Showing papers on "Hartley transform published in 1991"
TL;DR: In this article, the authors compare scalare and vector transform methods for global spectral models of the shallow-water equations and show that the vector transform method is algebraically equivalent to the more usual scalar transform methods.
Abstract: We compare scalare and vector transform methods for global spectral models of the shallow-water equations. For the scalar transform methods, we demonstrate some economies in the number of Legendre transforms required. It is shown that the vector transform method is algebraically equivalent to the more usual scalar transform methods, and the choice of transform grid is discussed.
54 citations
TL;DR: In this article, it is shown that the interconnections between the linear arrays can be realized in a regular fashion governed by a permutation cycle that can be determined by simple arithmetic involving a primitive root of the transform length.
Abstract: Fast computation of the discrete Hartley transform (DHT) may be performed by employing a set of linear arrays of Givens rotors. It is shown that the interconnections between the linear arrays can be realized in a regular fashion governed by a permutation cycle that can be determined by simple arithmetic involving a primitive root of the transform length. A suitable implementation of the Givens rotor with add/subtract units and hard-wired shifters is also suggested. >
51 citations
14 Apr 1991
TL;DR: In this paper, an extended lapped transform (ELT) based on a type-IV discrete cosine transform (DCT-IV) is proposed for AR (autoregressive) signals and also for real speech signals.
Abstract: The author presents a fast algorithm for extended lapped transform (ELT), which is a modulated lapped transform (MLT) with longer basis functions. The proposed algorithm is based on a type-IV discrete cosine transform (DCT-IV). For AR (autoregressive) signals and also for real speech signals, the coding performance of the ELT is shown to be significantly higher than that of a block transform such as the DCT (discrete cosine transform), actually approaches the performance of ideal filter banks. Therefore, the ELT is a promising substitute for traditional block transforms in transform coding systems, and also a good substitute for less efficient filter banks in subband coding systems. >
47 citations
TL;DR: In this paper, the authors derived formulas for the two-dimensional Fourier transform of functions with polygonal support and linear amplitude variation from the corresponding formula for a constant function, valid for all nonzero values of the transform variable k, which fail when k is perpendicular or parallel to any edge of the polygon.
Abstract: New formulas for the two-dimensional Fourier transform of functions with polygonal support and linear amplitude variation are derived from the corresponding formula for a constant function. These expressions, valid for all nonzero values of the transform variable k, are superior to those previously reported, which fail when k is perpendicular or parallel to any edge of the polygon. These transforms have applications in diffraction theory and computational electromagnetics. >
40 citations
TL;DR: The method is extended, in a straightforward manner, to the two-dimensional FHT (2-D FHT) by implementing the vector-radix approach, which requires many fewer computational operations than the nonsplit vector- Radix 2- D FHT method.
Abstract: A simple matrix decomposition is provided as a derivation of the one-dimensional split-radix fast Hartley transform (FHT). The method is then extended, in a straightforward manner, to the two-dimensional FHT (2-D FHT) by implementing the vector-radix approach. As a result, the proposed algorithm requires many fewer computational operations than the nonsplit vector-radix 2-D FHT method. >
28 citations
Patent•
NEC1
TL;DR: In this paper, a linear transform calculation on a product signal produced by multiplying a predetermined transform window function and an apparatus input signal is described. But this is not applicable to either of forward and inverse transform units.
Abstract: In an apparatus for carrying out a linear transform calculation on a product signal produced by multiplying a predetermined transform window function and an apparatus input signal, an FFT part (23) carries out fast Fourier transform on a processed signal produced by processing the product signal in a first processing part (21). As a result, the FFT part produces an internal signal which is representative of a result of the fast Fourier transform. A second processing part (22) processes the internal signal into a transformed signal which represents a result of the linear transform calculation. The apparatus is applicable to either of forward and inverse transform units (11, 12).
23 citations
TL;DR: In this paper, the Hartley transform is used to calculate transients and nonsinusoidal waveshape propagation in electric power systems, and a general introduction to the use of Hartley transforms for electric circuit analysis is presented.
