Showing papers on "Discrete Hartley transform published in 1989"
TL;DR: In this article, the authors compared five real-valued orthogonal transforms in terms of learning characteristics and computational complexity, and showed that the effect of an ideal transform is to convert equal error contours that are initially hyperellipses in the parameter space into hyperspheres.
Abstract: It has been previously shown that a real-time decomposition of the incoming signal into a set of partially uncorrelated components via an orthogonal transform, and a subsequent adaptation on these individual components, leads to faster convergence rates. Here, transform domain processing is characterized by the effect of the transform on the shape of the mean-square error surface. It is shown that the effect of an ideal transform is to convert equal error contours that are initially hyperellipses in the parameter space into hyperspheres. Five specific real-valued orthogonal transforms are compared in terms of learning characteristics and computational complexity. Since the Karhunen-Loeve transform (KLT) is the ideal transform for this application, and since the KLT is defined in terms of the statistics of the input signal, it is certain that no fixed-parameter transform can deliver optimal learning characteristics for all input signals. However, the simulations suggest that transforms can be found which give much improved performance in a given situation. >
165 citations
TL;DR: The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT), and compare its performance to other on-chip DFT implementations.
Abstract: The authors present an electronic circuit, based on a neural (i.e. multiply connected) net to compute the discrete Fourier transform (DFT). They show both analytically and by simulation that the circuit is guaranteed to settle into the correct values within RC time constants (on the order of hundreds of nanoseconds), and they compare its performance to other on-chip DFT implementations. >
76 citations
TL;DR: A new class of nonlinear matched filters is discussed, which involve the transformation of the signal spectrum and the filter transfer function through a nonlinearity before they are multiplied in the transform domain.
Abstract: A new class of nonlinear matched filters is discussed These filters involve the transformation of the signal spectrum and the filter transfer function through a nonlinearity before they are multiplied in the transform domain The resulting filter structures can be considered to be analogous to three-layer neural nets They have better performance in terms of signal discrimination and lack of false correlation signals and artifacts than previously known filters The matched filters are further subdivided into two major classes according to whether the filtering is based on a discrete Fourier transform (DFT) or a real discrete Fourier transform (RDFT) The DFT and the RDFT are approximations to the complex and real Fourier transforms, respectively The RDFT-based filtering gives better performance in terms of signal discrimination and lack of false correlation signals and artifacts than the DFT-based filtering
49 citations
TL;DR: A description is given of a novel algorithm, the fast Fourier transform in part (FFTP), for the computation of the discrete pseudo-Wigner distribution (DPWD), which reduces the computational cost by making full use of symmetries and removing redundancies in the FFTP computation.
Abstract: A description is given of a novel algorithm, the fast Fourier transform in part (FFTP), for the computation of the discrete pseudo-Wigner distribution (DPWD). The FFTP computes the cosine and sine parts of the discrete Fourier transform (DFT) separately by employing real inverse sinusoidal twiddle factors. Unlike the conventional methods which directly utilize the complex DFT, the FFTP yields real output since the DPWD is always real. In addition, the new method reduces the computational cost by making full use of symmetries and removing redundancies in the FFTP computation. The authors also describe a simple algorithm for computing the discrete Hilbert transform (DHT) to produce the nonaliased DPWD. A pipeline structure for real-time and a bulk processing technique for offline implementations of the method are presented. >
43 citations
TL;DR: A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT), where the computation complexity can be greatly reduced from two complex FFTs into two real FHTs.
Abstract: A fast algorithm is proposed to compute the discrete Hilbert transform via the fast Hartley transform (FHT). Instead of the conventional fast Fourier transform (FFT) approach, the processing is carried out entirely in the real domain. Also, since many efficient FHT algorithms exist, the computation complexity can be greatly reduced from two complex FFTs into two real FHTs. >
34 citations
23 May 1989
TL;DR: The result is that a 3-D DCT can be obtained from a 3,D DFT (discrete Fourier transform) of the same size on reals at the cost of permutations and O(3/2N/sup 3/) multiplications.
Abstract: An overview of some alternative algorithms for one- and two-dimensional DCTs (discrete cosine transforms) is given. Operation counts are derived for typical examples useful in image processing. It is shown that it is possible to generalize the 2-D schemes to 3-D DCTs as well. The result is that a 3-D DCT can be obtained from a 3-D DFT (discrete Fourier transform) of the same size on reals at the cost of permutations and O(3/2N/sup 3/) multiplications. The scheme involves rotations on eight output points at a time. Improvements through scaling are discussed, and implementation issues (both in hardware and software) are addressed. >
32 citations
27 Mar 1989
TL;DR: This paper presents a recursive, radix two by two, fast algorithm for computing the two dimensional discrete cosine transform (2D-DCT), which allows the generation of the next higher order 2D- DCT from four identical lower order 2Ds with the structure being similar to the twodimensional fast Fourier transform.
