DocumentCode :
1204830
Title :
A Note on Stable, Physically Realizable, Linear, Time Invariant Systems
Author :
Wax, Nelson
Volume :
9
Issue :
4
fYear :
1962
fDate :
12/1/1962 12:00:00 AM
Firstpage :
405
Lastpage :
408
Abstract :
A time invariant system is said to be physically realizable if its unit impulse response h(t) is zero for t < 0 . It is often assumed, in treatments of physical realizability, that the Fourier transform of h(t) is square integrable (L_2(-\\infty , \\infty )) . Some use is then made of the regularity of the transform, for real frequencies, to derive further properties of the transform. The condition that the system be stable leads to a different assumption, that |h(t)| be integrable (is L(-\\infty , \\infty ) ); this implies only uniform continuity of the transform for real frequencies. Physically realizable, stable systems are discussed in this note, and several necessary, and a few sufficient, conditions on the Fourier transform of h(t) are summarized. In particular, the behavior of the transform for complex frequencies, the Bode relations, and the Paley-Wiener criterion, are reviewed.
Keywords :
Bibliographies; Books; Convolution; Dispersion; Feedback amplifiers; Fourier transforms; Frequency; Helium; Time invariant systems; Vectors;
fLanguage :
English
Journal_Title :
Circuit Theory, IRE Transactions on
Publisher :
ieee
ISSN :
0096-2007
Type :
jour
DOI :
10.1109/TCT.1962.1086976
Filename :
1086976
Link To Document :
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