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IEEE Transactions on Electronic Computers, 1964
Beweis einer Vermutung von \textit{W. K. Henderson} [ IEEE Trans. Electron. Comput. 13, 50--52 (1964; Zbl 0137.25203)], nach der alle Walsh-Matrizen symmetrisch sind.
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Beweis einer Vermutung von \textit{W. K. Henderson} [ IEEE Trans. Electron. Comput. 13, 50--52 (1964; Zbl 0137.25203)], nach der alle Walsh-Matrizen symmetrisch sind.
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On an Ordering of Walsh Functions
IEEE Transactions on Computers, 1978Summary: In addition to the automorphism between the sequency and the Gray-code-of-sequency ordering for Walsh functions there is also one for Kacsmarz ordering. This is shown by using a matrix definition suggested by \textit{K. W. Henderson} some years ago [IEEE Trans. Electron. Comput. 13, 50--52 (1964; Zbl 0137.25203)].
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IEEE Transactions on Computers, 1974
Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocal1 except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series
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Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocal1 except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series
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Recursive evaluation of walsh coefficients for multiple integrals of walsh series
Automatica, 1984The paper refers to the problem of error propagation resulting from truncation of the operational matrix in Walsh series. Algebraic properties of the partitioned operational matrix and of the partitioned coefficient vectors are given. Using these properties, recursive expressions are derived for evaluating residual terms associated with truncation of ...
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2005 IEEE International Symposium on Circuits and Systems, 2005
The new ternary Walsh transform is introduced in this article. It is based on Kronecker product as well as the known Galois field (3) (GF(3)) and new ternary operations and its big advantage is that the same hardware implementation can be used for both forward and inverse ternary Walsh transforms.
Bogdan J. Falkowski, Shixing Yan
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The new ternary Walsh transform is introduced in this article. It is based on Kronecker product as well as the known Galois field (3) (GF(3)) and new ternary operations and its big advantage is that the same hardware implementation can be used for both forward and inverse ternary Walsh transforms.
Bogdan J. Falkowski, Shixing Yan
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Walsh Functions, Walsh Filters and Self-Similarity
2020Walsh functions, Walsh filters and their self-similarity are discussed in this chapter. One and two-dimensional Walsh functions in rectangular and polar co-ordinates are defined. The concepts of radial and azimuthal Walsh functions are introduced. The method of generation of azimuthal Walsh functions of different orders has been demonstrated. Azimuthal
Indrani Bhattacharya +1 more
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New Capabilities of Walsh Functions and Walsh Transforms
1977Abstract : Research progress has been in four areas: solution of difference equations; sequency ordering of Hadamard functions; generalized orthogonal transformation matrix; and analysis of nonlinear systems.
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Diskrete WALSH-Transformationen, schnelle WALSH-Transformationen
1994In diesem Kapitel besprechen wir Zusammenhange, welche fur die numerische Behandlung von WALSH-Transformationen wichtig sind. Wir leiten sog. „schnelle WALSH-Transformationen“ her. Das sind Produktzerlegungen der Transformationsmatrix, welche die Anzahl der Rechenoperationen reduzieren.
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