Abstract: This paper presents a recursive, radix two by two, fast algorithm for computing the two dimensional discrete cosine transform (2D-DCT). The algorithm allows the generation of the next higher order 2D-DCT from four identical lower order 2D-DCT's with the structure being similar to the two dimensional fast Fourier transform (2D-FFT). As a result, the method for implementing this recursive 2D-DCT requires fewer multipliers and adders than other 2D-DCT algorithms.
23 citations
TL;DR: The proposed transform offers a higher computational efficiency than the traditional even discrete cosine transform and yields a mean-squared error close to that of the DCT.
Abstract: A computationally efficient DCT- (discrete-cosine-transform) type orthogonal transform obtained by using a construction method developed by W. Kou and H. Zu (1986) is proposed. A recursive relation exists between a higher order and a lower order form of the kernel matrix of the transform and includes the DCT matrices as submatrices. The characteristics of the proposed transform and several fast transform algorithms are discussed. The proposed transform offers a higher computational efficiency than the traditional even discrete cosine transform and yields a mean-squared error close to that of the DCT. Since the HDCT has window spectral structures, it can be used in signal filtering and speech and image processing. >
23 citations
Journal Article•
22 citations
TL;DR: In this article, a least squares IIR (infinite impulse response) algorithm, in the transformed domains, which fits each of the retained subsets of the complex transform components accurately, is presented.
Abstract: The mixed transform representation of time-varying signals uses partial sets of basis functions from the discrete Fourier transform (DFT) and the Walsh-Hadamard transform. The location, magnitude, and phase of the transform components have to be specified for proper signal reconstruction. A least-squares IIR (infinite impulse response) algorithm, in the transformed domains, which fits each of the retained subsets of the complex transform components accurately, is presented. The IIR function, while characterized by real coefficients about twice the number of the retained complex transform components, carries enough location, magnitude, and phase information for accurate signal reconstruction. To illustrate the technique's accuracy and efficiency, its application to model the DFT part of a voice speech segment is given. >
19 citations
TL;DR: A new fast algorithm for computing the two-dimensional discrete Hartley transform that requires the lowest number of multiplications compared with other related algorithms is presented.
Abstract: A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.
TL;DR: The use of the Hartley transform (HT) in cepstrum analysis, as a substitute for the more commonly used Fourier transform (FT), is examined.
Abstract: The use of the Hartley transform (HT) in cepstrum analysis, as a substitute for the more commonly used Fourier transform (FT), is examined. With this substitution, the input to the cepstrum must be in the real domain only. The benefits of using the HT are approximately 50% less data memory required and approximately 40% faster program execution, at no loss in accuracy. >
TL;DR: In this paper, the switched-capacitor realization of the discrete Fourier transform (DFT) is treated as well as the inverse DFT (1DFT), and the output of the DFT has a sinusoidal waveform including the amplitude and phase information of the required spectra.
Abstract: The switched-capacitor realization of the discrete Fourier transform (DFT) is treated in this paper as well as the inverse discrete Fourier transform (1DFT). The output of the DFT has a sinusoidal waveform including the amplitude and phase information of the required spectra. These spectra are given simultaneously and almost in real time. The output of the 1DFT is given merely by adding DFT outputs. Furthermore, the circuit configuration of this system-from input to DFT, from DFT to 1DFT, and from 1DFT to output-is a very simple configuration constructed by a non-recursive filter circuit.
01 May 1989
TL;DR: This paper shows how a rectangular array of N CORDIC (co-ordinate digital computer) processing elements can be used to carry out an efficient two-dimensional systolic implementation of the N-point DFT, offering highly attractive throughput rates in relation to other N-processor solutions.
Abstract: A number of systolic architectures have appeared over the past few years for performing the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms, using both linear and orthogonal processing networks. The paper shows how a rectangular array of N CORDIC (co-ordinate digital computer) processing elements can be used to carry out an efficient two-dimensional systolic implementation of the N-point DFT, offering highly attractive throughput rates in relation to other N-processor solutions, such as the conventional linear systolic array. >
TL;DR: The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform.
