Showing papers on "Hadamard transform published in 1989"
TL;DR: A generalized matrix product is introduced, which inherits some useful algebraic properties from the standard Kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula.
Abstract: Discrete unitary transforms are extensively used in many signal processing applications, and in the development of fast algorithms Kronecker products have proved quite useful. In this semitutorial paper, we briefly review properties of Kronecker products and direct sums of matrices, which provide a compact notation in treating patterned matrices. A generalized matrix product, which inherits some useful algebraic properties from the standard Kronecker product and allows a large class of discrete unitary transforms to be generated from a single recursion formula, is then introduced. The notation is intimately related to sparse matrix factorizations, and examples are included illustrating the utility of the new notation in signal processing applications. Finally, some novel characteristics of Hadamard transforms and polyadic permutations are derived in the framework of Kronecker products.
182 citations
TL;DR: The accuracy and reliability of four fringe analysis algorithms have been assessed, using Young's fringe patterns calculated from computer generated speckle patterns, with the lowest errors given by the 2-D Fourier transform method.
Abstract: The accuracy and reliability of four fringe analysis algorithms have been assessed, using Young's fringe patterns calculated from computer generated speckle patterns. The 1-D integration, 1-D autocorrelation, 2-D Fourier transform, and 2-D Walsh transform methods all estimated the two in-plane displacement components with negligible systematic error; the random errors were found to vary in proportion to sigma(2)/VR (speckle diameter = sigma, fringe visibility = V, and radius of laser probe beam = R), with the lowest errors given by the 2-D Fourier transform method.
124 citations
01 Jan 1989
TL;DR: In this article, it was shown that for every n > 1, the nth partial sum of f E R, s,(z, f), is univalent in E, and R is closed with respect to Hadamard convolution.
Abstract: Let R denote the class of functions f(z) = z + a2z2 +* that are analytic in the unit disc E = {z: Izi K 1 } and satisfy the condition Re(f'(z) + zf"(z)) > 0, z E E. It is known that R is a subclass of St, the class of univalent starlike functions in E. In the present paper, among other things, we prove (i) for every n > 1, the nth partial sum of f E R, s,(z, f), is univalent in E, (ii) R is closed with respect to Hadamard convolution, and (iii) the Hadamard convolution of any two members of R is a convex function in E.
120 citations
TL;DR: The center weighted Hadamard transform (CWHT) as mentioned in this paper is a transform that weights the region of mid-spatial frequencies of the signal more than the HT, which is similar to the HT in that it requires only real operations.
Abstract: The center weighted Hadamard transform (CWHT) is defined. This transform is similar to the Hadamard transforms (HT) in that it requires only real operations. The CWHT, however, weights the region of mid-spatial frequencies of the signal more than the HT. A simple factorization of the weighted Hadamard matrix is used to develop a fast algorithm for the CWHT. The matrix decomposition is of the form of the Kronecker products of fundamental Hadamard matrices and successively lower-order weighted Hadamard matrices. >
82 citations
TL;DR: A fast Fourier transform is used to transform normalized signatures into the frequency domain and results in an error rate of 2.5 per cent with the generally more conservative jackknife procedure yielding the same small error rate.
60 citations
Book•
23 May 1989
TL;DR: Part 1 Data: data representation files - algorithm for the generation of inverted files elementary algorithms - Hash algorithms and preprocessing of instrumental data transformations - autocorrelation, Fourier transformation, Hadamard transformation optimization - the SIMPLEX method.
Abstract: Part 1 Data: data representation files - algorithm for the generation of inverted files elementary algorithms - Hash algorithms. Part 2 Preprocessing of data: preprocessing of instrumental data transformations - autocorrelation, Fourier transformation, Hadamard transformation optimization - the SIMPLEX method. Part 3 Data handling: clustering of data - clustering of small sets, Lance-Williams equation pattern recognition computer handling of chemical structures - Morgan's algorithm fractal forms and processes - algorithm A27 for generating Von Koch islands, the cellular automat algorithm, algorithm A29 for calculation of the Mandelbrot set expert systems.
54 citations
45 citations
TL;DR: The classification of Hadamard matrices of order 24 is completed by this paper and Ito-Leon-Longyear [3] and this matrix must be appear in [11].
Abstract: In this paper we give a new Hadamard matrix of order 24 and its properties. This matrix must be appear in [11]. By this paper and Ito-Leon-Longyear [3] the classification of Hadamard matrices of order 24 is completed.
