Showing papers on "Discrete sine transform published in 1983"
TL;DR: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable and promises to speed up Fourier-transform calculations.
Abstract: The discrete Hartley transform (DHT) resembles the discrete Fourier transform (DFT) but is free from two characteristics of the DFT that are sometimes computationally undesirable. The inverse DHT is identical with the direct transform, and so it is not necessary to keep track of the +i and −i versions as with the DFT. Also, the DHT has real rather than complex values and thus does not require provision for complex arithmetic or separately managed storage for real and imaginary parts. Nevertheless, the DFT is directly obtainable from the DHT by a simple additive operation. In most image-processing applications the convolution of two data sequences f1 and f2 is given by DHT of [(DHT of f1) × (DHT of f2)], which is a rather simpler algorithm than the DFT permits, especially if images are. to be manipulated in two dimensions. It permits faster computing. Since the speed of the fast Fourier transform depends on the number of multiplications, and since one complex multiplication equals four real multiplications, a fast Hartley transform also promises to speed up Fourier-transform calculations. The name discrete Hartley transform is proposed because the DHT bears the same relation to an integral transform described by Hartley [ HartleyR. V. L., Proc. IRE30, 144 ( 1942)] as the DFT bears to the Fourier transform.
465 citations
TL;DR: In this paper, a new scheme is presented for the determination of the parameters that characterize a multifrequency signal, where the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation.
Abstract: A new scheme is presented for the determination of the parameters that characterize a multifrequency signal. The essential innovation is that the signal is weighted before the discrete Fourier transform (DFT) is calculated from which the frequencies and complex amplitudes of the various components of the signal are obtained by interpolation. It is shown that by using the Hanning window for tapering substantial improvements are achieved in the following respects: i) more accurate results are obtained for interpolated frequencies, etc., ii) harmonic interference is much less troublesome even if many tones with comparable strengths are present in the spectrum, iii) nonperiodic signals can be handled without an a priori knowledge of the tone frequencies. The stability of the new method with respect to noise and arithmetic roundoff errors is carefully examined.
440 citations
Book•
11 Feb 1983
TL;DR: This chapter discusses Fourier Series and Fourier Transform Algorithms, Discrete Fourier Transforms, DFT Filter Shapes and Shaping, and Spectral Analysis Using the FFT.
Abstract: Preface. Acknowledgments. List of Acronyms. Notation. Introduction. Fourier Series and Fourier Transform. Discrete Fourier Transforms. Fast Fourier Transform Algorithms. FFT Algorithms That Reduce Multiplications. DFT Filter Shapes and Shaping. Spectral Analysis Using the FFT. Walsh-Hadamard Transforms. The Generalized Transform. Discrete Orthogonal Transforms. Number Theoretic Transforms. Appendix. References. Index.
320 citations
Book•
01 Jan 1983
TL;DR: This paper presents a meta-modelling framework for system modeling and analysis in the Time Domain of Discrete-Time Signals and Systems using the Fourier Transform, and some of the techniques used in this framework are described.
Abstract: 1. Signal and System Modeling Concepts. 2. System Modeling and Analysis in the Time Domain. 3. The Fourier Series. 4. The Fourier Transform and Its Applications. 5. The Laplace Transformation. 6. Applications of the Laplace Transform. 7. State-Variable Techniques. 8. Discrete-Time Signals and Systems. 9. Analysis and Design of Digital Filters. 10. The Discrete Fourier Transform and Fast Fourier Transform Algorithms. Appendix A: Comments and Hints on Using MATLAB. Appendix B: Functions of a Complex Variable--Summary of Important Definitions and Theorems. Appendix C: Matrix Algebra. Appendix D: Analog Filters. Appendix E: Mathematical Tables. Appendix F: Answers to Selected Problems. Appendix G: Index of MATLAB Functions Used. Index.
201 citations
TL;DR: Under certain conditions it is shown that discrete-time sequences carry redundant information which then allow for the detection and correction of errors.
Abstract: The relationship between the discrete Fourier transform and error-control codes is examined. Under certain conditions we show that discrete-time sequences carry redundant information which then allow for the detection and correction of errors. An application of this technique to impulse noise cancellation for pulse amplitude modulation transmission is described.
