Showing papers on "Discrete sine transform published in 1995"
TL;DR: In this paper, the same rules can be applied to create a new type of fractional-order Fourier transform which results in a smooth transition of a function when transformed between the real and Fourier spaces.
112 citations
TL;DR: In this article, a collocation method based on an expansion in rational eigenfunctions of the Hilbert transform operator is proposed, which is implemented through the Fast Fourier Transform.
Abstract: We introduce a new method for computing the Hilbert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hilbert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares favorably with existing methods
82 citations
TL;DR: In this article, the authors present general design formulae for optically implementing the two-dimensional fractional Fourier transform in two orthogonal dimensions and specify the two orders and the input, output scale parameters simultaneously.
64 citations
TL;DR: The fractional Fourier transform can also be helpful for lens design, especially for specifying a lens cascade, according to its role in wave propagation and signal processing.
Abstract: The fractional Fourier transform has been used in optics so far for wave propagation and for signal processing. Now we show that this new transform can also be helpful for lens design, especially for specifying a lens cascade.
63 citations
TL;DR: This work shows that the original bulk-optics configuration for performing the fractional-Fourier-transform operation provides a scaled output using a fixed lens and suggests an asymmetrical setup for obtaining a non-scaled output.
Abstract: Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.
61 citations
TL;DR: The authors define a new class of real-number linear block codes using the discrete cosine transform (DCT) and show that a subclass with a BCH-like structure can be defined and, therefore, encoding/decoding algorithms for BCH codes can be applied.
Abstract: The authors define a new class of real-number linear block codes using the discrete cosine transform (DCT). They also show that a subclass with a BCH-like structure can be defined and, therefore, encoding/decoding algorithms for BCH codes can be applied, A (16,10) DCT code is given as an example. >
53 citations
TL;DR: Clenshaw's recurrence formula provides a unified development for the recursive DCT and IDCT algorithms and applies to arbitrary length algorithms and are appropriate for VLSI implementation.
Abstract: Clenshaw's recurrence formula is used to derive recursive algorithms for the discrete cosine transform (DCT) and the inverse discrete cosine transform (IDCT). The recursive DCT algorithm presented requires one fewer delay element per coefficient and one fewer multiply operation per coefficient compared with two other proposed methods. Clenshaw's recurrence formula provides a unified development for the recursive DCT and IDCT algorithms. The recursive algorithms apply to arbitrary length algorithms and are appropriate for VLSI implementation. >
51 citations
TL;DR: A new preconditioner for symmetric, positive definite Toeplitz systems is presented, an element of the n--dimensional vector space of matrices that are diagonalized by the discrete sine transform that is comparable, and in some cases superior, to the standard circulants of Tony Chan.
Abstract: We present a new preconditioner for $n\times n$ symmetric, positive definite Toeplitz systems. This preconditioner is an element of the $n$--dimensional vector space of matrices that are diagonalized by the discrete sine transform. Conditions are given for which the preconditioner is positive definite and for which the preconditioned system has asymptotically clustered eigenvalues. The diagonal form of the preconditioner can be calculated in $O(n\log(n))$ operations if $n=2^k-1.$ Thus only $n$ additional parameters need be stored. Moreover, complex arithmetic is not needed. To use the preconditioner effectively, we develop a new technique for computing a fast convolution using the discrete sine transform (also requiring only real arithmetic). The results of numerical experimentation with this preconditioner are presented. Our preconditioner is comparable, and in some cases superior, to the standard circulant preconditioner of Tony Chan. Possible generalizations for other fast transforms are also indicated.
34 citations
TL;DR: In this paper, it was shown that information of order six suffices to determine a structure uniquely, where six is the number of atoms in a set of equal atoms that can occupy positions on a circle subdivided into equally spaced markings.