Abstract: Because the Fourier transform causes the convolution operation to become a simple complex product, it has been used to solve power system problems. A similar convolution property of the Hartley transform is used to calculate transients and nonsinusoidal waveshape propagation in electric power systems. The importance of this type of calculation relates to the impact of loads, particularly electronic loads, whose demand currents are nonsinusoidal. An example is given in which the Hartley transform is used to assess the impact of an electronic load with a demand which contains rapidly changing current. The authors also present a general introduction to the use of Hartley transforms for electric circuit analysis. A brief discussion of the error characteristics of discrete Fourier and Hartley solutions is presented. Because the Hartley transform is a real transformation, it is more computationally efficient then the Fourier or Laplace transforms. >
21 citations
TL;DR: An Nth-order Hankel transform (also called Fourier-Bessel transform) algorithm designed for many analytically defined functions is presented, which provides greater generality than many others.
Abstract: An Nth-order Hankel transform (also called Fourier-Bessel transform) algorithm designed for many analytically defined functions is presented. This algorithm is not restricted to order zero. As such, it provides greater generality than many others. The traditional difficulty in the evaluation of Hankel transforms, the presence of Bessel functions in the kernel of the integral transform, is eliminated in this new Hankel transform algorithm. The algorithm presented is composed of a fast (linear time) Nth-order Chebyshev transform followed by a fast Fourier transform. >
20 citations
16 Jun 1991
TL;DR: The discrete Hartley transform (DHT) is generalized into 4 classes in the same way as the generalized discrete Fourier transform to achieve fast computation of skew-circular convolution with the generalized transforms.
Abstract: The discrete Hartley transform (DHT) is generalized into 4 classes in the same way as the generalized discrete Fourier transform. The fast algorithms for the resulting transforms are derived. The generalized transforms are expected to be useful in applications such as digital filter banks, computing convolution and signal representation. The fast computation of skew-circular convolution with the generalized transforms is discussed in detail. >
20 citations
TL;DR: In this paper, a general relation between the least mean square (LMS) algorithm and the discrete orthogonal transforms is established, and it is shown that the LMS algorithm could provide a means for the calculation of forward and inverse orthogonality by properly choosing the input vector and adaptation speed.
Abstract: A general relation between the least mean square (LMS) algorithm and the discrete orthogonal transforms is established. Discrete orthogonal transforms, including the discrete Fourier transform (DFT), the discrete Hartley transform (DHT), the discrete cosine transform (DCT), the discrete sine transform (DST), and the Walsh-Hadamard transform (WHT), etc. are extensively used in signal and image processing. It is shown that the LMS algorithm could provide a means for the calculation of forward orthogonal transforms as well as inverse orthogonal transforms by properly choosing the input vector and adaptation speed. >
18 citations
TL;DR: The concept of multidimensional mixed domain transform/spatiotemporal (MixeD) filtering is extended beyond the discrete Fourier transform (DFT) to include other types of discrete sinusoidal transforms, including the discrete Hartley transform (DHT) and the discrete cosinetransform (DCT).
Abstract: The concept of multidimensional mixed domain transform/spatiotemporal (MixeD) filtering is extended beyond the discrete Fourier transform (DFT) to include other types of discrete sinusoidal transforms, including the discrete Hartley transform (DHT) and the discrete cosine transform (DCT). Two MixeD filter examples are given, one using the two-dimensional (2-D) DHT and the other using the 2-D DCT, to selectively enhance a 3-D spatially planar (SP) pulse signal. The authors define the notation and provide a review of the MixeD filter method. MD and partial P-dimensional discrete transform operators are defined, and the design of MixeD filters is discussed. MixeD filters based on the 2-D DHT and the 2-D DCT are designed to selectively enhance a 3-D SP pulse. Experimental verification of these 3-D SP MixeD filters is described. >
TL;DR: A novel method of implementing FIR (finite impulse response) adaptive filters using the discrete Hartley transform (DHT) and the overlap-save method is proposed, which not only has the advantage of fast convergence for highly correlated input signals, but also provides a significant reduction in computation over the conventional time-domain and frequency-domain least mean square adaptive filters.