185 citations
TL;DR: Some corrections are made for the original paper "A fast computational algorithm for the discrete cosine transform," 1 which contains some errors of indexes and of multiplication factors.
Abstract: Some corrections are made for the original paper "A fast computational algorithm for the discrete cosine transform," 1 which contains some errors of indexes and of multiplication factors.
51 citations
TL;DR: In this article, it was shown that the set of signals whose z transform is reducible is contained in the zero set of a certain multidimensional polynomial, and the zero-measure property is obtained as a simple byproduct.
Abstract: The problem of Fourier-transform phase reconstruction from the Fourier-transform magnitude of multidimensional discrete signals is considered. It is well known that, if a discrete finite-extent n-dimensional signal (n ≥ 2) has an irreducible z transform, then the signal is uniquely determined from the magnitude of its Fourier transform. It is also known that this irreducibility condition holds for all multidimensional signals except for a set of signals that has measure zero. We show that this uniqueness condition is stable in the sense that it is not sensitive to noise. Specifically, it is proved that the set of signals whose z transform is reducible is contained in the zero set of a certain multidimensional polynomial. Several important conclusions can be drawn from this characterization, and, in particular, the zero-measure property is obtained as a simple byproduct.
41 citations
TL;DR: New algorithms for DFT(p; k), the discrete Fourier transform on a k-dimensional data set with p points along each array, where p is a prime are exhibited.
Abstract: We exhibit new algorithms for DFT(p; k), the discrete Fourier transform on a k-dimensional data set with p points along each array, where p is a prime. At a cost of additions only, these algorithms compute DFT(p; k) with (pk- 1)/(p - 1) distinct DFT(p; 1) computations.
34 citations
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TL;DR: An approximation to the discrete cosine transform (DCT), called the C-matrix transform (CMT), has been developed by Jones et al. as mentioned in this paper for N = 8.
Abstract: An approximation to the discrete cosine transform (DCT), called the C-matrix transform (CMT), has been developed by Jones et al. [3] for N = 8. This is extended to N = 16 and 32 and its performance is compared with the DCT based on some standard criteria. CMT is computationally simpler as it involves only integer arithmetic. It has potential in signal processing applications because of its closeness to the DCT.
28 citations
14 Apr 1983
TL;DR: The performance of this new version of the DCT for digital filtering and transform coding is compared to the old version of DCT with various criteria; i.e., variance distribution, residual correlation, Wiener filtering, and maximum-reducible-bits.
Abstract: A new version of the discrete cosine transform (DCT) is introduced. The performance of this new version of the DCT for digital filtering and transform coding is compared to the old version of DCT [1] with various criteria; i.e., variance distribution, residual correlation, Wiener filtering, and maximum-reducible-bits.
25 citations
TL;DR: An approximation to the discrete cosine transform (DCT) called the C -matrix transform (CMT) has been developed by Jones et al. as mentioned in this paper for N = 8 and its performance is compared with the DCT based on some standard criteria.
TL;DR: Two VLSI structures for the computation of the discrete Fourier transform are presented; the first is a pipeline working concurrently on different transforms, and it matches within a constant factor the theoretical area-time lower bounds.
Abstract: Two VLSI structures for the computation of the discrete Fourier transform are presented. The first structure is a pipeline working concurrently on different transforms. It is shown that it matches, within a constant factor, the theoretical lower bounds for area versus data rate. The second structure is a simple modification of the first one; it works on a single transform at a time, and it matches within a constant factor the theoretical area-time lower bounds.
01 Oct 1983
TL;DR: It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently and the total number of real multiplications for a length-P DFT is reduced to (P — 1).
Abstract: Indexing terms: Mathematical techniques, Transforms Abstract: It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shift adds per point is approximately the same as the number of additions required for FFT algorithms.
28 Nov 1983
TL;DR: Discrete fourier transform is represented as a real transform through using number groups and removing redundancy, and is further written in terms of (skew) circular correlations, which can be implemented by fast correlation techniques.
Abstract: Discrete fourier transform is represented as a real transform through using number groups and removing redundancy. The resulting configuration is further written in terms of (skew) circular correlations, which can be implemented by fast correlation techniques. The number of data points considered is a power of 2, even though the method can be generalized to any number of data points.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: This paper investigates the use of polynomial transforms for the implementation of uniform digital bandpass filter banks and shows that this technique reduces significantly the number of arithmetic operations when compared to conventional methods, and yields a regular structure in which most of the computations are performed with FFT-type algorithms.
