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Showing papers on "Non-uniform discrete Fourier transform published in 1985"



Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: The relationship among different versions of DWT and their relation with the discrete Fourier transform (DFT) are given and Convolution theorems represented by different version of the DWT are derived.

120 citations


Proceedings ArticleDOI
26 Apr 1985
TL;DR: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented and a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.
Abstract: A fast radix-2 two dimensional discrete cosine transform (DCT) is presented. First, the mapping into a 2-D discrete Fourier transform (DFT) of a real signal is improved. Then an usual polynomial transform approach is used in order to map the 2-D DFT into a reduced size 2-D DFT and one dimensional odd DFT's. Finally, optimized odd DFT algorithms for real signals are developped. All together, a reduction of more than 50% in the number of multiplications and a comparable amount of additions is obtained in comparison to other algorithm.

117 citations


Journal ArticleDOI
TL;DR: An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transform.
Abstract: An efficient algorithm based on real matrix decomposition is developed for computing a class of sinusoidal transforms, that include the discrete Fourier and cosine transform

96 citations


Journal ArticleDOI
O. Ersoy1
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


Journal ArticleDOI
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


Journal ArticleDOI
TL;DR: It is shown that an elegant way to represent the signal directly in terms of the sample values of the sliding-window spectrum, is in the form of Gabor's signal representation, and it is shown how the window and the reciprocal window are related.
Abstract: The short-time Fourier transform of a discrete-time signal, which is the Fourier transform of a "windowed" version of the signal, is interpreted as a sliding-window spectrum. This sliding-window spectrum is a function of two variables: a discrete time index, which represents the position of the window, and a continuous frequency variable. It is shown that the signal can be reconstructed from the sampled sliding-window spectrum, i.e., from the values at the points of a certain time-frequency lattice. This sampling lattice is rectangular, and the rectangular cells occupy an area of 2π in the time-frequency domain. It is shown that an elegant way to represent the signal directly in terms of the sample values of the sliding-window spectrum, is in the form of Gabor's signal representation. Therefore, a reciprocal window is introduced, and it is shown how the window and the reciprocal window are related. Gabor's signal representation then expands the signal in terms of properly shifted and modulated versions of the reciprocal window, and the expansion coefficients are just the values of the sampled sliding-window spectrum.

62 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


Journal ArticleDOI
TL;DR: In this paper, a relationship between the Fourier transform of a potential field at the Earth's surface and the transform of the inducing source distribution is derived, which can be used to determine all possible source distributions compatible with the data.
Abstract: A relationship is derived between the Fourier transform of a potential field at the Earth’s surface and the transform of the inducing source distribution. The Fourier transform of the field is the Laplace transform of the source distribution spectrum when the Laplace transform variable p is equal to the wavenumber. This relationship can be used to determine all possible source distributions compatible with the data. The solution is the superposition of a particular solution to an inhomogeneous problem and of the general solution to the homogeneous problem (i.e., for which the field vanishes at the surface). Source distribution can be expanded into a set of known functions; coefficients of the expansion are determined by solving a system of linear equations. Physical constraints can be introduced to restrict the variation range of the coefficients of expansion. Two examples are presented to illustrate the method: a synthetic gravity profile and a heat flow profile are inverted to determine density or heat ...

27 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the infinite dimensional integral equation for the stochastic Fourier transform of the surface current can be reduced to the three dimensions associated with the random surface height and slopes.
Abstract: Further developments in the application of the stochastic Fourier transform approach (SFTA) to random surface scattering are presented. It is first shown that the infinite dimensional integral equation for the stochastic Fourier transform of the surface current can be reduced to the three dimensions associated with the random surface height and slopes. A three-dimensional integral equation of the second kind is developed for the average scattered field in stochastic Fourier transform space using conditional probability density functions. Various techniques for determining the transformed current (and, subsequently, the incoherent scattered power) from the average scattered field in stochastic Fourier transform space are developed and studied from the point of view of computational suitability. The case of vanishingly small surface correlation length is reexamined and the SFTA is found to provide erroneous results for the average scattered field due to the basic failure of the magnetic field integral equation (MFIE) in this limit.

Journal ArticleDOI
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.

Book ChapterDOI
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.

Journal ArticleDOI
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.

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.

Journal ArticleDOI
J. Sanz1, T. Huang
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.

Journal ArticleDOI
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


Journal ArticleDOI
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.

Proceedings ArticleDOI
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.

Journal ArticleDOI
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.

Journal ArticleDOI
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.



Journal ArticleDOI
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.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: It is shown that the real formalism of the discrete Fourier transform is basically equivalent to the direct sum of the other two transforms, with modifications in the pre- and post-computations with the data vector.
Abstract: The relationship among a real formalism of the discrete Fourier transform, discrete sine transform, and discrete symmetric cosine transform is discussed. It is shown that the real formalism of the discrete Fourier transform is basically equivalent to the direct sum of the other two transforms, with modifications in the pre- and post-computations with the data vector.

Journal ArticleDOI
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.

Journal ArticleDOI
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.

Proceedings ArticleDOI
11 Jul 1985
TL;DR: The DHT coding system incorporated with a human visual system model is studied and this system offers about the same subjective image quality as a straight-forward DCT coding system.
Abstract: The discrete Hartley transform (DHT) and its fast algorithm were introduced recently. One of the advantages of the DHT is that the forward and inverse transforms are of the same form except for a normalization constant. Therefore, the forward and the inverse transform can be implemented by the same subroutine or hardware when the normalization constant is properly taken care of. In this paper, the applications of the DHT to image compression are studied. The distribution of the DHT coefficients is tested using the Kolmogorov-Smirnov goodness-of-fit test. The compression efficiency of DHT coding is found to be about the same as discrete Fourier transform (DFT) coding. The DHT coding system incorporated with a human visual system model is also studied and this system offers about the same subjective image quality as a straight-forward DCT coding system.