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A review of orthogonal square-wave functions and their application to linear networks

✍ Scribed by J.L. Hammond Jr.; R.S. Johnson

Publisher
Elsevier Science
Year
1962
Tongue
English
Weight
591 KB
Volume
273
Category
Article
ISSN
0016-0032

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✦ Synopsis

Attention is called to the Haar and Walsh functions as being potentially useful in engineering applications. The Walsh functions have a single magnitude with either a positive or negative sign in the range of definition. Each member of the Haar family also has a single magnitude although this magnitude is different for different members of the set. This interesting property makes the Haar and Walsh functions easy to generate as physical signals and enables analog multiplication by these functions to be performed by an appropriate sequence of sign changes.

In this paper the well-known properties of the Haar and Walsh functions are summarized. Equations are derived which give the output of linear electric networks in terms of Haar and Walsh functions. Expressions relating the Haar and Walsh "spectra" to the complex Fourier spectrum are presented, and practical applications of the results are suggested. An example illustrating the properties of the Haar and ~,Valsh functions is worked out in detail.

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