Showing papers on "Hadamard transform published in 1977"
TL;DR: The equivalence of M -sequence matrices to Walsh-Hadamard matrices can be exploited to take advantage of the latter's fast transform algorithm.
Abstract: The equivalence of M -sequence matrices to Walsh-Hadamard matrices can be exploited to take advantage of the latter's fast transform algorithm. The nature of the obvious equivalence, its relation to the M -sequence and its implementation as address modifications realized by linear feedback shift-registers are discussed.
128 citations
TL;DR: The Walsh-Hadamard transform has recently received increasing attention in engineering applications due to the simplicity of its implementation and to its properties which are similar to the familiar Fourier transform.
Abstract: The Walsh-Hadamard transform has recently received increasing attention in engineering applications due to the simplicity of its implementation and to its properties which are similar to the familiar Fourier transform. The transform matrices found so far to possess fast algorithms are the naturally ordered and dyadically ordered matrices, whose algorithms are similar to the Cooley-Tukey algorithm, and to the machine-oriented algorithm of Corinthios [2], respectively.
65 citations
TL;DR: Rate-distortion functions for 2-dimensional homogeneous isotropic images are compared with the performance of five source encoders designed for such images and 6-pel DPCM with entropy coding performed best with the mean-square error distortion measure.
Abstract: Rate-distortion functions for 2-dimensional homogeneous isotropic images are compared with the performance of five source encoders designed for such images. Both unweighted and frequency weighted mean-square error distortion measures are considered. The coders considered are a) differential pulse code modulation (DPCM) using six previous samples or picture elements (pels) in the prediction--herein called 6-pel DPCM, b) simple DPCM using single-sample prediction, c) 6-pel DPCM followed by entropy coding, d) 8 \times 8 discrete cosine transform coding, and e) 4 \times 4 Hadamard transform coding. Other transform coders were studied and found to have about the same performance as the two transform coders above. With the mean-square error distortion measure, 6-pel DPCM with entropy coding performed best. Next best was the 8 \times 8 discrete cosine transform coder and the 6-pel DPCM--these two had approximately the same distortion. Next were the 4 \times 4 Hadamard and simple DPCM, in that order. The relative performance of the coders changed slightly when the distortion measure was frequency weighted mean-square error. From R = 1 to 3 bits/pel, which was the range studied here, the performances of all the coders were separated by only about 4 dB.
64 citations
TL;DR: In this article, it was shown that Aα ≡ (aijα) is positive definite for all real α ⩾ n − 2 positive definite matrices with non-negative entries.
59 citations
TL;DR: An algorithm has been developed for calculating sequency-ordered fast Walsh-Fourier transforms (FWT's) using an additive recursion formula that is fast, computer efficient, and applied to time-dependent spectral analysis of nonstationary phenomena such as speech.
Abstract: An algorithm has been developed for calculating sequency-ordered fast Walsh-Fourier transforms (FWT's) using an additive recursion formula. Sequency-ordered FWT's of an N-dimensioned sampled data set are generated by a summation recursion of FWT's on subintervals of the data set. The algorithm is fast (N log2 N summations), computer efficient, and can be applied to time-dependent spectral analysis of nonstationary phenomena such as speech.
42 citations
TL;DR: A set of recursive rules which generate unitary transforms with a fast algorithm (FUT) are presented and generalization to complex and multidimensional unitary transform is considered and some structural relations between transforms are established.
Abstract: A set of recursive rules which generate unitary transforms with a fast algorithm (FUT) are presented For each rule, simple relations give the number of elementary operations required by the fast algorithm The common Fourier, Walsh-Hadamard (W-H), Haar, and Slant transforms are expressed with these rules The framework developed allows the introduction of generalized transforms which include all common transforms in a large class of “identical computation transforms” A systematic and unified view is provided for unitary transforms which have appeared in the literature This approach leads to a number of new transforms of potential interest Generalization to complex and multidimensional unitary transforms is considered and some structural relations between transforms are established
38 citations
TL;DR: In this article, the existence of all Hadamard matrices of order 4t is proved via construction of a complete set of mutually orthogonal $F$-squares of order n = 4t, t being a positive integer.
Abstract: The purpose of this paper is to demonstrate the existence via construction of a complete set of mutually orthogonal $F$-squares of order $n = 4t, t$ a positive integer, with two distinct symbols. The proof assumes that all Hadamard matrices of order $4t$ exist; they are known to exist for all $1 \leqq t \leqq 50$ and for 2$^p$. Two methods of construction, that is, Hadamard matrix theory and factorial design theory, are given; the methods are related, but the approaches differ.
27 citations
TL;DR: Upper and lower bounds for w ( n) are derived for the weight of H to be w ( H ) = number of 1's in H , and w(n) = max {w(H); H ∈ Ω n } .
