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Walsh Functions, Walsh Filters and Self-Similarity

2020
Walsh 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, Lakshminarayan Hazra   +1 more
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Ordering of Walsh Functions

IEEE Transactions on Electromagnetic Compatibility, 1983
The construction of Walsh functions is derived by means of the concepts of "symmetric copy" and "shift copy." Recursive relations based on the Kronecker product of matrices are also deduced from these concepts. There is a fourth useful ordering of the Walsh functions, called here X-ordering, in addition to the three known orderings usually referred to ...
Li Zhihua, Zhang Qishan
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Walsh-function generator

Proceedings of the IEEE, 1971
In recent years several papers dealing with the mathematical theory as well as the technical applications of Walsh functions have been published. One method of defining Walsh functions is by using the Rademacher functions and the multiplication law of Walsh functions which is in fact a binary addition modulo 2 (no carry).
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Function Approximation by Walsh Series

IEEE Transactions on Computers, 1975
Function approximation by a finite Walsh series is considered. There are two methods for selecting the terms of a series. The process of threshold sampling gives a least-square error approximation, but no error analysis technique is available. However, error analysis is possible if terms are selected according to degrees and subdegrees.
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Some Comments Concerning Walsh Functions

IEEE Transactions on Information Theory, 1972
The use of explicit forms for Walsh functions removes much of the confusion surrounding these interesting functions and permits simple proofs of their properties. Thus, for example, their period is far easier to determine than Alexandridis found, but their Fourier spectra are more complex than Schreiber's approximation suggests. For wave-form analysis,
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A Simplified Definition of Walsh Functions

IEEE Transactions on Computers, 1971
A simple method is presented which defines Walsh functions in terms of products of Rademacher functions, but which preserves the ordering of the Walsh functions necessary to retain the notion of increasing number of zero crossings, or sequency.
Lackey, Robert B., Meltzer, David
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Model reduction by walsh function techniques

Mathematics and Computers in Simulation, 1985
This paper discusses the application of Walsh functions expansion to reduce the order of a linear time-invariant system. First, model reduction of linear continuous systems by matching the Walsh spectra of output responses of the original and reduced models, subject to the specific inputs, is discussed.
Kawaji, S., Shiotsuki, T.
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Sinusoids versus Walsh functions

Proceedings of the IEEE, 1974
In most of the applications contemplated for Walsh functions these binary waveforms would replace the more usual sinusoids, as the fast-Walsh-transform algorithm appears to make them very attractive for many kinds of signal processing. This paper begins with a brief review of the characteristics of Walsh functions and of their applications.
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Walsh Function Imagery Analysis

IEEE Transactions on Electromagnetic Compatibility, 1971
This paper presents some new results on the subject of imagery analysis by transform methods. Two transform techniques are presented. The first is the Hadamard-Walsh transform and the second is an eigenvector expansion technique. Experimental results are shown in terms of the degree of imagery data compression that can be obtained for each method ...
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Walsh function generation (Corresp.)

IEEE Transactions on Information Theory, 1969
The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered. The maximum likelihood estimation procedure is assumed. Bounds are derived for the probability of large estimation errors.
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