DocumentCode :
821928
Title :
Boundedness of Multidimensional Filters Over a Prescribed Frequency Domain
Author :
Zhou, Tong
Author_Institution :
Dept. of Autom., Tsinghua Univ., Beijing
Volume :
56
Issue :
11
fYear :
2008
Firstpage :
5487
Lastpage :
5499
Abstract :
Signal processing often requires the magnitude of a filter simultaneously upper and lower bounded on some specified frequency domains. In this paper, on the basis of the structure of the span of a multivariate matrix polynomial, a sufficient condition is derived for the boundedness of a multidimensional multiple-input multiple-output (MIMO) infinite-impulse-response (IIR) filter over a cuboid frequency domain. This condition is expressed through a linear matrix inequality (LMI) and can be proved to be less conservative than a condition derived from an upper bound of matrix structured singular value. Moreover, using parameter dependent LMIs and the linear fractional transformation structure of the filter, two necessary and sufficient conditions are also obtained for this boundedness verification problem, which are again expressed by LMIs. Furthermore, LMI based conditions are derived for filter output matrix and direct transmission matrix, which are applicable to filter design. Numerical examples are included to illustrate the efficiency and characteristics of the derived theoretical results.
Keywords :
IIR filters; MIMO systems; frequency-domain analysis; linear matrix inequalities; network synthesis; singular value decomposition; transient response; boundedness verification problem; cuboid frequency domain; direct transmission matrix; filter design; filter output matrix; infinite-impulse-response filter; linear fractional transformation structure; linear matrix inequality; matrix structured singular value; multidimensional filters boundedness; multiple-input multiple-output filter; multivariate matrix polynomial; prescribed frequency domain; signal processing; IIR filter; Infinite-impulse-response (IIR) filter; linear matrix inequality; multi-dimensional filter; multi-input multi-output system; multidimensional filter; multiple-input–multiple-output (MIMO) system; multivariate matrix polynomial; parameter dependent LMI; parameter-dependent linear matrix inequality (LMI); spectral masks;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2008.929130
Filename :
4585352
Link To Document :
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