DocumentCode :
1166951
Title :
Power-series equivalence of some functional series with applications
Author :
Schetzen, M.
Volume :
17
Issue :
3
fYear :
1970
fDate :
8/1/1970 12:00:00 AM
Firstpage :
305
Lastpage :
313
Abstract :
In this paper, we show that the Laplace transform of the expansion h(t) = \\sigma _{n = 0}^{\\infty } c_{n} g_{n} (t) for some important sets g_{n} (t) is equivalent to a power-series expansion. Techniques based on this result are presented for obtaining the coefficients c. as those of a power series; also, methods are presented for obtaining the functional series inverse. The set of Laguerre functions is discussed in detail and, using the power-series equivalence, the truncation error is obtained. The application of the power-series equivalence to the summing of series is shown and illustrated with the Neumann series. Finally, the extension of the power-series equivalence to the expansion of functions of several variables is given. The areas for which the techniques developed are relevant include the analysis and design of signals and the identification and synthesis of processes and systems.
Keywords :
Circuit theory; Functional series; Power series; Series expansions; Australia; Circuit synthesis; Circuit theory; Finite wordlength effects; Laplace equations; Reflection; Scattering; Signal analysis; Signal design; Signal processing;
fLanguage :
English
Journal_Title :
Circuit Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9324
Type :
jour
DOI :
10.1109/TCT.1970.1083120
Filename :
1083120
Link To Document :
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