Showing papers on "Hadamard transform published in 1987"
TL;DR: In this paper, a stationary Hadamard encodement mask was designed from a liquid crystal display, which can be installed and positioned in a dispersive instrument, allowing the selected Hadamards encoded spectral elements to be focused on a single detector.
Abstract: A stationary Hadamard encodement mask has been designed from a liquid crystal display. This mask, when properly installed and positioned in a dispersive instrument, allows the selected Hadamard encoded spectral elements to be focused on a single detector. Discussion of the advantages derived by this technique is presented. Several emission spectra in the visible and near-infrared region demonstrate the usefulness of the Hadamard transform technique. This novel spectrometer can provide a no-moving-parts spectroscopy for future spectral applications.
60 citations
TL;DR: In this paper, the LC-SLM Hadamard transform spectrometer was used as a selectively tunable optical filter for Rayleigh line rejection and optical band notching.
Abstract: The successful application of LC-SLM Hadamard transform spectrometry as a simultaneous multiwavelength detection system to Raman spectroscopy is presented. Multiplexed Raman data are obtained with the use of an Ar+ laser lasing at 514.5 nm and a room-temperature silicon photodiode. A conventional 90° scattering geometry is employed for measurements. It is demonstrated that the LC-SLM Hadamard transform Raman spectrometer possesses the capability of performing spectral subtraction and the ability to obtain depolarization ratios of Raman bands, and can function as a selectively tunable optical filter for both Rayleigh line rejection and optical band notching. It is also demonstrated that, for the Hadamard transform Raman experiment, the silicon photodiode used as the detector produces spectra with slightly better signal-to-noise ratios than those obtained with the photomultiplier tube (PMT) used as the detector, although the PMT shows an increase in sensitivity.
43 citations
TL;DR: The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.
Abstract: One of the main results says that ifC is a binary linear code of length 4t and of dimension greater than 2t, thenC contains a word of weight 2t and this bound is best possible. Several results of similar flavor are established both for linear and non-linear codes. For the proof a lemma introducing the binormal forms of binary matrices is needed. The results are applied to determine the coset chromatic number of Hadamard graphs, to solve a problem of Galvin and to give a short proof of a theorem of Gleason on self-dual doubly-even codes.
37 citations
01 Apr 1987
TL;DR: A Gaussian probabilistic model was developed to screen and select from the large set of features and the significant harmonics of the signature were sorted according to the chi-square value, which is equivalent to the signal-to-noise ratio.
Abstract: Features such as shape, motion and pressure, minutiae details and timing, and transformation methods such as Hadamard and Walsh have been used in signature recognition with various degrees of success. One of the better studies was done by Sato and Kogure using nonlinear warping function. However, it is time consuming in terms of computer time and programming time. In this research, the signatures were normalized for size, orientation, etc. After normalization, the X and Y coordinates of each sampled point of a signature over time (to capture the dynamics of signature writing) were represented as a complex number and the set of complex numbers transformed into the frequency domain via the fast Fourier transform. A Gaussian probabilistic model was developed to screen and select from the large set of features (e.g. amplitude of each harmonics). The significant harmonics of the signature were sorted according to the chi-square value, which is equivalent to the signal-to-noise ratio. Fifteen harmonics with the largest signal-to-noise ratios from the true signatures were used in a discriminant analysis. A total of eight true signatures from a single person and eight each from nineteen forgers were used. It results in an error rate of 2.5%, with the normally more conservative jacknife procedure yielding the same small error rate.
37 citations
TL;DR: Walsh transform is a simple, fast and reliable method for separating complex Chinese characters with similar peripheries that have most separability power.
33 citations
TL;DR: Application to the SNR of a general algorithm for the calculation of the average mean square error in the estimate of the spectrum shows that reasonable SNR improvements can be expected when compared to conventional dispersive instruments.
Abstract: The effect of a uniform bistable optical transmission defect in the encoding mask on the multiplex efficiency is investigated for solid-state Hadamard transform spectrometry with thermal detection. It is demonstrated that encoding masks which possess nonideal optical transmission properties, i.e., bistable transmission defects, need not impare the multiplex capability provided a sufficient number of resolution elements are multiplexed. Application to the SNR of a general algorithm for the calculation of the average mean square error in the estimate of the spectrum shows that reasonable SNR improvements can be expected when compared to conventional dispersive instruments.
32 citations
TL;DR: Hadamard matrices of order n with maximum excess σ ( n ) are constructed for n =40, 44, 48, 52, 80, 84 and the largest values achieved for the excess are given.
29 citations
26 citations
TL;DR: Results show that a simple and generally suboptimum two-dimensional LPT coder operating at 2 bit pixer has approximately one third the complexity of a 4 × 4 Hadamard coder while yielding a better SNR.
