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Showing papers on "Discrete sine transform published in 1986"


Journal ArticleDOI
TL;DR: A refinement of the Fourier transform fringe-pattern analysis technique which uses a 2-D Fouriertransform permits better separation of the desired information components from unwanted components than a 1-D transform.
Abstract: A refinement of the Fourier transform fringe-pattern analysis technique which uses a 2-D Fourier transform is described. The 2-D transform permits better separation of the desired information components from unwanted components than a 1-D transform. The accuracy of the technique when applied to real data recorded by a system with a nonlinear response function is investigated. This leads to simple techniques for optimizing an interferogram for analysis by these Fourier transform methods and to an estimate of the error in the retrieved fringe shifts. This estimate is tested on simulated data and found to be reliable.

363 citations


Journal ArticleDOI
TL;DR: In this paper, the influence of time-domain noise on the results of a discrete Fourier transform (DFT) was studied and it was shown that the resulting frequency domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal.
Abstract: An analysis is made to study the influence of time-domain noise on the results of a discrete Fourier transform (DFT). It is proven that the resulting frequency-domain noise can be modeled using a Gaussian distribution with a covariance matrix which is nearly diagonal, imposing very weak assumptions on the noise in the time domain.

150 citations


Patent
19 Jun 1986
TL;DR: In this paper, a discrete transform cosine circuit utilizing symmetries of the cosine matrix of coefficients was proposed to allow all multiplications to be done by "constant multipliers" comprising combinations of look-up tables and adders.
Abstract: A discrete transform cosine circuit utilizing symmetries of the cosine matrix of coefficients to allow all multiplications to be done by "constant multipliers" comprising combinations of look-up tables and adders. Transform coefficients are developed by dividing each into a sequence of blocks of preselected size, the information in the blocks is sorted to develop a specific order and the reordered blocks are applied seriatim to a first one-dimensional cosine transform circuit employing the constant multipliers. The output of the first cosine transform circuit is applied to a transposing memory and then to a second cosine transform circuit that also employs "constant multipliers".

76 citations


Journal ArticleDOI
TL;DR: A relationship between the discrete cosine transform (DCT) and the discrete Hartleytransform (DHT) is derived and it leads to a new fast and numerically stable algorithm for the DCT.
Abstract: A relationship between the discrete cosine transform (DCT) and the discrete Hartley transform (DHT) is derived. It leads to a new fast and numerically stable algorithm for the DCT.

76 citations


Journal ArticleDOI
TL;DR: It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform, and a Chinese remainder theorem is derived for integer lattices.
Abstract: In this paper, the prime factor algorithm for the evaluation of a one-dimensional discrete Fourier transform is generalized to the evaluation of multidimensional discrete Fourier transforms defined on arbitrary periodic sampling lattices. It is shown that such an algorithm is equivalent in computational complexity to the evaluation of a rectangular discrete Fourier transform. As a sidelight to the derivation of the algorithm, a Chinese remainder theorem is derived for integer lattices.

64 citations


Journal ArticleDOI
TL;DR: A technique whereby both lowpass filtering and subsampling can be combined in the transform domain results in greater computational efficiency as the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.

42 citations


Journal ArticleDOI
01 May 1986
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.

41 citations



Patent
20 May 1986
TL;DR: In this article, the first adder stage receives the cosine transform for a group of (N/2) points and a lower half-stages receives the sequence (y i ) and supplying the sequence(X 2q+1 + 1 ) of the odd components of the cosines transform.
Abstract: A circuit for the fast calculation of the discrete cosine transform (X i ), 0≦i≦N-1, in which N=2 n and n is an integer of a signal defined by a sequence (x i ), 0≦i≦N-1 includes a first adder stage receiving the sequence (x i ), 0≦i≦N-1, and supplying two sequences (x i o ) and y i i ) and 0≦i≦(N/2)-1, a group of upper half-stages receiving the sequence of x o i ) and supplying the sequence (X 2q ) of the even components of the cosine transform. That group constitutes a circuit for the fast calculation of the cosine transform for a group of (N/2) points and a group of lower half-stages receiving the sequence (y i ) and supplying the sequence (X 2q+1 ) of the odd components of the cosine transform.