26 citations
TL;DR: A truly random sequence of numbers has an asymptotically flat Walsh power spectrum, which is used to devise a new test for the randomness of the output of random number generators.
Abstract: A truly random sequence of numbers has an asymptotically flat Walsh power spectrum. This fact is used to devise a new test for the randomness of the output of random number generators. Because it takes little computing time to obtain the Walsh power spectrum of even very long sequences, generators with large periods can be tested. Some computed examples are shown.
22 citations
TL;DR: In this paper, it was shown that for any pair M,N of n by n M-matrices, the Hadamard product M°N -1 is again an Mmatrix.
Abstract: We show that for any pair M,N of n by n M-matrices, the Hadamard (entry-wise) product M°N -1 is again an M-matrix. For a single M-matrix M, the matrix M°M -1 is also considered.
TL;DR: It is shown that there are no other block designs with these parameters, i.e., each such design is embeddable in a symmetric design.
08 Dec 1977
TL;DR: A conditional replenishment transform video compressor has been simulated in preparation for hardware design, which operates at a fixed rate and uses compressed frame memories at the transmitter and receiver.
Abstract: Most interframe video compression using transforms uses three-dimensional transforms or differential pulse code modulation (DPCM) between successive frames of two-dimensionally transformed video. Conditional replenishment work is nearly all based on DPCM of individual picture elements, although conditional replenishment of transform subpictures can take advantage of the predefined subpictures for addressing and can use the most significant transform vectors for change detection without decoding the compressed image. A conditional replenishment transform video compressor has been simulated in preparation for hardware design. The system operates at a fixed rate and uses compressed frame memories at the transmitter and receiver. Performance is a function of transmission rate and memory capacity and is dependent on the motion content of the compressed scene.© (1977) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: A methodology is developed to obtain subjectively optimum quantizers for Hadamard-transformed still pictures and it is indicated that the mmssd quantizers based on subjective visibility of the quantization noise are less companded than the MMSE quantizers.
Abstract: A methodology is developed to obtain subjectively optimum quantizers for Hadamard-transformed still pictures. To exploit the perceptual redundancies that depend upon the local properties of the picture, a small block (2 × 2 × 2, horizontal-vertical-temporal) is used. A series of subjective tests was carried out to determine the visibility of impairment in the reconstructed picture when noise, which simulated the quantization noise, was added to the Hadamard coefficients in the transform domain (H-noise). A design procedure for quantizers was developed using these visibility functions. These quantizers minimize the “mean-square subjective distortion” (mmssd) due to quantization noise. The resulting picture Quality and entropy were compared with that of Max-type quantizers which minimize the “mean-square error” (mmse). This comparison indicates that the mmssd quantizers based on subjective visibility of the quantization noise are less companded than the MMSE quantizers. Also for the same number of quantization levels, pictures coded with mmssd quantizers have better quality and less entropy than the pictures coded with minimum mean-square quantizers.
TL;DR: In this paper, the dispersion equation for elastic waves of small amplitude in a pre-stressed plate of restricted Hadamard material is derived and its solutions are investigated in detail.
Abstract: The dispersion equation for elastic waves of small amplitude in a pre-stressed plate of restricted Hadamard material is derived and its solutions are investigated in detail. The implications for stability are discussed.
TL;DR: A simple algorithm is developed for obtaining the sequency vector of high-order Hadamard transform matrices without the need for converting the order of individual hadamard functions to sequency.
Abstract: A simple algorithm is developed for obtaining the sequency vector of high-order Hadamard transform matrices without the need for converting the order of individual Hadamard functions to sequency.
07 Nov 1977
TL;DR: A hybrid version of Haar (HT) and Walsh-Hadamard transforms (WHT) which effectively combines the advantages of both the transforms has been developed and fast algorithms for efficient implementation of rationalized HHT (RHHT)r based on sparse matrix factors are developed.
Abstract: A hybrid version of Haar (HT) and Walsh-Hadamard transforms (WHT) called Hadamard-Haar trans form (HHT)r which effectively combines the advantages of both the transforms has been developed. Recently HT has beet rationalized such that the Powers of Y'2 are replaced by integer powers of 2 [11-131. Besides, the rationalized HT (RHT) retains all the properties of HT. Similar to (RHT), the (HHT)r 'IS now rationalized. Fast algorithms for efficient implementation of rationalized HHT (RHHT)r based on sparse matrix factors are now developed. Also by using pipeline structure, realrtime digital processors are now designed. These hardware utilize only adders, subtractors and delay units.
01 Oct 1977
TL;DR: The results of an extensive investigation of the properties of 64-point Hadamard transformed speech are presented in this article, where detailed information is given about the probability density functions of the hadamard coefficients, the average power-density spectrum in the Hasamard domain and the logical-autocorrelation function.
