Showing papers on "Discrete-time Fourier transform published in 1985"
263 citations
TL;DR: In this paper, a technique reduisant le temps de calcul d'une transformation de Fourier discrete d'un facteur 4 a 6, sans perte significative de precision, is presented.
Abstract: On presente une technique reduisant le temps de calcul d'une transformation de Fourier discrete d'un facteur 4 a 6, sans perte significative de precision
173 citations
TL;DR: RDFT has better performance than DFT in the computation of real convolution because of the reduced number of operations, and the fact that forward and inverse transforms can be implemented with the same signal flowgraph, thereby facilitating hardware and software design.
Abstract: The real discrete Fourier transform (RDFT) corresponds to the Fourier series for sampled periodic signals with sampled periodic frequency responses just as discrete Fourier transform (DFT) corresponds to the complex Fourier series for the same type of signals RDFT has better performance than DFT in data compression and filtering for all signals in the sense that Pearl's measure for RDFT is less than Pearl's measure for DFT by an amount ΔW RDFT also has better performance than DFT in the computation of real convolution because of the reduced number of operations, and the fact that forward and inverse transforms can be implemented with the same signal flowgraph, thereby facilitating hardware and software design
77 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 architecture for a radix- R fast Fourier transform algorithm using a residue number system over Z[\omega] , where \omega is a primitive R th root of unity, is developed; and range and error estimates for this algorithm are derived.
Abstract: A new method is described for computing an N = R^{m} = 2^{\upsilon m} -point complex discrete Fourier transform that uses quantization within a dense ring of algebraic integers in conjunction with a residue number system over this ring The algebraic and analytic foundations for the technique are derived and discussed The architecture for a radix- R fast Fourier transform algorithm using a residue number system over Z[\omega] , where \omega is a primitive R th root of unity, is developed; and range and error estimates for this algorithm are derived
73 citations
TL;DR: This paper deals with the problem of retrieving a finite-extent function from the magnitude of its Fourier transform and presents a brief review of the main results known for both discrete and continuous phase retrieval models giving special emphasis to the algebraic problem of the uniqueness of the solution.
Abstract: In this paper, we deal with the problem of retrieving a finite-extent function from the magnitude of its Fourier transform. This so-called phase retrieval problem will first be posed under its different underlying models. We will present a brief review of the main results known in this area for both discrete and continuous phase retrieval models giving special emphasis to the algebraic problem of the uniqueness of the solution. Several important issues which are yet unresolved will be pointed out and discussed. We will then consider the discrete phase retrieval problem as a special case of a more general problem which consists of recovering a real-valued sequence x from the magnitude of the output of a linear distortion: $| Hx | ( j ),\, j = 1, \cdots ,n$. A number of important results will be obtained for this general setting by means of algebraic-geometric techniques. In particular, the problems of the existence of a solution for phase retrieval, number of feasible solutions, stability of the (essential...
59 citations
46 citations
01 Jan 1985
TL;DR: In this paper, it was shown that bit rates as low as 0.3 bit per pixel can be achieved by encoding a combination of the Fourier phase and amplitude data, which is achieved by low-pass filtering together with a clustering procedure in Fourier plane which seeks out the more important Fourier amplitude coefficients and their associated phases.
Abstract: The scientific advantages are pointed out from the Fourier transform encoding optical and electron microscope images and source data for computer-plotted Fourier-plane holograms, especially if bit compression ratios may be achieved, with comparable reconstructions, at the level found for the adaptive cosine transform. The relative importance is considered of image reconstruction based on the Fourier phase data alone and on combined phase and amplitude data. It is shown that bit rates as low as 0.3 bit per pixel can be achieved by encoding a combination of the Fourier phase and amplitude data. This is achieved by low-pass filtering together with a clustering procedure in the Fourier plane which seeks out the more important Fourier amplitude coefficients and their associated phases.
39 citations
TL;DR: In this article, the analytical and numerical properties of the Fourier transform of a two-center product of exponentially declining functions (exponential-type functions, ETFs) are derived with the help of Fourier convolution theorem and Feynman's identity.
29 citations
TL;DR: In this article, the inverse spectral transform for the periodic Korteweg-de Vries equation is investigated in the limit for small-amplitude waves and the inverse Fourier transform is recovered.
Abstract: The inverse spectral transform for the periodic Korteweg-de Vries equation is investigated in the limit for small-amplitude waves and the inverse Fourier transform is recovered. In the limiting process we find that the widths of the forbidden bands approach the amplitudes of the Fourier spectrum. The number of spectral bands is estimated from Fourier theory and depends explicitly on the assumed spatial discretization in the wave amplitude function (potential). This allows one to estimate the number of degrees of freedom in a discrete (and, therefore, finite-banded) potential. An essential feature of the calculations is that all results for the periodic problem are cast in terms of the infinite-line reflection and transmission coefficientsb(k), a(k). Thus the connection between the whole-line and periodic problems is clear at every stage of the computations.
25 citations
TL;DR: It is shown that prime length discrete Fourier transform algorithms developed by Winograd have considerable structure, and this can be exploited to develop a straightforward design procedure which does not use the Chinese remainder theorem and which includes any allowed permutations.
Abstract: This paper examines the structure of the prime length discrete Fourier transform algorithms that are developed by Winograd's approach. It is shown that those algorithms have considerable structure, and this can be exploited to develop a straightforward design procedure which does not use the Chinese remainder theorem and which includes any allowed permutations. This structure also allows the design of real-data programs and the improvement of the data transfer properties of the prime factor algorithm.
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.
TL;DR: In this article, an alternative discrete Fourier transform algorithm with suppressed aliasing is presented, inspired by work done by Sorella and Ghosh [Rev. Sci. Instrum.
