DocumentCode
21617
Title
Zero Crossings, Overshoot and Initial Undershoot in the Step and Impulse Responses of Linear Systems
Author
Damm, Tobias ; Muhirwa, Luc N.
Author_Institution
Dept. of Math., Univ. of Kaiserslautern, Kaiserslautern, Germany
Volume
59
Issue
7
fYear
2014
fDate
Jul-14
Firstpage
1925
Lastpage
1929
Abstract
We consider functions in the time and the frequency domain, and show how the occurrence of real zeros in the frequency domain is related to the number of zero crossings, overshoot and initial undershoot in the time domain. This leads to simple proofs of known facts for linear time-invariant systems and their generalizations in various directions. In particular, we consider time-delay systems and differential systems of fractional order.
Keywords
delays; frequency-domain analysis; linear systems; time-domain analysis; transient response; fractional order differential systems; frequency domain; impulse response; initial undershoot; linear time-invariant systems; overshoot; time domain; time-delay systems; zero crossings; Delays; Frequency-domain analysis; Laplace equations; Linear systems; Polynomials; Transfer functions; Linear system; polynomials;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2013.2294616
Filename
6681959
Link To Document