45 citations
TL;DR: In the letter a fast and efficient algorithm is presented for calculating both the DFT and the WHT through the factorisation of the intermediate transform into a product of sparse matrices.
Abstract: In the letter a fast and efficient algorithm is presented for calculating both the DFT and the WHT. This is achieved through the factorisation of the intermediate transform into a product of sparse matrices. The algorithm can implemented using a single butterfly structure, and is amenable for both software and hardware implementations.
40 citations
TL;DR: A general method unifying the known constructions of binary self-orthogonal codes from designs is described, finding more than 70 inequivalent extremal doubly even self-dual codes of length 40 constructed from Hadamard matrices of order 20.
38 citations
01 Mar 1989
TL;DR: It is shown that key instruments for composition of four-symbol 6-codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences, a set of normal or near normal sequences and base sequences.
Abstract: It is shown that key instruments for composition of four-symbol 6-codes are the Lagrange identity for polynomials, a certain type of quasisymmetric sequences (i.e., a set of normal or near normal sequences) and base sequences. The following is proved: If a set of base sequences for length t and a set of normal (or near normal) sequences for length n exist then four-symbol 3-codes of length (2n + 1 )t (or nt) can be composed by application of the Lagrange identity. Consequently a new infinite family of Hadamard matrices of order 4uw can be constructed, where w is the order of Williamson matrices and u = (2n + 1 )t (or nt) . Other related topics are also discussed.
TL;DR: In this paper, the Hadamard transform Raman microprobe is used for spectroscopic microscopy of polycrystalline materials with near-diffraction limited resolution of 1.3 μm.
Abstract: The design of a Hadamard transform Raman microprobe is presented. The spatially multiplexed imaging system provides true spectroscopic microscopy. Near-diffraction limited resolution, 1.3 μm, is demonstrated with Raman images of polycrystalline materials.
TL;DR: In this paper, the status and significance of the question concerning a linear quantum scalar field theory on a globally hyperbolic spacetime is clarified. But it is not yet known whether the laws of quantum field theory are local laws.
Abstract: The authors clarify the status and significance of the (still open) question concerning a linear quantum scalar field theory on a globally hyperbolic spacetime. Can a (quasi-free) locally Hadamard state possess (spacelike) non-local singularities? Previously, one of them has conjectured the answer is no. They challenge the conjecture by investigating examples (some new, one previously introduced by Najmi and Ottewill) of locally Hadamard symmetric bisolutions with non-local singularities. They show that each of the examples considered fails to arise as the anticommutator function of a quantum state-thus removing some 'potential threats' to the validity of the conjecture. They argue that the question raised here is of physical significance in that it addresses the extent to which the laws of quantum field theory are (or can be) local laws.
TL;DR: In this article, a computationally inexpensive method for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks is presented, requiring only O(N[log 2N + 2] arithmetic operations.
Abstract: A computationally inexpensive method is presented for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks. Normally, N measurements are required in order to recover an N-point spectrum; this method requires N + N0 measurements to be taken, where, typically, N0 ≤ 10. Once the additional measurements have been taken, only O(N[log2N + 2]) arithmetic operations—mostly additions or subtractions—are needed in order to recover the spectrum; a conventional procedure requires O(2N2) operations. Preliminary work for this method is minimal, requiring O(N) operations as opposed to O(N3) for a conventional procedure; this work needs to be done only once for a given spectrometer. The spectrum-estimate obtained is unbiased.
TL;DR: A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks.
Abstract: A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3N preliminary arithmetic operations are performed once for a given spectrometer, where N is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional O[N(log2N + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O(N3) preliminary operations, and O(2N2) operations during each spectrum-recovery.
TL;DR: Four new doubly-even codes are constructed from Hadamard matrices of order 28 from EMMARM, including 56, 28, 12 and 56/28.
Patent•
21 Sep 1989
TL;DR: In this paper, a Hadamard mask is placed in the entrance plane of a standard flat field grating spectrograph, and a planar array is used as the detector.
Abstract: A Hadamard mask is placed in the entrance plane of a standard flat field grating spectrograph. A planar array is used as the detector. The Hadamard mask contains 2n-1 elements, where n is the number of elements in the detector array. This configuration produces a spectrograph with a wide aperture and hence high throughput, and allows rapid spectral measurements with no moving parts. It also allows simultaneous measurement of a randomly occurring pulse source.