27 citations


DOI
01 Jun 1986
TL;DR: Two new transforms which can be used as substitutes for the Walsh transform are generated using the theory of dyadic symmetry, and have an efficiency, defined in terms of their ability to decorrelate signal data, which lies between that ofThe Walsh transform and that of the discrete cosine transform.
Abstract: Two new transforms which can be used as substitutes for the Walsh transform are generated using the theory of dyadic symmetry. The new transforms have virtually the same complexity and computational requirements as the Walsh transform, employing additions, subtractions and binary shifts only, but have an efficiency, defined in terms of their ability to decorrelate signal data, which lies between that of the Walsh transform and that of the discrete cosine transform.

24 citations


01 Jan 1986
TL;DR: Fast algorithms for computation of the discrete cosine transform (DCT) are evaluated through the fast Fourier transform and also by the direct method.
Abstract: Fast algorithms for computation of the discrete cosine transform (DCT) are evaluated. Implementation via the fast Fourier transform and also by the direct method are considered. DCT algorithms for arbitrary sequence lengths are also included.

Proceedings ArticleDOI
01 Apr 1986
TL;DR: An efficient discrete cosine transform image coding system using the gain/shape vector quantizers (DCT-G/S VQ) is presented and their performance is compared to that of previously reported discretecosine transform coding systems using the Max-type scalor quantizers.
Abstract: An efficient discrete cosine transform image coding system using the gain/shape vector quantizers (DCT-G/S VQ) is presented. In the coding system, AC transform coefficients in a subblock are partitoned into several bands according to the Schaming's method, and the normalized AC transform coefficients of each band are quantized with the gain/shape vector quantizer designed on a spherically symmetric probability model. In addition, an adaptive DCT-G/S VQ (A-DCT-G/S VQ) is presented by incorporating a modification of the recursive quantization technique in the DCT-G/S VQ. The coding systems are simulated on color images, and their performance is compared to that of previously reported discrete cosine transform coding systems using the Max-type scalor quantizers.



Proceedings ArticleDOI
07 Apr 1986
TL;DR: The transform domain oriented estimation algorithm introduced in [1] in which the calculation of the displacement vector was obtained from the transform domain coefficients is extended and it is shown that the latter approach results in an improved performance of the estimation procedure.
Abstract: In this paper we extend the transform domain oriented estimation algorithm introduced in [1] in which the calculation of the displacement vector was obtained from the transform domain coefficients. The performance of the algorithm is verified within a hybrid coding configuration. In this paper only transform domain block matching algorithms are considered. The block-match procedure makes use of the displacement matrix H defined in [1]. A matrix decomposition method is described in order to show that a practical implementation is very well possible. The properties of the translation invariant matrices are explained by using the ordered Walsh Hadamard transform as an example. The procedure however enables the use any other orthogonal transform. An important issue with respect to the hardware complexity of this motion compensated hybrid coder is the use of only one transform. The performance of the proposed new algorithm is shown and a video tape containing a very critical videoconferencing scene (i.e. split screen and a hard switch to full screen with heavy motion) will be presented. The sequences are coded at a bitrate of 384 kbit/s and 64 kbit/s respectively. Results of the compensation in the pixel domain and in the transform domain are compared and it is shown that the latter approach results in an improved performance of the estimation procedure.

Journal ArticleDOI
TL;DR: In this paper, a numerical method of solution for the transient phenomena on transmission line terminated by simple load, including a nonlinear element, is proposed based on the discrete numerical Laplace transform and its inverse, utilizing the discrete Fourier transform.
Abstract: This paper proposes a numerical method of solution for the transient phenomena on transmission line terminated by simple load, including a nonlinear element. The method is based on the discrete numerical Laplace transform and its inverse, utilizing the discrete Fourier transform. Problems and the solutions in the method are discussed. The feature of the method is that the voltage, current and surge impedance matrix of the transmission line are specified on the complex frequency (s) plane, while the boundary condition is given on the time (t) domain. Numerical solutions in the two regions are combined by Laplace transform and its inverse. The Laplace transform and its inverse by discrete Fourier transform have a drawback in that the accuracy of the computation deteriorates at t = 0 for stepwise change of the waveform. A method to solve this problem is described. For the latter half of the sampling point sequence in the Laplace and inverse transforms, the computation error is increased, which effectively halves the sampling points in the computation of the reflected wave. For this problem, a method is presented by which the accuracy of the computation is retained for each calculation of the reflected wave, keeping constant the number of sampling points. The convolution required in the calculation of the boundary condition is time-consuming, and a solution for this is proposed. As an example of the solution, the transient phenomenon in the multiconductor transmission-line terminated by the surge arrester is calculated, taking the skin effect into consideration.

