrate the similarity of the FHT and FFT butterflies in their simplest forms.
27 citations
TL;DR: In this paper, a new algorithm, by means of which noise may be extracted from electrochemical measurements, is presented, explained and applied, in order to extract the noise from the measurements.
23 citations
TL;DR: This chapter has described the mathematical basis of the fast Fourier transform as applied to the calculation of crystallographic Fourier syntheses, and program organizations have been presented for performing general crystallography Fourier transforms on computer systems ranging from the very largest systems down to minicomputers.
Abstract: This chapter has described the mathematical basis of the fast Fourier transform as applied to the calculation of crystallographic Fourier syntheses. The relationship between real space and reciprocal space symmetry operators has been described. Finally, program organizations have been presented for performing general crystallographic Fourier transforms on computer systems ranging from the very largest systems down to minicomputers. Programs are available from the author, written in FORTRAN IV and in Ratfor, which are suitable for building blocks in these program designs.
23 citations
01 Jan 1985
TL;DR: This chapter is for establishing the basis of this combined approach in dealing with computer tomography, computer holography and hologram matrix radar.
Abstract: The Fast Fourier Transform (FFT) is one of the most frequently used mathematical tools for digital signal processing. Techniques that use a combination of digital and analogue approaches have been increasing in numbers. This chapter is for establishing the basis of this combined approach in dealing with computer tomography, computer holography and hologram matrix radar.
22 citations
Patent•
19 Mar 1985
TL;DR: In this article, a method and apparatus for representing a multi-dimensional, finite extent information containing signal in a locally sensitive, frequency domain representation employs transforming the digital signal using a Short Space Fourier transform having overlapping basis functions.
Abstract: A method and apparatus for representing a multi-dimensional, finite extent, information containing signal in a locally sensitive, frequency domain representation employs transforming the digital signal using a Short-Space Fourier transform having overlapping basis functions. The theory and application of the Short-Space Fourier transform provide, in one particular application of picture image transmission, an improved image quality over previously employed block transform coding methods and apparatus. A particularly preferred window function for use in connection with image signal processing is the multi-dimensional sinc function which has the unique advantage of a rectangular bandpass signal in the frequency domain.
20 citations
TL;DR: A hybrid system has been constructed to perform the complex Fourier transform of real 2-D data based on the Radon transform, which is performed with SAW filters via the chirp transform algorithm.
Abstract: A hybrid system has been constructed to perform the complex Fourier transform of real 2-D data The system is based on the Radon transform; ie, operations are performed on 1-D projections of the data The projections are derived optically from transmissive or reflective objects, and the complex Fourier transform is performed with SAW filters via the chirp transform algorithm The real and imaginary parts of the 2-D transform are produced in two bipolar output channels
16 citations
TL;DR: In this article, an extension of the Discrete Fourier Transform (DFT) is defined as a linear combination of the forward and inverse DF's of a sequence, and the coefficients of the linear combinations can be chosen to define a real transform for a real sequence.
Abstract: An extension of the Discrete Fourier Transform (DFT) is defined as a linear combination of the forward and inverse DF's of a sequence. The coefficients of the linear combinations can be chosen to define a real transform for a real sequence. A fast algorithm can be used to compute the transform for a sequence whose length is a power of two.
26 Apr 1985
TL;DR: A new multidimensional Hartley transform is defined and a vector-radix algorithm for fast computation of the transform is developed that is shown to be faster (in terms of multiplication and addition count) compared to other related algorithms.
Abstract: A new multidimensional Hartley Transform is defined and a vector-radix algorithm for fast computation of the transform is developed. The algorithm is shown to be faster (in terms of multiplication and addition count) compared to other related algorithms.
TL;DR: In this article, the authors proposed a method for phase retrieval from the observed modulus at the Fourier transform plane of an object in two dimensions, which consists of the logarithmic Hilbert transform in one dimension.
Abstract: This paper proposes a method for solving the phase retrieval problem from the observed modulus at the Fourier transform plane of an object in two dimensions. This method consists of the logarithmic Hilbert transform in one dimension, based on the reduction by the sampling theorem of the two-dimensional (2-D) Fourier transform of the object to the one-dimensional (1-D) Fourier transform of an effective object function. The usefulness of the method is shown in computer simulation studies of the phase retrieval from the 2-D modulus at the Fourier transform plane, for the 2-D real and positive objects. The zero information in the complex lower half-plane must be obtained from another observation for the phase evaluation using the logarithmic Hilbert transform.
TL;DR: In this paper, the authors adapt the split-step Fourier transform (SSFFT) algorithm to the problem of calculating the energy band diagrams and associated wavefunctions of solid-state lattices.
Abstract: The authors adapt the split-step Fourier transform (SSFFT) algorithm to the problem of calculating the energy band diagrams and associated wavefunctions of solid-state lattices. The analysis is accompanied with a study of the accuracy of the technique in several test cases. They conclude from these calculations that the SSFFT method can be applied to a wide variety of solid-state physical problems.
TL;DR: The new SFIT algorithm gives results which are much closer to the analytic Fourier transform for discrete signals, Especially in the calculation of the phase spectra considerable improvement is obtained.
TL;DR: In this paper, the complete Fast Fourier Transform (FFT) was applied to an analytical waveform in order to discuss its accuracy and analyze the associated errors, and an experimentally acquired waveform for demonstration purposes.
Abstract: The complete Fast Fourier Transform (FFT) technique for the computation of the spectrum amplitude of step-like waveforms is presented in this paper. The complete FFT technique offers an enhanced resolution, and produces a dc and equally spaced harmonic components for the spectrum amplitude. The technique is applied to an analytical waveform in order to discuss its accuracy and analyze the associated errors. It is also applied to an experimentally acquired waveform for demonstration purposes.