Abstract: A novel method of implementing FIR (finite impulse response) adaptive filters using the discrete Hartley transform (DHT) and the overlap-save method is proposed. It not only has the advantage of fast convergence for highly correlated input signals, but also provides a significant reduction in computation over the conventional time-domain and frequency-domain least mean square (LMS) adaptive filters. Compared with the previously proposed unconstrained frequency-domain FLMS algorithm, the convergence performance is similar, but an approximate saving of 30% in computation can be obtained for the usual filter length. >
TL;DR: It is shown that for many applications, such as interpolation and convolution of signals, a significant number of zeros are padded to the nonzero valued samples before the transform is computed, and significant savings can be obtained by pruning the FHT algorithm.
Abstract: The discrete Hartley transform (DHT) is discussed as a tool for the processing of real signals. Fast Hartley transform (FHT) algorithms which compute the DHT in a time proportional to N log/sub 2/ N exist. In many applications, such as interpolation and convolution of signals, a significant number of zeros are padded to the nonzero valued samples before the transform is computed. It is shown that for such situations, significant savings in the number of additions and multiplications can be obtained by pruning the FHT algorithm. The modifications in the FHT algorithm as a result of pruning are developed and implemented in an FHT subroutine. The amount of savings in the operation is determined. >
TL;DR: The authors derive a matrix factorization of the coefficient variances for any fixed transformation which significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices.
Abstract: The authors derive a matrix factorization of the coefficient variances for any fixed transformation. This factorization formulation provides a better framework for understanding the role of transform on the one hand, and the signal source model on the other. It also greatly simplifies the number of computational operations required for each variance calculation. A transform-specific matrix which links the transform to the signal correlation model is derived. This factorization provides a conceptual framework for understanding the behaviour of the transform for different source models. It also significantly simplifies the calculation of the variance of each transform coefficient from a quadruple sum over four indices to a double sum over two indices. This simplification can be used in adaptive transform coding which requires an estimate of the variances. Test results demonstrate that this mode-based variance calculation provides an accurate basis for adaptive transform coding, particularly at low bit rates. >
TL;DR: This technique is based on analyzing the Hartley transform spectrum of the image sequence directly, instead of using it to compute other transforms, and is faster than other techniques based on the Fourier transform.
Abstract: A technique for motion estimation of large moving objects is presented. This technique is based on analyzing the Hartley transform spectrum of the image sequence directly, instead of using it to compute other transforms. In this technique, the fast Hartley transform (FHT) is applied to the image sequence and followed by a peak detection procedure. The location of the peak is related to the velocity of the moving object. Dividing the temporal frequency (f/sub p/) corresponding to the detected peak by the corresponding spatial frequency (k/sub p/) gives the velocity of the moving object. The Fourier spectrum for a spatial frequency of k/sub p/ is then computed. This is followed by a peak detection of the Fourier spectrum to validate the previous results and find the direction of the velocity of the moving object. This method is faster than other techniques based on the Fourier transform. >
TL;DR: A fast algorithm is presented which computes the two-dimensional Hartley transform using the decimation in frequency decomposition and, due to its in-place property, it does not require midmemory devices or matrix transposition.
Abstract: A fast algorithm is presented which computes the two-dimensional Hartley transform. This algorithm is referred to as the split vector radix algorithm. It uses the decimation in frequency decomposition and, due to its in-place property, it does not require midmemory devices or matrix transposition. Its computational structure is simpler than that of the algorithm of L.Z. Chen (1983), and it is easy to program. Compared with the vector radix algorithm of R. Kumaresan and P.K. Gupta (1986), the proposed algorithm saves about 35% of the multiplication and 10% of the additions for the discrete Fourier transform (DFT) of a 4096*4096 real valued input sequence. >
TL;DR: In this article, the disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them.
Abstract: The disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Delta(omega) = pi/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter, m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally spaced samples of the inverse Laplace transform function can be obtained by (m/2) + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations.