TL;DR: For Hadamard numbers t and n with t ≤ n and n ≥ 4, the authors showed that there is a saturated orthogonal 4 t−1 × 2 nt−3t+2 main effect plan with nt runs.
Abstract: Hadamard matrices are used to construct some saturated asymmetrical main-effect plans of types 4 s × 2 t and n × 4 s × 2 t . For Hadamard numbers t and n with t ≤ n and n ≥ 4, I show that there exists a saturated orthogonal 4 t−1 × 2 nt−3t+2 main-effect plan with nt runs. If t and n are Hadamard numbers such that t, n ≥ 4 and t/2 is also a Hadamard number, then there exists a saturated orthogonal n × 4 h−1 × 2 n(t−1)−3(h−1) main-effect plan with nt runs, where h = min(t, n).
TL;DR: Hadamard transform spectrometry using a liquid crystal optical shutter array (LC-OSA) as a stationary Hadamard encoding mask is shown to be a viable technique for near-IR Raman spectrometer with the 1064-nm line of a Nd:YAG laser as mentioned in this paper.
Abstract: Hadamard transform spectrometry using a liquid crystal optical shutter array (LC-OSA) as a stationary Hadamard encoding mask is shown to be a viable technique for near-IR Raman spectrometry with the 1064-nm line of a Nd:YAG laser. Spectra are presented and discussed and future plans are outlined.
TL;DR: A modified motion estimation algorithm via Hadamard transform suitable for time-varying space-invariant (TVSI) illumination is proposed, and the latter is shown to be a special case of the authors' formula in the time- Invariant illumination case.
25 Apr 1989
TL;DR: In this article, the authors consider a special class of problems in which the dominant noise source in the spectrum measurements is the noise generated in the detector itself and they show that the signal-to-noise ratio of the spectrum estimates can be improved by a multiplexing technique known as Hadamard spectrometry.
Abstract: The authors consider a special class of problems in which the dominant noise source in the spectrum measurements is the noise generated in the detector itself. In this case, the signal-to-noise ratio of the spectrum estimates can be improved by a multiplexing technique known as Hadamard spectrometry. Specifically, if the MSE (mean-square error) of a single-slit spectrometer is sigma /sup 2/, the MSE of a Hadamard system will be approximately 4/ sigma /sup 2//N. In this expression, N is the number of spectral components to be estimated and the number of measurements to be taken. >
TL;DR: It is shown that anSBIBD(4k2, 2k2 +k,k2 -k) is equivalent to a regular Hadamard matrix of order 4k2 which is equivalent for evenk and for all 2k (in particular all 2K ≤ 210).
Abstract: We show that anSBIBD(4k2, 2k2 +k,k2 +k) is equivalent to a regular Hadamard matrix of order 4k2 which is equivalent to an Hadamard matrix of order 4k2 with maximal excess.
01 Nov 1989
TL;DR: A sub-band coding scheme suitable for advanced television (ATV) transmission in Broadband ISDN is described based on the above simulations, which uses the shortest kernel (2-tap) quadrature mirror filter pairs for signal decomposition and reconstruction.
Abstract: The effect of different finite impulse response analysis/synthesis filter pairs on sub-band coding performance is investigated based on spatial domain considerations. Deterministic as well as real video signals are used for rate and distortion evaluations of various filter pairs. A sub-band coding scheme suitable for advanced television (ATV) transmission in Broadband ISDN is then described based on the above simulations. The scheme uses the shortest kernel (2-tap) quadrature mirror filter (QMF) pairs for signal decomposition and reconstruction. The short span of the filter not only avoids quantization noise spread but also allows simple implementation in the high rate, high quality application considered here. Through successive QMF operations, the signal is decomposed into six bands to achieve low noise coding at the desired rate. The resultant coding scheme is identical to a Hadamard transform (HT) with non-constant block sizes. In addition to excellent coding performance, the hardware architecture is also much simpler than conventional transform coding or sub-band coding schemes.
TL;DR: In this article, it was shown that if q ≡ 1 (mod 8) is a prime power and there exists a Hadamard matrix of order (q − 1)/2, then we can construct a hadamard matrices of order 4q.
