Showing papers on "Harmonic wavelet transform published in 1980"
Book•
01 Jan 1980
TL;DR: In this paper, Fourier transform is used for spectral analysis of periodical signals and some properties of the spectrum are analyzed, and it is demonstrated that the spectrum is strongly depended of signal duration.
Abstract: This paper analyses Fourier transform used for spectral analysis of periodical signals and emphasizes some of its properties. It is demonstrated that the spectrum is strongly depended of signal duration that is very important for very short signals which have a very rich spectrum, even for totally harmonic signals. Surprisingly is taken the conclusion that spectral function of harmonic signals with infinite duration is identically with Dirac function and more of this no matter of duration, it respects Heisenberg fourth uncertainty equation. In comparison with Fourier series, the spectrum which is emphasized by Fourier transform doesn’t have maximum amplitudes for signals frequencies but only if the signal lasting a lot of time, in the other situations these maximum values are strongly de-phased while the signal time decreasing. That is why one can consider that Fourier series is useful especially for interpolation of nonharmonic periodical functions using harmonic functions and less for spectral analysis. Key-Words — signals, Fourier transform, continuous spectrum properties, Quantum Physics, Fourier series, discrete spectrum
609 citations
TL;DR: In this article, the authors developed a representation for discrete-time signals and systems based on short-time Fourier analysis and showed that a class of linear-filtering problems can be represented as the product of the time-varying frequency response of the filter multiplied by the short time Fourier transform of the input signal.
Abstract: This paper develops a representation for discrete-time signals and systems based on short-time Fourier analysis. The short-time Fourier transform and the time-varying frequency response are reviewed as representations for signals and linear time-varying systems. The problems of representing a signal by its short-time Fourier transform and synthesizing a signal from its transform are considered. A new synthesis equation is introduced that is sufficiently general to describe apparently different synthesis methods reported in the literature. It is shown that a class of linear-filtering problems can be represented as the product of the time-varying frequency response of the filter multiplied by the short-time Fourier transform of the input signal. The representation of a signal by samples of its short-time Fourier transform is applied to the linear filtering problem. This representation is of practical significance because there exists a computationally efficient algorithm for implementing such systems. Finally, the methods of fast convolution age considered as special cases of this representation.
600 citations
233 citations
88 citations
TL;DR: In this paper, the authors proposed a numerical technique for the computation of Fourier transforms using a bilateral expansion of the unknown transformed function with respect to Laguarre functions using trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform.
Abstract: In this paper we propose a numerical technique for the computation of Fourier transforms. It uses a bilateral expansion of the unknown transformed function with respect to Laguarre functions. The expansion coefficients are obtained via trigonometric interpolation and may be computed very efficiently by means of the Fast Fourier Transform. The convergence of the algorithm is analyzed and numerical results are presented which confirm that it works well.
27 citations
TL;DR: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions provides sufficient justification for usage of Walsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
Abstract: A basis for the processing of EEG signals using the discrete, orthogonal set of Walsh functions is presented. The Walsh power spectrum is examined from the point of view of its statistical properties, especially as it relates to spectral resolution. Features, selected from the spectrum of sleep EEG data are compared to corresponding Fourier features. Each feature set is used to classify the data using a minimum-distance clustering algorithm. The results show that the Walsh spectral features classify the data in much the same way as the Fourier spectral features. This provides sufficient justification for usage ofWalsh spectral features in place of Fourier spectral features, enabling one to take advantage of the vast computational superiority of the fast Walsh transform over the fast Fourier transform.
22 citations
01 May 1980
TL;DR: Using the variance measure of duration, it was shown that the duration of a signal is composed of two terms as mentioned in this paper, i.e., the duration in the zero-phase equivalent signal, and the variance of the phase derivative of the Fourier transformed signal.
Abstract: Using the variance measure of duration, it is shown that the duration of a signal is composed of two terms. The first term is the duration of the zero-phase equivalent signal, and the second term is the variance of the phase derivative of the Fourier transformed signal.
18 citations
13 citations
TL;DR: A simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.
Abstract: A simple, yet complete and detailed description of the fast Fourier transform for general N is given with the aim of making the underlying idea quite apparent. To help with this didactic goal, a simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.
12 citations
TL;DR: Theory and practice of an optical ambiguity processor based on space-variant joint Fourier transform holography and a different technique of implementing the matched filter correlator concept advanced by Vander Lugt are presented.