28 Sep 1991
TL;DR: An analog to the Fourier series based on the cosine-and-sine function is considered in this paper, which is related to the Hartley transform and thus it is termed Hartley series.
Abstract: An analog to the Fourier series based on the cosine-and-sine function is considered. The new series is related to the Hartley transform and thus it is termed the Hartley series. Properties and applications of the Hartley series are discussed in general. It is pointed out that the technique is valuable for the assessment of power quality in industrial and commercial power distribution systems. In particular, the impact of switched and pulse-modulated loads and AC/DC converters may be analyzed. An example is presented in which an industrial distribution system impacted by a six-pulse rectifier is analyzed. >
11 Jun 1991
TL;DR: The feature extraction capability of discrete cosine transform, Walsh-Hadamard transform, WHT, discrete Hartley transform and their sign transformations are investigated and compared and it is shown that the noise immunity of the transform-based feature extraction is rather promising.
Abstract: The feature extraction capability of discrete cosine transform (DCT), Walsh-Hadamard transform (WHT), discrete Hartley transform (DHT) and their sign transformations are investigated and compared for the recognition of two-dimensional binary patterns. It is shown that the noise immunity of the transform-based feature extraction is rather promising. >
01 Jan 1991
TL;DR: The analysis of the Hartley spectrum indicates that the velocities of moving objects are related to the locations of the spectral peaks, and this method is simple, fast, and computationally efficient.
Abstract: A novel technique for motion estimation of moving objects is presented. The analysis of the Hartley spectrum indicates that the velocities of moving objects are related to the locations of the spectral peaks. The presented formulations and simulations demonstrate the applicability of this technique. This method is simple, fast, and computationally efficient. >
01 Jan 1991
TL;DR: A new method of implementing FIR adaptive filters using the discrete Hartley transform (DHT) and the overlap-save method is proposed that not only has the advantage of fast convergence for highly correlated input signals, but also provides a significant reduction in noise.
Abstract: A new method of implementing FIR adaptive filters using the discrete Hartley transform (DHT) and the overlap-save method is proposed. It not only has the advantage of fast convergence for highly correlated input signals, but also provides a significant reduction in
01 Dec 1991
TL;DR: A parallel architecture is presented for the calculation of the fast Hartley transform (FHT) radix 2 which is adequate for its implementation in VLSI technology and is characterised by its modular design and its interconnection regularity.
Abstract: A parallel architecture is presented for the calculation of the fast Hartley transform (FHT) radix 2 which is adequate for its implementation in VLSI technology. As a first step, a constant geometry (decimation in frequency) algorithm for computing the FHT has been developed. The circuit proposed is characterised by its modular design and its interconnection regularity. It can be considered as semi-systolic. It is highly efficient and flexible. It permits the computation of arbitrarily sized FHTs as a consequence of data recirculation over the processing units in all the stages of the transform. The number of communications is the least possible due to the use of a constant geometry algorithm. Each calculation stage requires N/4Q cycles where N and Q are the length of the input real sequence and the number of processors (N = 2n, Q = 2q), respectively. The system proposed calculates the FHT in n stages, therefore, the total calculation time is (N log2N)/4Q cycles.
TL;DR: In this article, a new algorithm for the reconstruction of a real signal (image) from its Hartley-transform modulus only is presented, based on the general theory of the amplitude-phase retrieval problem.
Abstract: A new algorithm for the reconstruction of a real signal (image) from its Hartley-transform modulus only is presented, based on the general theory of the amplitude-phase-retrieval problem. The quality of the recovered image is strongly dependent on the properties of the frequency components in the Hartley-transform space and can be significantly improved by extending the band limit of the Hartley-transform spectrum. The accuracy of the recovered image at high-resolution levels depends on the initial image intensity distribution used in the iteration algorithm. To obtain the best recovery of the image, we propose an instructive method to determine the initial image distribution. The influence of noise contained in the Hartley-transform modulus on the convergent solution is also examined in detail.
30 Sep 1991
TL;DR: Three theorems are proven concerning the ability of various methods to discriminate between similar patterns and second-order neurons are shown to have several advantages over the transform methods.
