Showing papers on "Hadamard transform published in 1969"
01 Jan 1969
TL;DR: A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed, which provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
Abstract: The introduction of the fast Fourier transform algorithm has led to the development of the Fourier transform image coding technique whereby the two-dimensional Fourier transform of an image is transmitted over a channel rather than the image itself. This devlopement has further led to a related image coding technique in which an image is transformed by a Hadamard matrix operator. The Hadamard matrix is a square array of plus and minus ones whose rows and columns are orthogonal to one another. A high-speed computational algorithm, similar to the fast Fourier transform algorithm, which performs the Hadamard transformation has been developed. Since only real number additions and subtractions are required with the Hadamard transform, an order of magnitude speed advantage is possible compared to the complex number Fourier transform. Transmitting the Hadamard transform of an image rather than the spatial representation of the image provides a potential toleration to channel errors and the possibility of reduced bandwidth transmission.
634 citations
TL;DR: An efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.
Abstract: The discrete, orthogonal Walsh functions can be generated by a multiplicative iteration equation. Using this iteration equation, an efficient Walsh transform computation algorithm is derived which is analogous to the Cooley-Tukey algorithm for the complex-exponential Fourier transform.
172 citations
38 citations
28 citations
TL;DR: In this article, Walsh functions are used in transform Spectroscopy to replace the sinusoidal functions appearing in the Fourier transform, and they take only the values + 1 and − 1 and are therefore suitable for the binary digital computer.
Abstract: THIS article suggests that Walsh functions1–3 might be used in transform Spectroscopy4–6 to replace the sinusoidal functions appearing in the Fourier transform. We think this might be the case because Walsh functions are a complete orthonormal set, and therefore give rise to an integral transform of Fourier type; and they take only the values + 1 and − 1 and are therefore likely to be well suited to the binary digital computer.
23 citations
TL;DR: In this article, it was shown that A and B are equivalent over the integers (that is, B can be obtained from A using elementary row and column operations which involve only integers).
Abstract: Supposem is a square-free odd integer, andA andB are any two Hadamard matrices of order 4m. We will show thatA andB are equivalent over the integers (that is,B can be obtained fromA using elementary row and column operations which involve only integers).
18 citations
18 citations
TL;DR: This paper presents an alternate approach to this problem based on the direct product of matrices, easily understood by anyone familiar with matrix theory, and it yields results in a form convenient for implementation and generalization.
Abstract: Posner (1968) has recently discussed a decoding scheme for certain orthogonal and biorthogonal codes which is based on the fast Fourier transform on a finite abelian group. In this paper, we present an alternate approach to this problem based on the direct product of matrices. This approach is easily understood by anyone familiar with matrix theory, and it yields results in a form convenient for implementation and generalization.
14 citations
TL;DR: In this article, the theory of characteristics is extended to include elastic waves in two-spatial dimensions by making use of Hadamard's work on surfaces of discontinuity in the dependent variables and their derivatives.
14 citations
10 citations
TL;DR: In this article, the authors established infinite classes of regular graphs with the property that any two distinct vertices have a fixed number of other vertices joined to both of them, which correspond to certain Hadamard matrices.
Abstract: We establish several infinite classes of regular graphs with the property that any two distinct vertices have a fixed number of other vertices joined to both of them. The graphs are found by constructing their incidence matrices, which correspond to certain Hadamard matrices.
TL;DR: For a quasi-skew Hadamard matrix of order 4m and (4n−1, k, m−n+k) configurations with circulant incidence matrices, there exists an HadAMard matrix (4m(4n − 1).
TL;DR: A matrix factorization is presented for a Hadamard matrix of order twelve that permits a hadamard transform of this order to be computed with substantially fewer operations than by simple matrix multiplication.
Abstract: a matrix factorization is presented for a Hadamard matrix of order twelve that permits a Hadamard transform of this order to be computed with substantially fewer operations than by simple matrix multiplication. The matrix factorization is extended to Hadamard matrices of order 2nX 12 where n is an integer.
TL;DR: Wallis as mentioned in this paper conjectured that an Hadamard matrix always exists for n = 4t, t any integer for any integer in the dimension n, where n is the number of elements in the matrix.
Proceedings Article•
01 Jan 1969
TL;DR: Fourier and Hadamard transformation codings for multidimensional data channel noise immunity and bandwidth reduction are presented.
Abstract: Fourier and Hadamard transformation codings for multidimensional data channel noise immunity and bandwidth reduction