Abstract: Theory and practice of an optical ambiguity processor based on space-variant joint Fourier transform holography are presented. The approach evolves from the joint Fourier transform optical correlator concept, which represents a different technique of implementing the matched filter correlator concept advanced by Vander Lugt. Experimental demonstration using photographic film for signal recording and the thermoplastic device for hologram recording will be reported.
11 citations
IBM1
TL;DR: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm.
Abstract: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.
DOI•
01 May 1980
TL;DR: In this article, the power spectra may be computed via a discrete fourier transform with severely rounded-off trigonometric terms, and recently the ultimate round-off to rectangular waves has been proposed.
Abstract: Power spectra may be computed via a discrete fourier transform with severely rounded-off trigonometric terms, and recently the ultimate round-off – that is to rectangular waves – has been proposed.1 A comparison is made between this and a 3 level round-off, +1, −1 and 0.
TL;DR: An all-spherical-mirror system for applications in coherent image processing is described and analyzed and the Fourier transform properties of this one-to-one system are acceptable for many applications.
Abstract: An all-spherical-mirror system for applications in coherent image processing is described and analyzed. This one-to-one system is panchromatic and can be made to have minimal cosmetic defects. Such a system offers advantages such as multiple wavelength operations and the introduction of minimal scattering noise into the final image. A sample design that is diffraction-limited (for f/8) over the entire area of a standard 35-mm slide is given. The Fourier transform properties of this system are acceptable for many applications.
TL;DR: A description of a new multichannel time-integrating optical Fourier transform chirp-Z system and a discussion of its use in Fourier spectroscopy signal processing are described.
Abstract: A review of multichannel long integration time, optical Fourier transform techniques for advanced Fourier spectroscopy systems is followed by the description of a new multichannel time-integrating optical Fourier transform chirp-Z system and a discussion of its use in Fourier spectroscopy signal processing.
TL;DR: By introducing a number of zeros as the elements in the transform matrices, a modified version of the transforms can be computed efficiently and can be used in the general area of information processing.
01 Nov 1980
TL;DR: This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values.
Abstract: Sampling and reconstruction of band-limited functions are fundamental problems in communications and signal processing. This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values. This work can be viewed as yet another comment and extension on the sampling theorem.
IBM1
TL;DR: A new fast computation algorithm for multidimensional DFTs by using a single polynomial transform and auxiliary calculations and all calculations are performed with a reduced number of additions by using FFT-type algorithms.
Abstract: In this paper, we introduce a new fast computation algorithm for multidimensional DFTs. This method maps efficiently some multidimensional DFTs into one-dimensional DFTs by using a single polynomial transform and auxiliary calculations. The polynomial transform is computed without multiplications and all calculations are performed with a reduced number of additions by using FFT-type algorithms. The relationship with earlier polynomial transform approaches is explored and it is shown that the new method yields a simpler structure at the expense of a slight increase in number of arithmetic operations. Various techniques for reducing the auxiliary calculations are investigated and schemes which combine different polynomial transform techniques are presented.
TL;DR: A technique based on the recently developed rectangular transforms is proposed for computing the autocorrelation function of a data sequence, which is computationally more efficient than Rader's algorithm using the fast Fourier transform and the Winograd-Fourier transform algorithm when the number of desired lag values is smaller than 30.
Abstract: A technique based on the recently developed rectangular transforms is proposed for computing the autocorrelation function of a data sequence. The refinements suggested with the technique make it computationally more efficient than Rader's algorithm using the fast Fourier transform and the Winograd-Fourier transform algorithm, when the number of desired lag values is smaller than 30. However, the technique as such can be used for higher values.
09 Apr 1980
TL;DR: A procedure is described for the computation of the discrete cosine transform (DCT) via the use of the arcsine transform, which eliminates time-consuming multiplications, the DCT being accomplished with only additions and table lookups.
Abstract: A procedure is described for the computation of the discrete cosine transform (DCT) via the use of the arcsine transform. The approach eliminates time-consuming multiplications, the DCT being accomplished with only additions and table lookups. While a fast Fourier transform (FFT) approach to computing the DCT involves on the order of N\log_{2}2N "butterfly" computations to evaluate all N coefficients, the arcsine method requires only 4N - 1 real additions and 2N table lookups to evaluate each DCT coefficient. Thus, for applications in which M coefficients are desired or when N is reasonably small (say, N \leq 256 ), the arcsine approach is favored over that of the FFT. Some approaches to hardware implementation are presented.