Abstract: This paper investigates the use of polynomial transforms for the implementation of uniform digital bandpass filter banks. The technique is based upon a decomposition of the N bandpass filters into a set of real polyphase filters followed by a DCT (discrete cosine transform) of size N. The DCT is converted into a DFT (discrete Fourier transform) of size N and the polyphase filters are evaluated by DFT's. This procedure yields a two-dimensional DFT which is computed by a polynomial transform and odd DFT's. We show that this technique reduces significantly the number of arithmetic operations when compared to conventional methods, and yields a regular structure in which most of the computations are performed with FFT-type algorithms.
TL;DR: A conceptual algorithm for reconstructing a two-dimensional (2-D) complex-valued finite sequence from an adequate set of samples of the magnitude of its Fourier transform is presented, which obtains, at least theoretically, all solutions of the 2-D magnitude-only reconstruction problem.
Abstract: In this paper, a conceptual algorithm for reconstructing a two-dimensional (2-D) complex-valued finite sequence from an adequate set of samples of the magnitude of its Fourier transform is presented. In particular, one obtains, at least theoretically, all solutions of the 2-D magnitude-only reconstruction problem, provided that the modulus of the DFT is available in a sufficiently large set of points. However, the practicability of this algorithm is limited to sequences with relatively small regions of support. The key for developing the method is shown to be an appropriate mapping of 2-D finite sequences into 1-D ones, such that 2-D discrete correlation can be formulated in terms of ordinary 1-D discrete correlation.
DOI•
01 Jun 1983TL;DR: In this article, it is demonstrated that the spectral response of the discrete cosine transform and its spectral response and the nature of the appropriate filtering characteristic are such that an operation of the above mentioned kind may be carried out, and the benefits of psychovisual coding obtained.
Abstract: It is becoming increasingly popular, when considering transform coding schemes for images, to attempt to take the spatial frequency response of the human observer into account by performing a classical one- or two-dimensional filtering (pre-emphasis) operation upon the coefficients of the Fourier transformed image, and it would be advantageous if such a procedure could be carried out with more commonly used image transforms, notably the discrete cosine and Walsh-Hadamard transforms. It is demonstrated here that, notwithstanding the theoretical difficulties associated with the convolution/multiplication operation where the discrete cosine transform is concerned, its spectral response and the nature of the appropriate filtering characteristic are such that an operation of the above mentioned kind may be carried out, and the benefits of psychovisual coding obtained. On the other hand, the results obtained in the case of the Walsh-Hadamard transform show that it is unlikely that its performance will be found satisfactory in such an application.
TL;DR: In this article, a frequency sampling filter approach is described to compute the discrete Fourier transform (DFT) and the resulting configuration requires delay elements and differential summers which are realizable by simple stray-insensitive switched-capacitor (SC) circuits.
Abstract: Frequency sampling filter approach is described to compute the discrete Fourier transform (DFT). The resulting configuration requires delay elements and differential summers which are shown to be realizable by simple stray-insensitive switched-capacitor (SC) circuits. The proposed scheme finds applications where short data blocks are processed like in radar.
TL;DR: In this paper, a computational algorithm for the discrete Fourier transform (DFT) via the discrete Walsh transform (DWT) was proposed, but the calculation equations for the conversion factors from the DWT coefficients to the DFT coefficients have not been shown.
Abstract: We have proposed a computational algorithm for the discrete Fourier transform (DFT) via the discrete Walsh transform (DWT). However, the calculation equations for the conversion factors from the DWT coefficients to the DFT coefficients have not been shown. This paper presents the equations for the conversion factors.
TL;DR: A fast algorithm for an N-point discrete cosine transform (DCT) is derived from a 4N-point Winograd Fourier transform algorithm (WFTA), suitable for a high-speed implementation using one-bit systolic arrays.
Abstract: A fast algorithm for an N-point discrete cosine transform (DCT) is derived from a 4N-point Winograd Fourier transform algorithm (WFTA). This algorithm, which has the same form as Winograd's Fourier transform and convolution algorithms, is suitable for a high-speed implementation using one-bit systolic arrays.
