Sparse Representation for Sampled-Data $$H^\infty $$ H ∞ Filters

Masaaki Nagahara () and Yutaka Yamamoto ()
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Masaaki Nagahara: The University of Kitakyushu
Yutaka Yamamoto: Kyoto University

A chapter in Realization and Model Reduction of Dynamical Systems, 2022, pp 427-444 from Springer

Abstract: Abstract We consider the problem of discretization of analog filters and propose a novel method based on sampled-data $$H^\infty $$ H ∞ control theory with sparse representation. For optimal discretization, we adopt minimization of the $$H^\infty $$ H ∞ norm of the error system between a (delayed) target analog filter and a digital system consisting of an ideal sampler, the zero-order hold, and an FIR (finite impulse response) filter. Also, for digital implementation, we propose a sparse representation of the FIR filter to reduce the number of nonzero coefficients with the $$\ell ^1$$ ℓ 1 norm regularization. We show that this multi-objective optimization is reducible to a convex optimization problem, which can be solved efficiently by numerical computation. We then extend the design method to multi-rate filters, and show a design example. We also give an application to the feedback filter design of delta-sigma modulators.

Keywords: Sparse representation; Compressed sensing; Sampled-data control; Filter design; Delta-sigma modulation; Convex optimization (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95157-3_23

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DOI: 10.1007/978-3-030-95157-3_23

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