Abstract: The data compression performance of the Hartley transform on a Markov-1 signal is theoretically compared to that of the Fourier transform. Covariance distribution and residue correlation measurements have been computed for the Hartley, Fourier, and cosine transforms. The Hartley transform achieves better coding performance than the Fourier transform, but is inferior to the cosine transform. >
TL;DR: A new method to evaluate the WVD of a real signal using the fast Hartley transform (FHT) is presented, compared with the existing fast Fourier transform (FFT) method in terms of computation time.
Abstract: The Wigner-Ville distribution (WVD) is of great significance in time-frequency signal analysis. In the letter we present a new method to evaluate the WVD of a real signal using the fast Hartley transform (FHT). This is compared with the existing fast Fourier transform (FFT) method in terms of computation time. The FHT method presented turns out to be much faster than the FFT method.
TL;DR: The Hartley transform as discussed by the authors represents real data by real transform values, rather than complex, a feature that carries over into optical interferometry and is used for object phase determination starting from only amplitude information in the transform domain.
TL;DR: The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware and describe the modifications required to convert existing fast Fourier transform programs to execute FHTs, showing the ease with which these modifications can be implemented.
Abstract: The authors investigated the implementation aspects of the fast Hartley transform (FHT) in both software and hardware. They describe the modifications required to convert existing fast Fourier transform (FFT) programs to execute FHTs, showing the ease with which these modifications can be implemented. They compare execution time and memory storage requirements of both transforms and present power spectrum calculation and convolution as illustrative examples to compare the performances of the two transform techniques. They also give a comparative survey of the performances of various microprocessors and digital signal processors in FFT and FHT computation. >
TL;DR: An algorithm is presented for factoring Fourier matrices into products of bidiagonal matrices, which make possible discrete Fourier transform (DFT) computation via a sequence of local, regular computations.
Abstract: An algorithm is presented for factoring Fourier matrices into products of bidiagonal matrices. These factorizations have the same structure for every n and make possible discrete Fourier transform (DFT) computation via a sequence of local, regular computations. A parallel pipeline technique for computing sequences of k-point DFTs, for every k >
08 May 1989
TL;DR: It is demonstrated that a separable, orthogonal transform like the 2D-DCT can efficiently be mapped on a very long instruction word multiprocessor architecture, which may accommodate other algorithms.
Abstract: The authors present an ASIC that is able to execute a two-dimensional discrete cosine transform (2D-DCT) algorithm and its inverse (2D-IDCT) at a maximum input sample rate of 13.5 MHz. It is demonstrated that a separable, orthogonal transform like the 2D-DCT can efficiently be mapped on a very long instruction word multiprocessor architecture, which may accommodate other algorithms. Some details and the test strategy are also elaborated. >
01 Oct 1989
TL;DR: The Hartley transform as mentioned in this paper is a real-to-real transform that can be implemented using transversal filter-type structures, and it is suitable for VLSI implementation.
Abstract: The advances in digital fabrication technology have led to a new generation of integrated circuits capable of performing fast arithmetic operations, and opened the door to the consideration of algorithms that may be implemented with simple structures. When the number of data samples in the input block is prime or a product of primes, the Hartley transform can readily be mapped to circular convolutions and then implemented using transversal filter-type structures. Such a structure is simple and regular, and hence it is suitable for VLSI implementation. The Hartley transform is real-to-real and it is the same for both forward and inverse transformations. Hence, it is simpler and may therefore be somewhat faster than the DFT implemented by the same approach.
TL;DR: The Johnson-Burrus method of in situ ordering for FFTs is applied to fast Hartley transforms, tying together two consecutive butterfly operations, involving eight real data, swapping some of their results.
Abstract: The Johnson-Burrus method of in situ ordering for FFTs is applied to fast Hartley transforms. It amounts to tying together two consecutive butterfly operations, involving eight real data, swapping some of their results. Pre- and postpermutation can thereby be avoided. The identification of negative indexes, significantly in Hartley transforms, is nontrivial but easily resolved. >
03 Jan 1989
TL;DR: The Fast Hartley Transform is a promising alternative to the Fast Fourier Transform when the processed data are real numbers but the slowness of the communication imposes a limitation on the speedup when a large number of processors are used.
Abstract: The Fast Hartley Transform is a promising alternative to the Fast Fourier Transform when the processed data are real numbers. The hypercube implementation of the FHT is largely dependent on the way the computation is partitioned. A partitioning algorithm is presented which generates evenly-loaded tasks on each node and demands only a regular communication topology — the Hartley graph. Mapping from the Hartley graph to the Gray graph (binary n-cube) is straightforward, since the Hartley graph has a similar structure as the Gray graph. However, the communication is not always between the nearest neighbors and thus may take some extra time. Moreover, the slowness of the communication in the presently available architectures imposes a limitation on the speedup when a large number of processors are used.