01 Jan 1986
TL;DR: A paired tensor representation of each component Fp,s of the spectrum of the signal in the form of the corresponding N/2-dimensional vector F̄ ′ p,s the paired vector representation is called.
Abstract: Since for each t ∈ [1, N/2], we have W t+N/2 = −W , one can also represent component (1) at the point (p, s) by the corresponding N/2-dimensional vector F̄ ′ p,s = (f ′ p,s,1, f ′ p,s,2, ..., f ′ p,s,N/2), whose components are calculated from the components of the corresponding initial vector F̄p,s by formula f ′ p,s,t = fp,s,t − fp,s,t+N/2, t = 1 ÷ N/2. (5) We call such representation of each component Fp,s of the spectrum in the form of the corresponding N/2-dimensional vector F̄ ′ p,s the paired vector representation, to distinct it from the original vector representation F̄p,s, and the constructed tensor of the 3rd order (f ′ p,s,t; p, s, = 1 ÷ N, t = 1 ÷ N/2 to be the paired tensor of the Fourier-spectrum. As for the original tensor representation of the spectrum of the signal, when for any p, s and k the following formula was valid [1]

Journal ArticleDOI
TL;DR: In this paper, the authors used multiplicative character theory to reprove results from a paper of Auslander-Feig-Winograd (Adv. in Appl. Math. 5.5 (1984), 31-55) on the multiplicative complexity of the discrete Fourier transform.

Journal ArticleDOI
TL;DR: In this paper, the discrete frequency Fourier transform (DFFT) is shown to be a useful transform in its own right for spatial domain image reconstruction, filling a gap in the theory and aids the designer in understanding problems which have inherently sampled frequency domains.
Abstract: In certain signal processing applications it may be required to reconstruct a spatial domain image form samples of its Fourier transform. For problems such as this it may be useful to use the dual of the well-known discrete time Fourier transform (DTFT) for purposes of analysis and design. In this paper, this dual concept, called the discrete frequency Fourier transform (DFFT), is shown to be a useful transform in its own right. In addition to being useful for certain physical problems, the DFFT fills a gap in the theory and aids the designer in understanding problems which have inherently sampled frequency domains.

Proceedings ArticleDOI
01 Apr 1986
TL;DR: A new algorithm for the inverse Cosine transform (IDCT) is developed which falls within the unified architecture if the authors allow ourselves the luxury of double length processing.
Abstract: A common architecture, which is based on the Cooley-Tukey[1] algorithm, is developed for the Fourier, Hadamard, and forward and inverse Cosine transforms. The theory to implement the first three transforms in this architecture is well known. However, the existing algorithms for the inverse Cosine transform (IDCT) would disqualify it from the unified architecture and this led us to develop a new IDCT algorithm which falls within the unified architecture if we allow ourselves the luxury of double length processing. Details of the unified architecture and the new algorithm for the IDCT will be given in this paper.

Proceedings ArticleDOI
N. Suehiro1, M. Hatori
01 Apr 1986
TL;DR: A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms and a new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm.
Abstract: A new matrix factorization is proposed for DCT-IV, which is the basis of fast algorithms for many sinusoidal transforms. A new fast algorithm for complex-data DFT based on the new factorization requires the same number of multiplications and far fewer additions than the Preuss algorithm. A new fast algorithm for real-data DFT based on a new algorithm for the discrete Hartley transform is also proposed.

Journal ArticleDOI
TL;DR: The present paper relies on the conjugate property of the generalized DFT in order to define novel, advantageous algorithms for the in-place calculation of the DFT of multidimensional sequences.
Abstract: The computation of the discrete Fourier transform (DFT) of real multidimensional sequences requires an extraordinary amount of computer memory. The in-place calculation of the discrete Fourier transform reduces the required memory and is thus highly desirable. The present paper relies on the conjugate property of the generalized DFT in order to define novel, advantageous algorithms for the in-place calculation of the DFT of multidimensional sequences.

Journal ArticleDOI
TL;DR: In this article, the effectiveness of the discrete sine transform in terms of residual correlation was evaluated for a Markov-1 signal with low correlation coefficient and it was concluded that the DST is effective for Markov signals with low residual correlation coefficient.

