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Frequency-Domain Analysis of Linear Time-Periodic Systems

Sandberg, Henrik LU (2003) In IML-R--29-02/03--SE+spring 32, 2002/2003.
Abstract
In this report we study how a time-varying system with a time-periodic integral kernel (impulse response), g(t,\tau)=g(t+T,\tau+T), can be expanded into a sum of essentially time-invariant systems. This allows us to define a linear frequency response operator for periodic systems, called the Harmonic Transfer Function (HTF). The HTF is a direct analog of the transfer function for time-invariant systems, but it captures the frequency coupling of a time-periodic system. It can, for example, be used to compute the induced L_2-norm of periodic systems. The report also includes analysis of convergence of truncated HTFs, which is essential for practical computations as the HTF is an infinite-dimensional operator.
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author
organization
publishing date
type
Book/Report
publication status
published
subject
in
IML-R--29-02/03--SE+spring
volume
32, 2002/2003
publisher
Institut Mittag-Leffler, The Swedish Royal Academy of Sciences
ISSN
1103-467X
language
English
LU publication?
yes
id
e9a14ceb-c009-4316-b5fd-da48c8b97ffb (old id 8602645)
date added to LUP
2016-02-15 18:42:44
date last changed
2016-07-06 14:46:01
@techreport{e9a14ceb-c009-4316-b5fd-da48c8b97ffb,
  abstract     = {In this report we study how a time-varying system with a time-periodic integral kernel (impulse response), g(t,\tau)=g(t+T,\tau+T), can be expanded into a sum of essentially time-invariant systems. This allows us to define a linear frequency response operator for periodic systems, called the Harmonic Transfer Function (HTF). The HTF is a direct analog of the transfer function for time-invariant systems, but it captures the frequency coupling of a time-periodic system. It can, for example, be used to compute the induced L_2-norm of periodic systems. The report also includes analysis of convergence of truncated HTFs, which is essential for practical computations as the HTF is an infinite-dimensional operator.},
  author       = {Sandberg, Henrik},
  institution  = {Institut Mittag-Leffler, The Swedish Royal Academy of Sciences},
  issn         = {1103-467X},
  language     = {eng},
  series       = {IML-R--29-02/03--SE+spring},
  title        = {Frequency-Domain Analysis of Linear Time-Periodic Systems},
  volume       = {32, 2002/2003},
  year         = {2003},
}