25 citations
24 citations
TL;DR: Then it is proved that two Hadamard equivalent matrices define equivalent codes.
TL;DR: A new class of codes for data compression is described that combines permutations with the fast Hadamard transform (FHT), invented for digital speech compression based on linear predictive coding (LPC), but may be useful for other data compression applications.
Abstract: A new class of codes for data compression is described that combines permutations with the fast Hadamard transform (FHT). It was invented for digital speech compression based on linear predictive coding (LPC), but may be useful for other data compression applications. One particular code with rate \frac{1}{2} is considered: a 16 -bit code for a block length of 32 samples. All coding and decoding steps are fast, so that real-time applications with cheap hardware can be anticipated.
16 Aug 1987
TL;DR: A new test for detecting nonrandomness in finite binary strings is constructed, which extends and quantifies Gait's test, and it is proved that the measure of the Walsh spectrum is equivalent to aMeasure of the skirts of the logical autocorrelation function.
Abstract: Two spectral tests for detecting nonrandomness were proposed in 1977. One test, developed by J. Gait [1], considered properties of power spectra obtained from the discrete Fourier transform of finite binary strings. Gait tested the DES [10,11] in output-feedback mode, as a pseudorandom generator. Unfortunately, Gait's test was not properly developed [3,4], nor was his design for testing the DES adequate.Another test, developed by C. Yuen [2], considered analogous properties for the Walsh transform. In estimating the variance of spectral bands, Yuen assumed the spectral components to be independent. Except for the special case of Gaussian random numbers, this assumption introduces a significant error into his estimate.We recently [3,4] constructed a new test for detecting nonrandomness in finite binary strings, which extends and quantifies Gait's test. Our test is based on an evaluation of a statistic, which is a function of Fourier periodograms [5]. Binary strings produced using short-round versions of the DES in output-feedback mode were tested. By varying the number of DES rounds from 1 to 16, it was thought possible to gradually vary the degree of randomness of the resulting strings. However, we found that each of the short-round versions, consisting of 1, 2, 3, 5 and 7 rounds, generated ensembles for which at least 10% of the test strings were rejected as random, at a confidence level approaching certainty.A new test, based on an evaluation of the Walsh spectrum, is presented here. This test extends the earlier test of C. Yuen. Testing of the DES, including short-round versions, has produced results consistent with those previously obtained in [3].We prove that our measure of the Walsh spectrum is equivalent to a measure of the skirts of the logical autocorrelation function. It is clear that an analogous relationship exists between Fourier periodograms and the circular autocorrelation function.
TL;DR: In this paper, a fast algorithm for computing the discrete Hartley transform (DHT) via the Walsh-Hadamard transform (WHT) is proposed, which is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two.
Abstract: A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh-Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.
TL;DR: The most general Cauchy data that produce Hadamard singularities in the propagator of a scalar field are obtained in the following backgrounds: space-times with general homogeneous plane cosmological metrics; Robertson-Walker space- times with arbitrary spatial curvature.
Abstract: We obtain the most general Cauchy data that produce Hadamard singularities in the propagator of a scalar field in the following backgrounds: (a) space-times with general homogeneous plane cosmological metrics; (b) Robertson-Walker space-times with arbitrary spatial curvature. Using this result we discuss the propagator's structure derived from two recently proposed Hamiltonian diagonalizations.
TL;DR: The design of an image processor for the total evaluation of cardiac function, which includes automatic boundary extraction, computation of volume, and three-dimensional display of a left ventricle is described.
Abstract: This paper describes the design of an image processor for the total evaluation of cardiac function. The system quantitatively evaluates cardiac function efficiently and accurately. Its functions include automatic boundary extraction, computation of volume, and three-dimensional display of a left ventricle. The method of automatic boundary extraction comprises: 1) processing to vignette and then correct blur using a Hadamard transformation, and 2) processing to extract the boundary automatically and reliably.
TL;DR: The relationship between perfect binary arrays and higher-dimensional Hadamard matrices has been investigated in this article, and it has been shown that there exists no one-dimensional perfect binary array with energy greater than four.
Abstract: The close relationship between perfect binary arrays and higher-dimensional Hadamard matrices is determined in the letter. With this relationship we have proved that there exists no one-dimensional perfect binary array with energy greater than four. We conjecture that this relationship may be helpful for the study of other higher-dimensional perfect binary arrays.
TL;DR: In this article, the feasibility of observing Raman spectra in the near i.r. spectral region using a Hadamard transform spectrometer is discussed, and the encoding mask for the HadAMT is fabricated from a liquid crystal spatial light modulator array (LC-SLM array).
TL;DR: Using the Fourier transform, this article showed that there are no symmetric circulant Hadamard matrices of order greater than 4, which is a theorem of Brualdi and Newman.
