Iterative gradient technique for the design of least squares optimal FIR magnitude squared Nyquist filters
Andre Tkacenko, Palghat P. Vaidyanathan · 2004
Recently, much attention has been given to the design of optimal finite impulse response (FIR) compaction filters. Such filters, which arise in the design of optimal signal-adapted orthonormal FIR filter banks, satisfy a magnitude squared Nyquist constraint in addition to the inherent FIR assumption. In this paper, we focus on the least squares optimal design of FIR filters whose magnitude squared response satisfies a Nyquist constraint. Using a complete characterization of such systems in terms of Householder-like building blocks, an iterative gradient based greedy algorithm is proposed to design such filters. Simulation results provided show the merit of the proposed technique for designing FIR compaction filters.