Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Multiple Fourier analysis in rectifier problems. II

Authors: Robert L. Sternberg, Michael R. Sheets, Helen M. Sternberg, Abraham Shigematsu and Alice L. Sternberg
Journal: Quart. Appl. Math. 32 (1974), 293-315
MSC: Primary 78.42
DOI: https://doi.org/10.1090/qam/434156
MathSciNet review: 434156
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Abstract: The nonlinear problem of the multiple Fourier analysis of the output from a cut-off power-law rectifier responding to a two-frequency input, reviewed in general in Part I of this study [1], is further scrutinized here for the special case of a zero-power-law device; i.e., a bang-bang device or a total limiter. Solutions for the modulation product amplitudes or multiple Fourier coefficients as in Part I appear as Bennett functions, and line graphs of the first fifteen basic functions for the problem are given. The new functions $ {A_{mn}}^{\left( 0 \right)}\left( {h,k} \right)$ studied, being based on a discontinuous device, then, together with the functions $ {A_{mn}}^{\left( 1 \right)}\left( {h,k} \right)$ studied in Part I, provide approximate solutions to the two-frequency modulation product problem for an arbitrary piecewise continuous nonlinear modulator, and the solution for this general problem is outlined. Finally, numerical tables of the zeroth-kind functions $ {A_{mn}}^{(0)}\left( {h,k} \right)$ graphed have been prepared and are available separately in the United States and Great Britain. As before, the entire theory is based on the original multiple Fourier methods introduced by Bennett in 1933 and 1947.

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DOI: https://doi.org/10.1090/qam/434156
Article copyright: © Copyright 1974 American Mathematical Society

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