Novel System Inversion Algorithm With Application to Oversampled Perfect Reconstruction Filter Banks

Wahls, Sander; Boche, Holger

doi:10.1109/tsp.2010.2044606

Cited by 10 publications

(6 citation statements)

References 22 publications

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“…Assume that the causal minimum-norm right-inverse of GH with latency time L, P zf := argmin{ P 2 2 : P ∈ RH p×q ∞ , GHP = z −L I}, is well-defined [7]. Then, the precoder Popt in Theorem 2 converges towards √ Etr P zf Power of the scaled receiver input for σ 2 η → 0 : Assume that the minimum-norm right-inverse P zf from the previous subsection is well-defined, G is square and we employ Popt and αopt.…”

Section: Iv-b Remarks and Discussionmentioning

confidence: 99%

Linear IIR-MMSE precoding for frequency selective MIMO channels

Wahls

Boche

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We consider the design of linear precoding filters with respect to the minimum mean square error (MMSE) criterion for systems that employ an additional scalar gain next to a fixed receive filter. The precoding filter and the scalar gain are to be jointly optimized. Currently, only the finite impulse response (FIR) solution to this problem is known. The goal of this paper is to derive the infinite impulse response (IIR) MMSE precoder both with and without causality constraint, i.e., finite and infinite latency time, respectively. We discuss the role of the scalar gain and its relationship to automatic gain control (AGC). We also show that causal precoding requires that the joint first arrival delay of channel and receive filter is not larger than the latency time, and that the IIR-MMSE precoder enjoys the same advantages over the FIR-MMSE precoder as the IIR-MMSE equalizer does over the FIR-MMSE equalizer, viz.: improved performance and no need for latency time optimization.

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Section: Iv-b Remarks and Discussionmentioning

confidence: 99%

Linear IIR-MMSE precoding for frequency selective MIMO channels

Wahls

Boche

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…, 0.4208−0.4208z −0.1584−z ] T . Algorithm 2 in [8] gives us the optimal synthesis filter bank for the decision delay L = 2, R(z) ≈ [ p1 (z) q(z) , p2(z) q(z) , p1(−z) q(z) ], where p 1 (z) := −0.005 − 0.006z + 0.189z 2 + 0.219z 3 + 0.453z 4 + 0.476z 5 + 0.096z 6 , p 2 (z) := −0.003 + 0.115z 2 + 0.070z 4 − 0.329z 6 , and q(z) := 0.028z 2 + 0.396z 4 + z 6 . The quantizer used is v q = argminṽ q ∈{−1,0,1} 3×1 ṽ q − v 2 F .…”

Section: Numerical Examplesmentioning

confidence: 99%

Design of optimal feedback filters with guaranteed closed-loop stability for oversampled noise-shaping subband quantizers

Wahls

Boche

2010

49th IEEE Conference on Decision and Control (CDC)

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We consider the oversampled noise-shaping subband quantizer (ONSQ) with the quantization noise being modeled as white noise. The problem at hand is to design an optimal feedback filter. Optimal feedback filters with regard to the current standard model of the ONSQ inhabit several shortcomings: the stability of the feedback loop is not ensured and the noise is considered independent of both the input and the feedback filter. Another previously unknown disadvantage, which we prove in our paper, is that optimal feedback filters in the standard model are never unique. The goal of this paper is to show how these shortcomings can be overcome. The stability issue is addressed by showing that every feedback filter can be "stabilized" in the sense that we can find another feedback filter which stabilizes the feedback loop and achieves a performance equal (or arbitrarily close) to the original filter. However, the other issues are inherent properties of the standard model. Therefore, we also consider a so-called extended model of the ONSQ, which includes the influence of the feedback filter on the noise power and indirectly also the influence of the inputs statistical properties. We show that the optimal feedback filter for this extended model is unique and automatically achieves a stable feedback loop. We also give an algorithm to compute it.

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“…Specifically, to those non-minimum phase systems with zero feedthrough matix (D) and those systems having special disturbance dynamics. The restrictive condition of requiring zero feed-through matrix appears in most works that are related to the input reconstruction problem [10]. Flouquet and his colleagues [11] have proposed a sliding mode observer for the input recon!…”

Section: Introductionmentioning

confidence: 99%

Inversion-based output tracking and unknown input reconstruction of square discrete-time linear systems

Naderi

Khorasani

2018

Automatica

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In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) systems as well as systems with transmission zeros on the unit circle. Towards this end, we first address the problem of unknown state and input reconstruction of non-minimum phase systems. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter for a delayed non-minimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the output-tracking control problem. We have also proposed a methodology to handle the output tracking prob! lem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros. Simulation case studies are also presented that demonstrate the merits and capabilities of our proposed methodologies.

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Novel System Inversion Algorithm With Application to Oversampled Perfect Reconstruction Filter Banks

Cited by 10 publications

References 22 publications

Linear IIR-MMSE precoding for frequency selective MIMO channels

Linear IIR-MMSE precoding for frequency selective MIMO channels

Design of optimal feedback filters with guaranteed closed-loop stability for oversampled noise-shaping subband quantizers

Inversion-based output tracking and unknown input reconstruction of square discrete-time linear systems

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