Abstract: The three-dimensional configuration of crystallized structures is obtained by reading off partial information about the Fourier transform of such structures from diffraction data obtained with an X-ray source. We consider a discrete version of this problem and discuss the extent to which `intensity only' measurements as well as `higher-order invariants' can be used to settle the reconstruction problem. This discrete version is an extension of the study undertaken by Patterson in terms of `cyclotomic sets', corresponding to arrangements of equal atoms that can occupy positions on a circle subdivided into N equally spaced markings. This model comes about when the usual three-dimensional Fourier transform is replaced by a one-dimensional discrete Fourier transform. The model in this paper considers molecules made up of atoms with possibly different (integer-valued) atomic numbers. It is shown that information of order six suffices to determine a structure uniquely.
33 citations
09 May 1995
TL;DR: A discrete version of the AFT (DRFT) that represents a rotation in discrete time-frequency space and some properties of the transform that support its interpretation as a rotation are presented.
Abstract: The continuous-time angular Fourier transformation (AFT) represents a rotation in continuous time-frequency space and also serves as an orthonormal signal representation for chirp signals. We present a discrete version of the AFT (DRFT) that represents a rotation in discrete time-frequency space and some properties of the transform that support its interpretation as a rotation. The transform is a generalization of the DFT. The eigenvalue structure of the DFT is then exploited to develop an efficient algorithm for the computation of this transform.
32 citations
Patent•
19 Dec 1995TL;DR: In this paper, a pair of scanners scan the respective transform coefficients output by the transform devices according to predetermined patterns, and a prediction is made as to which transform mode will produce the least amount of variable-length-code, and corresponding transform coefficients are selected to be sent to the variablelength-coder.
Abstract: An discrete cosine transform (DCT) apparatus is adaptive so as to choose between alternative transform modes for each successive pixel block to be transformed and subsequently variable-length-coded. A first transform device performs a DCT on a subject pixel block. A second transform device performs a DCT on the same subject pixel block of data which has been processed such that the frequency domain transformed data is distributed in a lower frequency compared with the transform coefficients produced by the first transform device. A pair of scanners scan the respective transform coefficients output by the transform devices according to predetermined patterns. A set of four counters accumulate information about the transform coefficients, as scanned by the scanners, so as to indicate the amount of data which would be produced by the respective sets of transform coefficients when variable-length-coded. Based upon the counts produced by the counters, a prediction is made as to which transform mode will produce the least amount of variable-length-code, and the corresponding transform coefficients are selected to be sent to the variable-length-coder.
TL;DR: In this paper, Cosine Products, Fourier Transforms, and Random Sums are discussed. But the authors focus on the Fourier transform and ignore the random sum method.
Abstract: (1995). Cosine Products, Fourier Transforms, and Random Sums. The American Mathematical Monthly: Vol. 102, No. 8, pp. 716-724.
09 May 1995
TL;DR: A method is presented for classifying multi-level PSK signals in the presence of additive white Gaussian noise (AGWN) based on the Discrete Fourier Transform of a phase histogram, which performs well at low SNR.
Abstract: A method is presented for classifying multi-level PSK signals in the presence of additive white Gaussian noise (AGWN). The technique is based on the Discrete Fourier Transform (DFT) of a phase histogram. The probability of correct classification is given and it is found that the technique performs well at low SNR. The benefits of this technique are that it is simple to implement and requires no prior knowledge of the SNR of the signal for the classification.
TL;DR: In this correspondence, new algorithms are presented for computing the l-D and 2-D discrete cosine transform (DCT) of even length by using the discrete Fourier transform (DFT).
Abstract: In this correspondence, new algorithms are presented for computing the l-D and 2-D discrete cosine transform (DCT) of even length by using the discrete Fourier transform (DFT). A comparison of the proposed algorithms to other fast ones points out their computational efficiency, which is mainly based on the advantages of prime-factor decomposition and a proper choice of index mappings. >
Patent•
07 Sep 1995
TL;DR: In this article, a contour encoding apparatus determines vertex points on the previous contour of the previous frame based on a polygonal approximation, and a set of second approximation errors is calculated at a predetermined number of sample points on each second line segment between two predicted vertex points.