Abstract: An alternative discrete (fast) Fourier transform algorithm with suppressed aliasing is presented. It is inspired by work done by Sorella and Ghosh [Rev. Sci. Instrum. 55, 1348 (1984)]. While using their idea of expanding the time function as a series (as Schutte [Rev. Sci. Instrum. 52, 400 (1981)] and Makinen [Rev. Sci. Instrum. 53, 627 (1982)] have done), it corrects a flaw in their method. The remarkable quality of the calculation is illustrated for an exponential decay by comparing the results to analytical values.
TL;DR: A coherent optical processor composed of two nonsymmetrical Fourier transformers is introduced which allows rotation-variant linear filtering operations and matched filtering and two configurations for such a processor are proposed.
Abstract: In this paper, we consider the properties of the nonsymmetrical Fourier transformation which is space-variant in both rectangular and polar coordinates A coherent optical processor composed of two nonsymmetrical Fourier transformers is introduced This processor allows rotation-variant linear filtering operations and matched filtering Two configurations for such a processor are proposed For certain parameters of both nonsymmetrical Fourier transformers it is possible to obtain a space-invariant processor with both lateral magnifications equal to unity However, introducing any filter operation results in a rotation-variant performance
IBM1
TL;DR: This paper presents a brief review of the algebraic problem of the uniqueness of the solution for both discrete and continuous phase retrieval models and considers the discrete phase retrieval problem as a special case of a more general problem of recovering a real-valued signal x from the magnitude of the output of a linear distortion.
Abstract: In this paper we deal with the problem of retrieving a finite-extent signal from the magnitude of its Fourier transform. We will present a brief review of the algebraic problem of the uniqueness of the solution for both discrete and continuous phase retrieval models. Several important issues which are yet unresolved will be pointed out and discussed. We will then consider the discrete phase retrieval problem as a special case of a more general problem which consists of recovering a real-valued signal x from the magnitude of the output of a linear distortion: |Hx|(j), j = 1, ..., n . An important result concerning the conditioning of this problem will be obtained for this general setting by means of algebraic-geometric techniques. In particular, the problems of the existence of a solution for phase retrieval, conditioning of the problem and stability of the (essentially) unique solution will be addressed.
Patent•
19 Mar 1985TL;DR: The Discrete Bracewell Transform (DBT) as discussed by the authors is a special purpose computer and method of computation for performing an N-length real-number discrete transform, which is performed without need for employing real and imaginary parts, and in efficient embodiments, is executed efficiently and in less time than the Discrete Fourier Transform (DFT).
Abstract: A special purpose computer (35) and method of computation for performing an N-length real-number discrete transform. For a real-valued function f(tau) where tau has the values 0,1,....,(N-1), the Discrete Bracewell Transform (DBT) H (v) is as in (I), where, v = 0,1,....,N-1; cas = cos + sin. The DBT is performed without need for employing real and imaginary parts, and in efficient embodiments, is executed efficiently and in less time than the Discrete Fourier Transform (DFT). The process steps for the original transform and the inverse retransformation are the same.
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
TL;DR: In this article, the covariance function of each property to be simulated is obtained from the variogram function estimated from mapped fracture set data and is typically referenced to the mean vector of the set.
Abstract: Fracture set properties such as orientation, spacing, trace length, and waviness tend to be spatially correlated. These properties can be efficiently simulated by spectral analysis procedures that take advantage of the computational speed of the fast Fourier transform. The covariance function of each property to be simulated is obtained from the variogram function estimated from mapped fracture set data and is typically referenced to the mean vector of the set. Simulation procedures for normally and exponentially distributed data involve generating uncorrelated Fourier coefficients that are assigned proper variance according to the spectral density, which is the Fourier transform of the covariance function. These coefficients are then reverse Fourier transformed to produce simulated set properties that have the desired variance and variogram function.
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.
TL;DR: In this paper, the authors give a description of various techniques for approximate Fourier transformation and present a modified version of the Filon method, and a comparison of different procedure and an anaylysis of the error limits are given.
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: In this article, the maximum entropy spectral analysis was applied to the time domain signals obtained in a Fourier transform mass spectrometer to produce mass spectra that are devoid of the sidelobes present in fast Fourier transformation and exhibit mass resolution that is superior to that obtained by the latter using several thousand data points.
NEC1
TL;DR: This paper proposes a new approach to computing the discrete Fourier transform (DFT) with the power of 2 length using the butterfly structure number theoretic transform (NTT), and an algorithm breaking down the DFT matrix into circular matrices with thePower of 2 size is newly introduced.
Abstract: This paper proposes a new approach to computing the discrete Fourier transform (DFT) with the power of 2 length using the butterfly structure number theoretic transform (NTT). An algorithm breaking down the DFT matrix into circular matrices with the power of 2 size is newly introduced. The fast circular convolution, which is implemented by the NTT based on the butterfly structure, can provide significant reductions in the number of computations, as well as a simple and regular structure, The proposed algorithm can be successively implemented following a simple flowchart using the reduced size submatrices. Multiplicative complexity is reduced to about 21 percent of that by the classical FFT algorithm, preserving almost the same number of additions.
TL;DR: In this article, the Fourier transform is generated optically by means of a periodic array of pinholes (the sampling filter), and the object is illuminated by a monochromatic, coherent plane wave and sampled by the pinhole array.
Abstract: The realization of the Fourier image of a two-dimensional object without using a lens is described. The two-dimensional Fourier transform is generated optically by means of a periodic array of pin-holes (the sampling filter). The object is illuminated by a monochromatic, coherent plane wave and sampled by the pin-hole array. Multiple Fourier images of the object appear in certain planes behind the sampling filter. The simple theory of this phenomenon, together with experimental results, is given.
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.