Abstract: Neural networks can use second-order neurons to obtain invariance to translations in the input pattern. Alternatively transform methods can be used to obtain translation invariance before classification by a neural network. The authors compare the use of second-order neurons to various translation-invariant transforms. The mapping properties of second-order neurons are compared to those of the general class of fast translation-invariant transforms introduced by Wagh and Kanetkar (1977) and to the power spectra of the Walsh-Hadamard and discrete Fourier transforms. A fast transformation based on the use of higher-order correlations is introduced. Three theorems are proven concerning the ability of various methods to discriminate between similar patterns. Second-order neurons are shown to have several advantages over the transform methods. Experimental results are presented that corroborate the theory. >
TL;DR: A set of new order-16 integer transforms is found and the kernel components of the new integer transforms can be represented by one-byte integers, which have better performance and basis restriction mean-square-error than the discrete cosine transform.
TL;DR: A comparison between the use of Fourier and Hartley transforms for motion estimation of multiple moving objects in image sequences is presented and shows that the Hartley technique is faster and requires less memory space than the Fourier technique.
Abstract: A comparison between the use of Fourier and Hartley transforms for motion estimation of multiple moving objects in image sequences is presented. The spectrum of the two transforms show that the temporal frequencies at the peaks (of the spectrum) is related to the velocity of the moving objects. The analysis shows that the Hartley technique is faster and requires less memory space than the Fourier technique. However, it gives the velocity of the moving objects but not the direction. The Fourier spectrum, on the other hand, gives the velocity and direction. An efficient implementation is possible by using the Hartley transform to estimate the temporal frequencies of the peaks and hence the velocities. The fast Fourier transform is then used to compute the spectrum at those peaks. The direction is easily found from the Fourier spectrum by reversing the sign of the temporal frequency corresponding to the peak.
TL;DR: It is shown that two permutation cycles involving primitive roots of M and N can be treated as a guideline to configure the interconnection patterns between different arrays.
TL;DR: The second program extends the use of the PC from performing algebraic operations on matrices to the case in which the matrix elements are complex numbers, providing a compact, easily applied tool for performing sinusoidal steady-state computations and other operations requiring the manipulation of arrays of complex numbers.
Abstract: Two programs are described. The first is a program for digital signal processing that provides for a wide range of input signals and uses the fast Hartley transform for conversions from the time domain to the frequency domain and vice versa. The desired input waveforms can be created internally by the program or imported from an appropriate disk file. The data obtained can be stored in a file as well as displayed on the screen. The second program extends the use of the PC from performing algebraic operations on matrices to the case in which the matrix elements are complex numbers. It provides a compact, easily applied tool for performing sinusoidal steady-state computations and other operations requiring the manipulation of arrays of complex numbers. Examples of the use of both programs are given. >
01 Jan 1991
TL;DR: Recovering weak signals out of noise is the central problem of experimental SETI, and most searches to date have been for narrowband signals, and, consequently, only Fourier transform techniques have been used.
Abstract: Recovering weak signals out of noise is the central problem of experimental SETI. Most searches to date have been for narrowband signals, and, consequently, only Fourier transform techniques have been used. However, from a theoretical point of view, this is not the only possible approach. A given stochastic process X(t) can be either studied by the classical Fast Fourier Transform (FFT) or by another more general transform, named Karhunen-Lo6ve (K-L) after its discoverers (refs. [1], [2], [311, and reading
11 Jun 1991
TL;DR: Using a simple relation between the two-dimensional discrete Fourier transform and the 2D DHT, methods for mapping 210 DFT to 1D DFT can be applied to the Hartley transform.
Abstract: Fast algorithms for computing the two-dimensional discrete Hartley transform (2D DHT) of length p/sup n/*p/sup n/, with p a prime number, are presented. Using a simple relation between the two-dimensional discrete Fourier transform (2D DFT) and the 2D DHT, methods for mapping 210 DFT to 1D DFT can be applied to the Hartley transform. Methods for computing the resulting 1D transforms are also discussed. >