Abstract: A contour encoding apparatus determines vertex points on the previous contour of the previous frame based on a polygonal approximation. A set of first approximation errors is calculated at a predetermined number of sample points on each first line segment between two vertex points, and a first set of discrete sine transform coefficients is obtained by discrete sine transforming the set of first approximation errors for each first line segment. Predicted vertex points are detected based on the vertex information and current contour of the current frame. A set of second approximation errors is calculated at the predetermined number of sample points on each second line segment between two predicted vertex points, and a second set of discrete sine transform coefficients is obtained by discrete sine transforming the set of second approximation errors for each second line segment. After determining a set of differences by subtracting the second set of discrete sine transform coefficients from the corresponding first set of discrete sine transform coefficients, the set of differences are encoded for transmission to thereby reduce the volume of transmission data.
TL;DR: The result is able to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform.
Abstract: In [2] we have considered a class of integral transforms which generalizs the classical Fourier tranform. We are able now to define a class of discrete tranformations which can be considered as a generalization of the discrete Fourier transform. Furthermore, when our result is considered in connnection with the particular kernel associated with th Fourier transform, the fast Fourier transform algorithm can be used in order to approximate the Hermite-Fourier coefficients of a class of functions *
09 May 1995
TL;DR: A procedure is presented for complete implementation of the scale transformation for discrete signals that complements discrete Mellin transforms and delineates steps whose implementation are specific to the scale transform.
Abstract: The scale transform introduced by Cohen (see IEEE Trans. Signal Processing, vo1.41, p.3275-3292, December 1993) is a special case of the Mellin transform. The scale transform has mathematical properties desirable for comparison of signals for which scale variation occurs. In addition to the scale invariance property of the Mellin transform many properties specific to the scale transform have been presented. A procedure is presented for complete implementation of the scale transformation for discrete signals. This complements discrete Mellin transforms and delineates steps whose implementation are specific to the scale transform.
TL;DR: A multidimensional fast Hartley transform algorithm is described that successively applies 1D Fourier transforms to reduceundant operations to a minimum in the processing of real-valued data.
Abstract: In the processing of real-valued data, a purely real transform such as the Hartley transform is more desirable than the complex Fourier transform because it avoids unnecessary complex computations. This advantage is most significant in multidimensional transformations, where a large amount of data has to be processed. A multidimensional fast Hartley transform algorithm is described that successively applies 1D Fourier transforms. Redundant operations are reduced to a minimum. Special indexing schemes (parity operators) are introduced to avoid unscrambling procedures. >
Patent•
13 Apr 1995
TL;DR: In this article, a polygonal approximation of the contour image of an object is presented, where a sampling circuit is used to provide N sample points for each of the line segments, an error detector for calculating an error for each sample points on each line segment, and a discrete sine transform and quantization block for transforming each set of errors into a set of discrete Sine transform coefficients.
Abstract: A contour approximation apparatus for representing a contour image of an object comprises a polygonal approximation section for determining a number of vertices on the contour image and fitting the contour image with a plurality of line segments to provide a polygonal approximation of the contour image, a sampling circuit for providing N sample points for each of the line segments, an error detector for calculating an error for each of the N sample points on each of the line segments to produce a set of errors for each of the line segments, a discrete sine transform and quantization block for transforming each set of errors into a set of discrete sine transform coefficients, and for converting the set of discrete sine transform coefficients into a set of quantized transform coefficients.
01 Jan 1995
TL;DR: In this article, the authors introduce Common Uses of the DFT Equation and Block Diagram Properties Real Input Signals Strengths Weaknesses Conclusions (i.e.
Abstract: This chapter contains sections titled: Introduction Common Uses of the DFT Equation and Block Diagram Properties Real Input Signals Strengths Weaknesses Conclusions
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01 Sep 1995
TL;DR: To design the CLB-efficient FFT/DCT processor in FPGAs, a pipelined bit-serial architecture with bit-parallel input data format is employed.