Abstract: The purpose of this paper is to prove (1) if q ≡ 1 (mod 8) is a prime power and there exists a Hadamard matrix of order (q − 1)/2, then we can construct a Hadamard matrix of order 4q, (2) if q ≡ 5 (mod 8) is a prime power and there exists a skew-Hadamard matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2), (3) if q ≡ 1 (mod 8) is a prime power and there exists a symmetric C-matrix of order (q + 3)/2, then we can construct a Hadamard matrix of order 4(q + 2).We have 36, 36 and 8 new orders 4n for n ≤ 10000, of Hadamard matrices from the first, the second and third theorem respectively, which were known to the list of Geramita and Seberry. We prove these theorems by using an adaptation of generalized quaternion type array and relative Gauss sums.
01 Jan 1989
TL;DR: Hadamard transform spectrometry (HTS) using a liquid crystal spatial light modulator (LC-SLM) as a stationary encoding mask is shown to be a viable technique for visible and Raman spectrometric as mentioned in this paper.
Abstract: Hadamard transform spectrometry (HTS) using a liquid crystal spatial light modulator (LC-SLM) as a stationary encoding mask is shown to be a viable technique for visible and Raman spectrometry. HTS is a multiplexing method that has many advantages similar to Fourier transform spectrometry. The theory of HTS is presented in simple detail using weighing designs to show the inherent advantages of the technique. Visible Hadamard transform Raman (HT-Raman) spectra are obtained and spectral subtraction is performed on a two liquid mixture.
Patent•
20 Sep 1989
TL;DR: In this paper, a matching zone is defined as the zone in which the sum of the absolute values of the differences between the Hadamard coefficients derived from the templet image and the hadamard coefficient derived from an image to be read takes a minimum value.
Abstract: A method of and device for processing an image by the pattern matching process wherein an image matched with a templet image is determined. In principle, a mismatch degree between the image to be read and the templet image is found by effecting Hadamard transformation on both images and then comparing the images while making use of the Hadamard coefficients found by the transformation of the images. In one embodiment, the matching zone is defined as the zone in which the sum of the absolute values of the differences between the Hadamard coefficients derived from the templet image and the Hadamard coefficients derived from the image to be read takes a minimum value. In another embodiment, differences in Hadamard coefficients of the templet image from those of the image zones each taking the maximum value for each block are added, and then the thus added sum is compared with a pre-set threshold value to determine that the both images, i.e. the image to be read and the corresponding templet image, are mismatched when the added sum is larger than the pre-set threshold value.
TL;DR: In this paper, the effect of a single defective mask element on the output signal-to-noise ratio (SNR) for a stationary-mask Hadamard transform (HT) spectrometer is investigated.
Abstract: The effect of a single defective mask element on the output signal-to-noise ratio (SNR) for a stationary-mask Hadamard transform (HT) spectrometer is investigated. The decrease in output-SNR from that of an HT spectrometer having a perfect mask is found to be dependent on the amount of energy impinging on the defective element. A method of compensating for the defective mask element is presented. The method is computationally inexpensive and can be fully automated.
Patent•
22 Aug 1989
TL;DR: In this article, the authors proposed a method to obtain a noise reducing device replying to the change of the S/N of an input signal by changing the characteristic of a nonlinear circuit corresponding to the noise level of the input signal.
Abstract: PURPOSE: To obtain a noise reducing device replying to the change of the S/N of an input signal by changing the characteristic of a nonlinear circuit corresponding to the noise level of the input signal CONSTITUTION: When the input signal is set at a level over a certain level, an AGC circuit is turned off, and a frame signal can be obtained with a γcorrection circuit 23, an A/D converter 2 and a subtractor 6, The signal is processed at a serial-parallel conversion circuit 7, an Hadamard conversion circuit 8 and a nonlinear processing circuit group 90, and a noise component having weight on a specific frequency level can be obtained The component is supplied to a subtractor 3 via an Hadamard reverse-conversion circuit 10, a serial-parallel conversion circuit 11, then, the noise component can be eliminated from an input video signal When the level of the input signal is lowered, the AGC circuit 22 is turned on, and a nonlinear processing control circuit 24 detects the fact that the control voltage of the AGC circuit 22 is set in a direction to raise a gain And the output of the Hadamard conversion circuit 8 is set differently based on the S/N, therefore, the circuit group 90 can be controlled corresponding to the S/N of the input video signal COPYRIGHT: (C)1991,JPO&Japio