Showing papers on "Discrete Hartley 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 article, the concept of transform domain adaptive filtering is introduced and the relationship between several existing frequency-domain adaptive filtering algorithms is established, and applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filter algorithms in the areas of speech processing and adaptive line enhancers are discussed.
Abstract: The concept of transform domain adaptive filtering is introduced. In certain applications, filtering in the transform domain results in great improvements in convergence rate over the conventional time-domain adaptive filtering. The relationship between several existing frequency domain adaptive filtering algorithms is established. Applications of the discrete Fourier transform (DFT) and the discrete cosine transform (DCT) domain adaptive filtering algorithms in the areas of speech processing and adaptive line enhancers are discussed.
447 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
01 Jan 1983
TL;DR: Applications of FFT procedures in the numerical calculation of Fourier coefficients, fast multiplication of large integers and computations which involve circulant matrices are closed.
Abstract: After introduction of the discrete Fourier transform and a short description of its main properties we concentrate on a discussion of some of the various methods which have been used for the derivation of fast Fourier transform (FFT) algorithms. The paper closes with applications of FFT procedures in the numerical calculation of Fourier coefficients, fast multiplication of large integers and computations which involve circulant matrices.
36 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
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.
24 citations
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.
15 citations
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.
13 citations
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.
12 citations
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.
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: 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.
TL;DR: A fast algorithm of finding the diagonal elements of the covariance matrix of the two-dimensional Walsh-Hadamard transform of data is described and its usefulness and other interesting properties are discussed.
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.
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.
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.
01 Nov 1983
TL;DR: An approach is presented for varying the discrete Fourier transform (DFT) frequency response by the use of a weighting sequence derived from convolved weightings that is attractive when the DFT is mechanized with Winograd's small N algorithms.
Abstract: An approach is presented for varying the discrete Fourier transform (DFT) frequency response by the use of a weighting sequence derived from convolved weightings. The nulls of the response may be varied within a finite set while maintaining low-amplitude sidelobes. The method is attractive when the DFT is mechanized with Winograd's small N algorithms.
01 Jan 1983
TL;DR: In this paper, the authors define the continuous Jacobi transform as an extension of the discrete Jacobi transformation, and derive an inversion formula for the transform which maps LI(R+) into L2(-I i)
Abstract: The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps LI(R+) into L2(-I i)
22 Jun 1983
TL;DR: In this paper, a general recursive and ongoing method for the calculation of discrete linear transform of order n is presented. But the method is not suitable for the analysis of continuous linear transform.
Abstract: New methods are given for the general recursive and ongoing calculation of discrete linear transforms. For any such transform of order n, each computational iteration updates the previous result to give the transform based upon the most recent n data points. Applications include Fourier, polynomial and Bessel transforms.