4 research outputs found
Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm
This paper presents a new method for signal reconstruction by leveraging
sampled-data control theory. We formulate the signal reconstruction problem in
terms of an analog performance optimization problem using a stable
discrete-time filter. The proposed H-infinity performance criterion naturally
takes intersample behavior into account, reflecting the energy distributions of
the signal. We present methods for computing optimal solutions which are
guaranteed to be stable and causal. Detailed comparisons to alternative methods
are provided. We discuss some applications in sound and image reconstruction
Sampling from a system-theoretic viewpoint
This paper studies a system-theoretic approach to the problem of reconstructing an analog signal from its samples. The idea, borrowed from earlier treatments in the control literature, is to address the problem as a hybrid model-matching problem in which performance is measured by system norms. \ud
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The paper is split into three parts. In Part I we present the paradigm and revise the lifting technique, which is our main technical tool. In Part II optimal samplers and holds are designed for various analog signal reconstruction problems. In some cases one component is fixed while the remaining are designed, in other cases all three components are designed simultaneously. No causality requirements are imposed in Part II, which allows to use frequency domain arguments, in particular the lifted frequency response as introduced in Part I. In Part III the main emphasis is placed on a systematic incorporation of causality constraints into the optimal design of reconstructors. We consider reconstruction problems, in which the sampling (acquisition) device is given and the performance is measured by the -norm of the reconstruction error. The problem is solved under the constraint that the optimal reconstructor is -causal for a given i.e., that its impulse response is zero in the time interval where is the sampling period. We derive a closed-form state-space solution of the problem, which is based on the spectral factorization of a rational transfer function