01 Jan 1980
TL;DR: The n-dimensional tomography problem is solved in closed form by means of the Fast Fourier Transform algorithm, thus requiring of the order of Nlog2N complex arithmetic add-multiply operations, where N is the number of data points specifying the problem.
Abstract: The n-dimensional tomography problem is solved in closed form by means of the Fast Fourier Transform algorithm, thus requiring of the order of Nlog2N complex arithmetic add-multiply operations, where N is the number of data points specifying the problem; vis-a-vis the conventional Radon transform solution which requires of the order of N 2 operations The extention from two-dimensional to three-dimensional tomography is achieved in a simple and natural fashion
TL;DR: An efficient method of achieving flexibility in the length of discrete convolutions, computed using Fourier and Fourier-like fast transform algorithms, is described and extended to discrete multidimensional convolutions computed using polynomial transforms.
TL;DR: Physically speaking, the edge effects become insignificant for large enough blocks, and these large blocks are entirely consistent with the aim of encoding optimally large amounts of data in a DFT.
Abstract: Codes. New York: Elsevier North-Holland, 1977. posed on the N-sequence, making the sequence u(k) wide-sense 121 R. J. Lechner, “Harmonic analysis of switching functions,” in Recent stationary with covariance relationships given in (2).’ Moreover, Developments in Switching Theoy, A. Mukhopadhyay, Ed. New York: in the limit of large N, with or without the random shift, as Academic, 1971, pp. 122-230. [31 M. A. Harrison, “Counting theorems and their applications to classificastated in the paper the eigenvalue distributions of K(p) and tion of switching functions,” in Recent Dmelopments in Switching Theory, R,(p) approach each other. That is all that is required for A. Mukhopadhyay, Ed. New York: Academic, 1971, pp. 86-122. deriving coding bounds. h,(p) is the appropriate circulant approximation to the Toeplitz form R,(p). Physically speaking, the edge effects become insignificant for large enough blocks. These large blocks are entirely consistent with the aim of encoding optimally large amounts of data in a DFT. Optimal source coding, as addressed in this paper, requires large N.
TL;DR: In this article, the relations between bandlimited one-dimensional object-plane fields which yield the same intensity distribution in the Fraunhofer (Fourier transform) plane were investigated.
Abstract: We consider the relations between bandlimited one-dimensional object-plane fields which yield the same intensity distribution in the Fraunhofer (Fourier transform) plane. In the case in which the Fraunhofer-plane fields differ by the conjugation of a single zero, a simple relation results which appears useful in phase-retrieval algorithms.
TL;DR: In this article, a programmable memory correlator based on the acousto-photorefractive effect has been demonstrated using two distinct writing modes and writing-laser wavelengths.
Abstract: A number of signal-processing devices have been developed that use the Bragg interaction between laser beams and surface acoustic waves in transparent delay lines. Convolvers and correlators having time-bandwidth products of up to 10,000 have been constructed and have been used to obtain signal-to-noise enhancement of signals buried in noise. A real-time, continuous Fourier transformer has been achieved. Initial results have been obtained in performing a discrete Fourier transform using an acoustooptic implementation of the triple-product convolver. A programmable memory correlator based on the acousto-photorefractive effect has been demonstrated using two distinct writing modes and writing-laser wavelengths.
TL;DR: In this paper, the Erikson intzgrated acoustic array system was modified to include acoustical holography, and the authors derived the system function which showed that the holographic processing is equivalent to standard sonar beamforming.
Abstract: We make an analysiv and feasibility studies of a new holographic system. We modify Erikson intzgrated acoustic array system to include acoustical holography. The advantage of using acoustical holography is to get three-dimensional images. We first have a system description based on that of Granger digital beamforming sonar system. Our system consists of: a hydrophone array, zn acoustic projector, a channel processor, a microprocessor system controller, a beamformer, and a storage display. The acoustic projector isonifies objects. We derive the system function which shows that the holographic processing is equivalent to standard sonar beamforming. For the holographic processing, we follow the Fourier transform method. This is sonar beamforming. We obtain fast holographic processing algorithms. The beam forminq is performed digitally using the Discrete Fourier Transform. A Fast Fourier Transform program was written using an in-plane algorithm with natural order input and scrambled output. We write ...