Patent•
23 Jul 1987
TL;DR: In this paper, the authors proposed to improve bit condensing rate by making predictive coding processing of color difference signals between signals modulated in the same modulating phase at the time of predictive coding.
Abstract: PURPOSE:To prevent increase of predictive error on color difference signals and improve bit condensing rate by making predictive coding processing of color difference signals between signals modulated in the same modulating phase at the time of predictive coding. CONSTITUTION:A predictive filter is provided with a predicting device 14Y for luminance signal and a predicting device 14C for color difference signal. A one line delay circuit 15Y is connected to the device 14Y and to one line delay circuits 15Ca, 15Cb are connected in series to the predicting device 14C, and these two systems are switched and selected by a change-over switch 16. Predictive data are obtained on Hadamard transformed data of color difference signals CW, CN basing on data two lines before, and accordingly, predictive coding processing is made between Hadamard transformed data of color differ ence signals modulated in the same modulating phase, that is, between color difference signals CW or between color difference signals CN. Thus, as correlation between color difference signals is high, accuracy of prediction is raised and condensing rate is improved.
TL;DR: A new fast algorithm is proposed here to compute the discrete Hartley transform (DHT) via the natural-ordered Walsh-Hadamard transform, which results in substantial saving in the number of multiplications required to obtain the DHT, relative to direct computation.
Abstract: A new fast algorithm is proposed here to compute the discrete Hartley transform (DHT) via the natural-ordered Walsh-Hadamard transform. The processing is carried out on an intraframe basis in (N × N) data blocks, where N is an integer power of 2. The Walsh-Hadamard transform (WHT)W coefficients are computed directly, and then used to obtain the DHT coefficients. This is achieved by an (N × N) transformation matrix (H transform matrix) which is orthonormal and has a block-diagonal structure. As such, it results in substantial saving in the number of multiplications required to obtain the DHT, relative to direct computation. Its total operation is almost equal to that of fast radix 2 DHT, but with a much more simple data transfer path. Using the binary fraction technique, we could get the result within 3 significant digits. The simple, regular and high immunity of round-off noise properties make it practical to be used in signal processing. Above all, it provides a good conversion for these two useful trans...
01 Jan 1987
TL;DR: In this paper, 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.
08 Jan 1987
TL;DR: In this paper, a special algorithm for the Hadamard transformation (HT) is proposed, which decomposes the space-variant HT into a sequence of convolution and undersampling operations.
Abstract: A special algorithm for the Hadamard transformation (HT) is proposed. It decomposes the space-variant HT into a sequence of convolution and undersampling operations, thereby simplifying the interconnection scheme for the transformation. This allows parallel processing of high-bandwidth signals, either 1-D time signals or 2-D images. We discuss two possibilities for the optical implementation of the HT.
TL;DR: A transform-LPC hybrid system for real-time coding of picture data has been presented and the MSE and SNR are seen to be comparable to previous work on transform-DPCM hybrid schemes.
Abstract: A transform-LPC hybrid system for real-time coding of picture data has been presented. The LPC has been made adaptive by using a correlation cancellation loop. Three different schemes for coding and reconstructing the transform components have been presented and their relative performances have been compared. The MSE and SNR are seen to be comparable to previous work on transform-DPCM hybrid schemes.
TL;DR: This correspondence investigates the symmetry and sparseness of the Walsh gain matrices and an efficient sparse matrix algorithm is used to calculate the Walsh Gain matrix.
Abstract: Zarowski and Yunik [1] demonstrated that an FIR filter can be realized with fewer multiplications in the fast Walsh transform (FWT) domain than in the fast Fourier transform (FFT) domain for some transform lengths. This correspondence investigates the symmetry and sparseness of the Walsh gain matrices. An efficient sparse matrix algorithm is used to calculate the Walsh gain matrix.
01 Jan 1987
TL;DR: Five coding techniques in the spatial and transform domains have been evaluated for SAR image compression: linear three-point predictor (LTPP), block truncation coding (BTC), microadaptive picture sequencing (MAPS), adaptive discrete cosine transform (ADCT), and adaptive Hadamard transform (AHT).
Abstract: Five coding techniques in the spatial and transform domains have been evaluated for SAR image compression: linear three-point predictor (LTPP), block truncation coding (BTC), microadaptive picture sequencing (MAPS), adaptive discrete cosine transform (ADCT), and adaptive Hadamard transform (AHT) These techniques have been tested with Seasat data Both LTPP and BTC spatial domain coding techniques provide very good performance at rates of 1-2 bits/pixel The two transform techniques, ADCT and AHT, demonstrate the capability to compress the SAR imagery to less than 05 bits/pixel without visible artifacts Tradeoffs such as the rate distortion performance, the computational complexity, the algorithm flexibility, and the controllability of compression ratios are also discussed