Abstract: Fast Fourier Transform (FFT) and Discrete Cosine Transform (DCT) processors are designed and implemented using a Xilinx Field Programmable Gate Array (FPGA) device XC 4010. This device allows a 16-point FFT/DCT processor implementation. To design the CLB-efficient FFT/DCT processor in FPGAs, a pipelined bit-serial architecture with bit-parallel input data format is employed. These processors operate with a 20 MHz bit-clock and 16-bit system word length, and compute an entire 16-point DFT/DCT transform for every 16-bit clock cycle.
TL;DR: A generalized signal flow graph for the DCT/DST of type II (DCT-II/ DST-II) computation and their inverses DCT-III/D ST-III is described, based on the fast, recursive and numerically stable Hou's algorithm.
TL;DR: By making a discrete finite time signal periodic, it is shown that nonorthogonal B-spline wavelets can be used in a discrete wavelet transform with exact decomposition and reconstruction.
Patent•
01 Jun 1995TL;DR: In this article, a forward discrete slant transform is implemented using pseudo-SIMD techniques to reduce the total number of lookup tables, table lookups, and column transform computations.
Abstract: Images are encoded by applying a two-dimensional forward transform to blocks of pixels or pixel differences to generate transform coefficients for each block. The two-dimensional transform is decomposed into two phases: (1) a first phase in which a first one-dimensional transform (e.g., a row transform) is applied to the input block using forward mapping, where the inputs are used as indices to lookup tables to retrieve contributions to intermediate coefficients, and (2) a computational phase in which a second one-dimensional transform (e.g., a column transform) is applied to the intermediate coefficients to generate the transform coefficients. In a preferred embodiment, a forward discrete slant transform is implemented using pseudo-SIMD techniques to reduce the total numbers of lookup tables, table lookups, and column transform computations.
TL;DR: An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated.
Abstract: An in-place algorithm for the fast, direct computation of the forward and inverse discrete cosine transform is presented and evaluated. The transform length may be an arbitrary power of two.
TL;DR: A novel architecture for the simultaneous, real-time computation of both the transforms, based on the decomposition of the odd-time, odd-frequency discrete Fourier transform (O/sup 2/ DFT), is proposed.
Abstract: Various options available for the on-line computation of discrete cosine transform-IV (DCT-IV) and discrete sine transform-IV (DST-IV) in hardware are considered and compared. A novel architecture for the simultaneous, real-time computation of both the transforms, based on the decomposition of the odd-time, odd-frequency discrete Fourier transform (O/sup 2/ DFT), is also proposed. >
30 Oct 1995
TL;DR: In this article, a parallel mixed transform technique employing a novel projection algorithm for signal representation is presented, achieving excellent performance with much less computation than required by existing mixed transform techniques, making real-time implementations possible.
Abstract: Mixed transform coders have been shown to consistently yield higher signal quality than those based on one transform for a fixed compression ratio. However, these coders have not been widely employed due to the very high computational complexity of formulations. This paper presents a new parallel mixed transform technique employing a novel projection algorithm for signal representation. Formulations are derived, algorithms are described and results of simulations are presented. Excellent performance is achieved with much less computation than required by existing mixed transform techniques, making real-time implementations possible.
19 Jan 1995
TL;DR: In this article, the authors discuss methods for the synthesis of fast algorithms of the discrete orthogonal transforms which are based on the inclusions of a rational number field including input data into different algebraic structures: cyclotomic fields, alternative algebras, etc.
Abstract: In the preset paper we discuss methods for the synthesis of fast algorithms of the discrete orthogonal transforms which are based on the inclusions of a rational number field including input data into different algebraic structures: cyclotomic fields, alternative algebras, etc.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
Patent•
31 Jul 1995
TL;DR: In this article, the inverse discrete cosine transform for image decompression is computed for MPEG-2 and MPEG-1 main level speed, and an apparatus for computing it with approximately 10,000 transistors.
Abstract: An apparatus and method for calculation of the inverse discrete cosine transform for image decompression are disclosed. The apparatus may be implemented with approximately 10,000 transistors for MPEG2 main level speed and with less than 10,000 transistors for MPEG1 main level speed.