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An Exact Solution for Wave‐Form Distortion of Arbitrary Signals in Ideal Wave Guides
Author(s) -
Vogler L. E.
Publication year - 1970
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs005i012p01469
Subject(s) - bessel function , ideal (ethics) , exact solutions in general relativity , exponential function , simple (philosophy) , transient (computer programming) , signal (programming language) , mathematics , distortion (music) , expression (computer science) , pulse (music) , series (stratigraphy) , mathematical analysis , physics , computer science , optics , telecommunications , bandwidth (computing) , amplifier , philosophy , epistemology , paleontology , detector , biology , programming language , operating system
An exact expression is derived for the transient response of an arbitrarily modulated signal propagating through an ideal wave guide. The solution is in the form of an infinite series of Bessel functions, the coefficients of which depend in a simple manner on the time derivatives of the input signal. It is shown that for the specific example of a step‐modulated carrier signal (the only earlier case for which an exact solution is known) the general expression reduces to that derived in earlier works. A particular case of a ‘double exponential’ pulse is evaluated and briefly discussed.