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Article Dans Une Revue Signal Processing Année : 2021

Forward-backward Filtering and Penalized Least-Squares Optimization: A Unified Framework

Arman Kheirati Roonizi
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Résumé

The paper proposes a framework for unification of the penalized least-squares optimization (PLSO) and forward-backward filtering scheme. It provides a mathematical proof that forwardbackward filtering (zero-phase IIR filters) can be presented as instances of PLSO. On the basis of this result, the paper then represents a unifying approach to the design and implementation of forward-backward filtering and PLSO algorithms in the time and frequency domain. A new block-wise matrix formulation is also presented for implementing the PLSO and forwardbackward filtering algorithms. The approach presented in this paper is particularly suited for understanding the task of zero-phase filters in the time domain and analyzing PLSO algorithms in the frequency domain. In this paper, we show that the task of a zero-phase digital Butterworth filter in the time domain is to fit the signal with impulse train and penalties on the derivatives of the fitted model. For a zero-phase digital Chebyshev filter, a linear combination of derivatives of the model is used in the penalty term.
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Dates et versions

hal-03019950 , version 1 (23-11-2020)

Identifiants

Citer

Arman Kheirati Roonizi, Christian Jutten. Forward-backward Filtering and Penalized Least-Squares Optimization: A Unified Framework. Signal Processing, 2021, 178, pp.107796. ⟨10.1016/j.sigpro.2020.107796⟩. ⟨hal-03019950⟩
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