Fast SDP design of FIR compaction filters with combined constraints

We propose in this paper efficient semidefinite programming methods for designing signal adapted compaction filters with (i) spectral mask and (ii) regularity constraints. In both cases, the initial problem, formulated with the Kalman-Yakubovich-Popov lemma, is transformed by simplifying its dual and the result is an SDP problem with Toeplitz matrices and small number of variables. All resulting methods, which may be gathered in a single unifying formulation, always give the optimal filter. We present experimental evidence showing convenient execution times and good numerical accuracy.