08 May 1989
TL;DR: The two-factor Cooley-Tukey FRFT algorithm is developed and expressed in terms of matrix factorization using Kronecker products, which is generalized to any number of factors.
Abstract: In many applications, it is desirable to have a fast algorithm (FRFT) for the computation of the real discrete Fourier transform (RDFT) for any number of data points. To achieve this, the two-factor Cooley-Tukey FRFT algorithm is developed and expressed in terms of matrix factorization using Kronecker products. This is generalized to any number of factors. Each factor M involves the computation of size M RDFTs, which is carried out by the best size M FRFT algorithm available. >
TL;DR: In this paper, the vector-radix algorithm was proposed for computing the two-dimensional discrete Hartley transform, which does not require separability and is the fastest known algorithm.
Abstract: Three methods have been described for computing the two-dimensional discrete Hartley transform. Two of these employ a separable transform, the third method, the vector-radix algorithm, does not require separability. In-place computation of the vector-radix method is described. Operation counts and execution times indicate that the vector-radix method is fastest.
TL;DR: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real.
Abstract: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real. An algorithm for taking the Hartley transform of a long sequence on a multiprocessor machine by simultaneously transforming short subsequences does not require complex arithmetic and is faster than analogous techniques which use the Fourier transform.
23 May 1989
TL;DR: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002, a general-purpose, dual-bus IEEE standard floating-point digital signal processor that provides the basis for efficient implementation of FFTs and other fast transforms.
Abstract: The authors describe the implementation of real and complex FFT (fast Fourier transform) algorithms on the Motorola DSP96002. The DSP96002 is a general-purpose, dual-bus IEEE standard floating-point digital signal processor (DSP). At a 74-ns instruction cycle, the DSP96002 implements a 1024-point real FFT in 0.905 ms and a 1024-point complex FFT in 1.55 ms. This performance is achieved by calculating up to three floating-point results in a single instruction cycle, or 40.5 MFLOPS peak. A radix-2 FFT butterfly is executed every four cycles, an average of 33.75 IEEE MFLOPS. The instruction set and architecture of the DSP96002 provide the basis for efficient implementation of FFTs and other fast transforms, such as the discrete Walsh-Hadamard transform, discrete cosine transform, and discrete Hartley transform. >
TL;DR: A new fast algorithm for computing the two-dimensional discrete Fourier transform DFT(2n; 2) using the fast discrete cosine transform algorithm that uses only real multiplications, which is more suitable for real input data.
Abstract: We present a new fast algorithm for computing the two-dimensional discrete Fourier transform DFT(2n; 2) using the fast discrete cosine transform algorithm. The algorithm has a lower number of multiplications and additions compared with other published algorithms for computing the two-dimensional DFT. Because it uses only real multiplications, the algorithm is more suitable for real input data.
Patent•
08 Jun 1989TL;DR: In this article, the discrete Fourier transform is continuously calculated at input signal sample rate using recursive filtering, rather than transversal filtering, and the number of complex digital multiplications per computational cycle is reduced to 2N, where a triangular truncation window is used.
Abstract: The discrete Fourier transform is continuously calculated at input signal sample rate using recursive filtering, rather than transversal filtering. This reduces the number of complex digital multiplications per computational cycle to N, the number of spectral components in the discrete Fourier transform, where rectangular truncation window or a new exponential window is used. Where a triangular truncation window is used the number of complex digital multiplications per computational cycle is reduced to 2N.
23 May 1989
TL;DR: A method is presented for computing the discrete Fourier transform (DFT) of data compressed using vector quantization (VQ), suitable for both one-dimensional and multidimensional DFTs or, in general, any linear process.
Abstract: A method is presented for computing the discrete Fourier transform (DFT) of data compressed using vector quantization (VQ). The VQ compressed data are not reconstructed before use; instead, a codebook that has been processed with the DFT (discrete Fourier transform) algorithm is used for VQ reconstruction. An overlap-and-add technique is used to combine the processed reconstruction codebook vectors to give the DFT directly. The technique is suitable for both one-dimensional and multidimensional DFTs or, in general, any linear process. The technique is called the computation compression technique (CCT). The CCT implementation yields exactly the same result as if the compressed data had been reconstructed and the DFT performed on the data directly. CCT convolution on a 68020/6881-based computer is described. Speedups of two orders of magnitude are obtained. >