TL;DR: In this paper, the Radon transform is carried out with a rotating prism and a flying-line scanner, while the one-dimensional Fourier transforms are performed with surface acoustic wave filters.
Abstract: The well-known central-slice, or projection-slice, theorem states that the Radon transform can be used to reduce a two-dimensional Fourier transform to a series of one-dimensional Fourier transforms. In this paper we describe a practical system for implementing this theorem. The Radon transform is carried out with a rotating prism and a flying-line scanner, while the one-dimensional Fourier transforms are performed with surface acoustic wave filters. Both real and imaginary parts of the complex Fourier transform can be obtained. A method of displaying the two-dimensional Fourier transforms is described, and representative transforms are shown. Application of this approach to Labeyrie speckle interferometry is demonstrated.
TL;DR: The generalized structure of the orthogonal transformation relation by using the vector space model has been presented in this paper, which can be used for potential extension or modification of the existing orthogonality transformations.
Abstract: The introduction of an orthogonal transformation pair is generally begun with the definition, followed by the proofs of the orthogonality and the associated Parseval's relation shown as one of the properties of the transform pair. This procedure has to be repeated for various transform relations. In this article, we present the generalized structure of the orthogonal transformation relation by using the vector space model. This method enables us to visualize the similarities as well as the differences among the orthogonal transformations used in signal processing. In addition to the examples, transform pairs including Fourier transform, Fourier series, discrete-time Fourier transform (DFI), Hankel transform, Hilbert transform, the sampling theorem, Legendre, Laguerre, Hermite, and Chebychev decomposition methods are tabulated and shown as special cases of the generalized model. This approach can be used for potential extension or modification of the existing orthogonal transformations. It can be also applied to the design of special-purpose orthogonal mapping techniques.
TL;DR: In this article, the split-step fast Fourier transform (SSFFT) algorithm is used to calculate the energy band diagrams and associated wavefunctions for essentially arbitrary solid-state lattices.
01 Apr 1985
TL;DR: A new Hankel transform algorithm designed for uniformly sampled data is presented, which is the most elementary of several algorithms derived from the Tchebycheff and Fourier transforms.
Abstract: A new Hankel transform algorithm designed for uniformly sampled data is presented. Although data of this type occur frequently, previous algorithms require interpolations and/or numerical evaluations of Bessel functions. These difficulties can be avoided by using a Tchebycheff transform followed by a Fourier transform. The basic structure and performance of any Hankel transform algorithm derived from this two-step process depends on the combined results from the numerical methods used to compute the Tchebycheff and Fourier transforms. The algorithm presented here is the most elementary of several algorithms derived from this procedure. Examples are presented and errors associated with the results are discussed.
01 Apr 1985
TL;DR: A new relationship between Filter/Detectors and the Short-Time Fourier Transform magnitude is derived and provides a common basis for comparison of speech spectrograms, the sliding Discrete Fourier transform, average power spectrum estimation techniques, perception-based speech analysis systems, and channel vocoders.
Abstract: A new relationship between Filter/Detectors and the Short-Time Fourier Transform magnitude is derived. The result provides a common basis for comparison of speech spectrograms, the sliding Discrete Fourier Transform, average power spectrum estimation techniques, perception-based speech analysis systems, and channel vocoders.
TL;DR: In this paper, an expression for the standard deviation associated with the estimation of the log modulus and phase of the Fourier transform of a photon-limited intensity distribution was derived.
01 Jan 1985
TL;DR: A bit-level systolic array system is proposed for the Winograd Fourier Transform Algorithm and it is demonstrated how long transforms can be implemented with components designed to perform short length transforms.
Abstract: A bit-level systolic array system is proposed for the Winograd Fourier Transform Algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest neighbour interconnections, regularity and high throughput. The short interconnections in this method contrast favourably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform short length transforms. These components build into longer transforms preserving the regularity and structure of the short length transform design.
TL;DR: In this paper, the performance of a Fourier transform data transmission system in white Gaussian noise was evaluated for various quantisation widths and transform sizes. But the performance was not analyzed for the case of white Gaussians.
Abstract: Results on the performance of a Fourier transform data transmission system in white Gaussian noise are presented for various quantisation widths and transform sizes.
01 Jan 1985
TL;DR: Several techniques are described, using MACSYMA, applicable for computing transforms, correlation functions and power spectra that are faster than radix-2 FFTs and the possibility of a quasi-analytic B-spline method for computing transformations is mentioned.
Abstract: The general problem of computing the power spectrum from N samples of a signal x(t) by Fourier Transform (FT) methods is considered. It is commonly, and erroneously, believed that fast (FFT) methods apply efficiently only when N is a power of 2. Instead, I describe several techniques, using MACSYMA, applicable for computing transforms, correlation functions and power spectra that are faster than radix-2 FFTs. I also mention the possibility of a quasi-analytic B-spline method for computing transforms. For these problems, I will illustrate certain systematic techniques to generate optimized FORTRAN code from MACSYMA.
01 Jan 1985
TL;DR: In this article, the DT Fourier series and the Discrete Fourier Transform (DFT) have been investigated in the context of Discrete-Time Fourier Filters.
Abstract: This chapter contains sections titled: Introduction, Properties of the Discrete-Time Fourier Transform, Discrete-Time Filters, The DT Fourier Series and the Discrete Fourier Transform (DFT), Properties of the DT Fourier Series and the DFT, Summary, Appendix To Chapter 18, Exercises for Chapter 18, Problems for Chapter 18