Abstract
We consider the problem of discretization of analog filters and propose a novel method based on sampled-data \(H^\infty \) control theory with sparse representation. For optimal discretization, we adopt minimization of the \(H^\infty \) 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 \(\ell ^1\) 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.
Supported in part by the JSPS grant JP20H02172 and 20K21008; Supported in part by the JSPS grant JP19H02161.
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Notes
- 1.
A real-rational transfer function is a rational function of s with real coefficients.
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Nagahara, M., Yamamoto, Y. (2022). Sparse Representation for Sampled-Data \(H^\infty \) Filters. In: Beattie, C., Benner, P., Embree, M., Gugercin, S., Lefteriu, S. (eds) Realization and Model Reduction of Dynamical Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-95157-3_23
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