Bounding the number of non-zero coefficients in minimal peak-to-peak gain shaping filters
| Autor: | Omer Tanovic, Alexandre Megretski |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
010102 general mathematics
Spectral mask Regular polygon 020206 networking & telecommunications 02 engineering and technology Filter (signal processing) 01 natural sciences Upper and lower bounds LTI system theory Intersymbol interference Quadratic equation Control theory Convex optimization 0202 electrical engineering electronic engineering information engineering Applied mathematics 0101 mathematics Mathematics |
| Zdroj: | ACC |
| DOI: | 10.1109/acc.2016.7526670 |
| Popis: | In this paper we consider the task of designing linear time invariant filters which minimize maximal peak-to-peak gain subject to certain “spectral mask” and “no intersymbol interference” constraints. This problem (as well as many other similar questions) can be formalized as infinite dimensional L1 minimization subject to a single convex quadratic constraint. We show that, under the assumption of strict feasibility, every optimal solution corresponds to a finite unit sample response (FIR) filter. Furthermore, a constructive upper bound for the number of nonzero coefficients of the optimal filter is given. The results do not rely on a “restricted isometry” assumption, and potentially offer an alternative method of predicting the degree of sparsity of a solution of a convex quadratic program. |
| Databáze: | OpenAIRE |
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