Abstract: The results of an extensive investigation of the properties of 64-point Hadamard transformed speech are presented. Detailed information is given about the probability density functions of the Hadamard coefficients, the average power-density spectrum in the Hadamard domain and the logical-autocorrelation function. The results indicate that good-quality speech can be reconstructed from 6 to 8 dominant Hadamard coefficients, but that the use of fewer coefficients is unlikely to lead to the reconstruction of speech of acceptable quality. The results of a preliminary series of listening tests are presented and these confirm conclusions drawn from the statistical properties of the transformed speech. It is shown that the number of bits needed for coefficient labelling constitutes a significant proportion of the total number of bits needed to represent Hadamard transformed speech. A technique is presented for reducing by more than 50% the number of labelling bits needed, and it is explained how, by using this technique, it should be possible to obtain good quality speech when using a transmission bit rate of 8 k bits/s.
TL;DR: In this paper, the Fast Hadamard Transform (F.H.T) was used for image coding in the near infrared (λ = 2 μm) with the code being materialised by a grid with transmission properties.
TL;DR: The effects of hardware round-off error when using the two-dimensional Hadamard transform to code 8 by 8 pixel subpicture blocks of imagery are presented and simulations show that at least 8 bits of precision are desirable.
Abstract: The effects of hardware round-off error when using the two-dimensional Hadamard transform to code 8 by 8 pixel subpicture blocks of imagery are presented. The simulations show that at least 8 bits of precision are desirable.
TL;DR: In this article, the authors investigated the application of Hadamard transform spectroscopy (HTS) to analytical atomic spectromopy and found that HTS offers a slight multiplex advantage over single slit scanning of the spectrum for the measurement of intense lines, as in atomic absorption, but is disadvantageous for measuring small signals in atomic emission and fluorescence.
TL;DR: In this article, Das and Bose showed that the Gelfand t rans forms of the gene-to-r s have no common z e r o r o c o c t in R = R(P|C) rather than in the Banach a lgebra R(p k ).
Abstract: In [2] Sen def ined a r ing R of e n t i r e f u n c t i o n s which t u r n s out to be a commutative Banach a lgebra wi th i d e n t i t y element. Das and Bose s tudied in [ 1 ] the idea l s t r u c t u r e of R, and the main r e s u l t s a re a c h a r a c t e r i z a t i o n of the f ixed maximal i d e a l s (Theorem 1) and the f a c t t ha t every f i n i t e l y generated idea l whose gene ra to r s have nonvanishing Gelfand t rans forms i s p r i n c i p a l (Theorem 2 j . Unfo r tuna te ly , Theorem 1 i s f a l s e (I(oi) i s not an idea l f o r oc^O) and Theorem 2 holds in any commutative Banach a lgebra with i d e n t i t y element, even under much weaker assumpt i o n s ( the Gelfand t rans forms of the gene ra to r s have no common z e r o ) . The aim of t h i s paper i s t o c o r r e c t the e r r o r s and solve the problems mentioned above in a s l i g h t l y more genera l s e t t ing. We def ine a r i ng R = R(pk) of e n t i r e f u n c t i o n s which i s the r ing R of Das and Bose f o r = k ! . Since we are mainly i n t e r e s t e d in the a l g e b r a i c s t r u c t u r e , we study only the r ing R = R(P|C) r a t h e r than the Banach a lgebra R(p k ) . The main r e s u l t s of the paper are the fo l lowing : 1. Every f i n i t e l y generated i dea l in R i s p r i n c i p a l . 2. The f ixed maximal i d e a l s a re exact ly the i dea l s
TL;DR: It is shown that the fast Walsh transform can be used to facilitate the necessary computation in Walsh-type signals exciting memoryless power-law systems.
Abstract: Walsh-type signals exciting memoryless power-law systems are considered. The input is assumed to consist of a sum of weighted Walsh functions. A method is given for finding the weights of the Walsh functions in the output when the input is a finite Walsh series. It is shown that the fast Walsh transform can be used to facilitate the necessary computation.
TL;DR: In this paper, an error detection and correction system is described which will correctly detect the amplitude of a sequency error in a transmitted Walsh-Hadamard-transformed picture, provided no more than one error per block occurs.
Abstract: An error detection and correction system is described which will correctly detect the amplitude of a sequency error in a transmitted Walsh--Hadamard-transformed picture, provided no more than one error per block occurs. For a head-and-shoulder picture, a planar prediction corrector will then remove any sequency error whose magnitude is ⩾ (10/256) Δ, where Δ is the quantisation step size.
TL;DR: In this paper, it was shown that the noncharacteristic Cauchy problem is always solvable in the class of real analytic functions in Iw if the operator has a principal part which is hyperbolic in the direction normal to the initial hyperplane.