Journal ArticleDOI
01 Feb 1986
TL;DR: In this article, it has been shown that the complex coefficients of a discrete Fourier transform (DFT) used in spectral analysis, can be replaced by an optimum set whose real and imaginary components are constrained to be integer powers of two or the sum of two integer powers-of-two.
Abstract: In a previous paper it has been shown that the complex coefficients of a discrete Fourier transform (DFT) used in spectral analysis, can be replaced by an optimum set whose real and imaginary components are constrained to be integer powers of two or the sum of two integer powers of two thus making multiplication trivial. However, the technique used ruled out any further increase in speed and reduction in hardware cost by factorisation of the DFT. The scheme presented in the paper overcomes this drawback and is applicable to the Cooley-Tukey fast Fourier transform algorithm.

Proceedings ArticleDOI
01 Apr 1986
TL;DR: The effect of using ideal filter transfer function in transform domain decimation on the quality of the decimated images is investigated and the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.
Abstract: Decimation is normally carried out in two passes; lowpass filtering and subsampling where the latter is normally performed in the time domain. This paper describes a technique whereby both the operations can be combined in the transform domain. The two-dimensional decimation scheme is first implemented in the discrete Fourier transform domain and then extended to the discrete cosine transform domain. It is further applied to a non-sinusoidal i.e. Hadamard transform domain. The effect of using ideal filter transfer function in transform domain decimation on the quality of the decimated images is investigated. This approach results in greater computational efficiency as the constraint of filter length to meet certain specifications is removed permitting the use of smaller transform block sizes.

Journal ArticleDOI
TL;DR: In this article, the authors pointed out two major errors contained in the referred paper and gave a new algorithm for the discrete sine transform. But they did not give a detailed description of the algorithm.
Abstract: Two major errors contained in the referred paper are pointed out. Reference of a new algorithm for the discrete sine transform is given.

Journal ArticleDOI
TL;DR: In this paper, the precise meaning of the Fourier transform of the real positive ν is examined. And a general expression is given for real positive ∆ for odd ∆, while even ∆ gives rise to derivatives of the delta function.
Abstract: The precise meaning of the Fourier transform of ‖x‖ν is examined. A general expression is given for real positive ν. For odd ν, derivatives of principal value integrals are obtained, while even ν gives rise to derivatives of the delta function.

Book ChapterDOI
17 Sep 1986
TL;DR: The full recursive forms of the discrete Fourier, Hadamard, Paley and Walsh transforms are developed using a theoretical group approach and a matrix pseudoinversion to reveal common and sometimes unexpected features of these transforms.
Abstract: In this paper the full recursive forms of the discrete Fourier, Hadamard, Paley and Walsh transforms are developed. The algebraic properties and computational complexity of the GFT are investigated on the basis of a theoretical group approach and a matrix pseudoinversion. The approach considered reveals common and sometimes unexpected features of these transforms, the parallel realization of the algorithms becoming thus possible.

Proceedings ArticleDOI
S. Ono1, T. Araseki
01 Apr 1986
TL;DR: An orthogonal transform, based on an autoregressive model of short-time input speech, which is applicable to low bit rate coding, is presented and its performance is evaluated in comparison with that for conventional transforms, KLT and DCT.
Abstract: This paper discusses the possibility of an input-dependent orthogonal transform for low bit rate speech coding. An orthogonal transform, based on an autoregressive model of short-time input speech, which is applicable to low bit rate coding, is presented. Its performance is evaluated in comparison with that for conventional transforms, KLT and DCT. The experiments confirm that the input-dependent orthogonal transform improves the average distortion versus average information rate performance over that for the input-independent transform DCT.

Proceedings ArticleDOI
01 Apr 1986
TL;DR: Criteria for measuring the closeness of a transform to the Karhunen-Loeve transform show that the phase shift cosine transform measures closer to the even part of the KLT than the version II of the discrete Cosine transform (DCT-II).
Abstract: A new transform, the phase shift cosine transform (PSCT), is introduced. It almost diagonizes the even part of the covariance matrix of a high correlated Markov-I sequence. Several criteria are established for measuring the closeness of a transform to the Karhunen-Loeve transform (KLT). All these criteria show that the PSCT measures closer to the even part of the KLT than the version II of the discrete cosine transform (DCT-II).