01 Apr 1983
TL;DR: An image coding algorithm is developed which exploits some of the desirable features of the spatial and the transform domains for image data compression using a two-dimensional polynomial and codes the residual intensities using a discrete cosine transform (DCT).
Abstract: An image coding algorithm is developed which exploits some of the desirable features of the spatial and the transform domains for image data compression. This scheme is based on a two-component source model similar to some previous results [1 ,2] , but has been generalized to include two-dimensional interpolation and transform coding. Rather than processing successive scan lines of image intensity, this algorithm approximates the image intensity over adjacent subpictures using a two-dimensional polynomial and codes the residual intensities using a discrete cosine transform (DCT). Compression results with rates in the 0.5 to 1.0 bits per pixel range are demonstrated by reconstructed images and rate-distortion characteristics.
TL;DR: A constrained transform coding procedure is developed which is a combination of transform coding with differential pulse code modulation, and includes the discrete cosine transformation and tensor products of splines as special cases.
Abstract: A constrained transform coding procedure is developed which is a combination of transform coding with differential pulse code modulation. The algorithm avoids block boundary mismatch errors, yet retains the coding efficiency of transform coding. A general theory of constrained transform coding is developed which includes the discrete cosine transformation and tensor products of splines as special cases. Results using the cosines and spines are given for two images. A complete discussion of the necessary linear algebra background is also given.
TL;DR: An algorithm is developed for evaluating the discrete cosine transform using DFT and polynomial transforms that is shown to be computationally more efficient than existing algorithms.
Abstract: An algorithm is developed for evaluating the discrete cosine transform using DFT and polynomial transforms. It is shown to be computationally more efficient than existing algorithms.
01 Mar 1983
TL;DR: In this article, the authors describe the problem of people downloading mathematical methods in continuous and discrete systems, but instead of enjoying a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their laptop.
Abstract: Thank you very much for downloading mathematical methods in continuous and discrete systems. Maybe you have knowledge that, people have search numerous times for their chosen books like this mathematical methods in continuous and discrete systems, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some malicious virus inside their laptop.
26 Oct 1983
TL;DR: The hybrid optical implementation of a real formalism of discrete fourier transform in terms of circular correlations is discussed in this article, which makes possible to develop new architectures which are fully parallel both for the electronic and the optical parts of the system.
Abstract: The hybrid optical implementation of a real formalism of discrete fourier transform in terms of circular correlations is discussed. This approach makes possible to develop new architectures which are fully parallel both for the electronic and the optical parts of the system. As applications of the proposed system, correlation of 2 signals and multidimensional DFT's are considered.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this paper, it was shown that the decorrelation behaviour of the transform is not affected by the choice of correlation coefficient for which the transform was optimised, and that the transform's energy compaction is virtually unaffected.
Abstract: The capabilities of various transforms in respect to their ‘energy compaction’ properties are well known. Their other important property—the ability to decorrelate a data sequence—has largely been taken for granted. In the letter, previously known results are extended to the case in which the optimum transform for a given correlation coefficient is used to transform data for which that value may vary widely. It is demonstrated that, although the decorrelation behaviour of the transform is markedly affected in such a situation, its energy compaction is virtually unaffected by the choice of correlation coefficient for which the transform is optimised.
TL;DR: In this paper, the Z-transform is used to solve heat-conduction problems in axisymmetric bodies of arbitrary shape for different types of boundary conditions, and it is shown that the Z transform can solve the problem of heat-convexity.
Abstract: The Z-transform (discrete Laplace transform) is used to solve heat-conduction problems in axisymmetric bodies of arbitrary shape for different types of boundary conditions.
01 Apr 1983
TL;DR: Several theoretical results concerning the discrete Fourier transform are derived and these are used to obtain an efficient algorithm for extending the range of lengths of a multi-dimensional convolver or correlator based on a transform processor or program.
Abstract: Several theoretical results concerning the discrete Fourier transform are derived. These are then used to obtain an efficient algorithm for extending the range of lengths of a multi-dimensional convolver or correlator based on a transform processor or program. Methods of implementing this algorithm in hardware and software are also considered.