Linear matrix inequality formulation of spectral mask constraints

T. N. Davidson, Z. Q. Luo, J. F. Sturm

Research output: Contribution to journalConference articlepeer-review

8 Scopus citations


The design of a finite impulse response filter often involves a spectral 'mask' which the magnitude spectrum must satisfy. This constraint can be awkward because it yields an infinite number of inequality constraints (two for each frequency point). In current practice, spectral masks are often approximated by discretization, but in this paper we will show that piecewise constant masks can be precisely enforced in a finite and convex manner via linear matrix inequalities. This facilitates the formulation of a diverse class of filter and beamformer design problems as semidefinite programmes. These optimization problems can be efficiently solved using recently developed interior point methods. Our results can be considered as extensions to the well-known Positive-Real and Bounded-Real Lemmas from the systems and control literature.

Original languageEnglish (US)
Pages (from-to)3813-3816
Number of pages4
JournalICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
StatePublished - 2001
Event2001 IEEE International Conference on Acoustics, Speech, and Signal Processing - Salt Lake, UT, United States
Duration: May 7 2001May 11 2001


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