Perfect reconstruction of signal—a new polynomial matrix inverse approach

Hunek, Wojciech P.; Majewski, Paweł

doi:10.1186/s13638-018-1122-5

Cited by 21 publications

(13 citation statements)

References 24 publications

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“…Theorem 2: Consider the second-order MISO system governed by Eqs. (1). Then, the x(k) for k ≥ 1 lies in the kernel of (z R I 2 − F), finally to obtain…”

Section: A Towards a General Theory Of Minimum-energy Perfect Contromentioning

confidence: 99%

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A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

Hunek

Feliks

2020

IEEE Access

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A new geometric approach providing the minimum-energy issue for inverse model controlrelated perfect regulation of linear time-invariant multi-input/single-output plants described in the discretetime state-space framework is proposed in the paper. Recent results have shown that the minimum-norm T-inverse does not guarantee the minimum-energy perfect control design, which has been confirmed by heuristic studies only. The new proposal, postulated throughout the manuscript, certifies the potential of nonunique σ-inverse regarding the minimum-energy behavior of inverse model control-based structures. After application of the proposed geometric approach dedicated to some class of state-space systems, we can precisely calculate the total energy of the multivariable perfect control runs. Thus, the analytical new methodology allows to obtain the minimum-energy inverse model control schemes, what constitutes the main accomplishment of the paper. Additionally, the aim of future analytical exploration covering the entire class of right-invertible state-space systems is clearly focused. INDEX TERMS Geometric solution, perfect control, minimum-energy problem, inverses of nonsquare matrices, discrete-time state-space domain, LTI MIMO.

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“…Theorem 2: Consider the second-order MISO system governed by Eqs. (1). Then, the x(k) for k ≥ 1 lies in the kernel of (z R I 2 − F), finally to obtain…”

Section: A Towards a General Theory Of Minimum-energy Perfect Contromentioning

confidence: 99%

“…The perfect control strategy, i.e. the deterministic case of the minimum variance control algorithm, is an attractive method due to its valuable properties [1]- [7]. For singleinput/single-output or square systems, i.e.…”

Section: Introductionmentioning

confidence: 99%

A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

Hunek

Feliks

2020

IEEE Access

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“…(9) we would like to delete any noises in terms of selection of appropriate degrees of freedom M(q -1 ). Therefore, the performance index is determined in the following form [24,25] …”

Section: New Approach To Wireless Signal Reconstruction In Polynomialmentioning

confidence: 99%

New approach to wireless data communication in a propagation environment

Hunek

Majewski

2017

E3S Web Conf.

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Abstract. This paper presents a new idea of perfect signal reconstruction in multivariable wireless communications systems including a different number of transmitting and receiving antennas. The proposed approach is based on the polynomial matrix S-inverse associated with Smith factorization. Crucially, the above mentioned inverse implements the so-called degrees of freedom. It has been confirmed by simulation study that the degrees of freedom allow to minimalize the negative impact of the propagation environment in terms of increasing the robustness of whole signal reconstruction process. Now, the parasitic drawbacks in form of dynamic ISI and ICI effects can be eliminated in framework described by polynomial calculus. Therefore, the new method guarantees not only reducing the financial impact but, more importantly, provides potentially the lower consumption energy systems than other classical ones. In order to show the potential of new approach, the simulation studies were performed by author's simulator based on wellknown OFDM technique.

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“…Measuring devices usually operate in noised environments. The source of the noise can vary, depending on the measured physical quantity [1,2]. In the electrical engineering area, one of the most-often measured quantities is the voltage value, derived from sensors (e.g., the weight transformed to the voltage output of tensometers).…”

Section: Introductionmentioning

confidence: 99%

Short Transient Parameter-Varying IIR Filter Based on Analog Oscillatory System

Okoniewski

Piskorowski

2019

Applied Sciences

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This paper presents a concept for digital infinite impulse response (IIR) lowpass filter with reduced transient response. The proposed digital filtering structure is based on an analog oscillatory system. In order to design the considered digital filter, the analog prototype is subjected to a discretization process and, then, the parameters describing the dynamical properties of the oscillatory system are temporarily varied in time, so as to suppress the transient response of the designed filter. An optimization method, aimed at reducing the settling time by proper parameter manipulation, is presented. Simulation results, along with a real-life application proving the usefulness of the proposed concept, are also shown and discussed.

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Perfect reconstruction of signal—a new polynomial matrix inverse approach

Cited by 21 publications

References 24 publications

A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

A New Geometric-Oriented Minimum-Energy Perfect Control Design in the IMC-Based State-Space Domain

New approach to wireless data communication in a propagation environment

Short Transient Parameter-Varying IIR Filter Based on Analog Oscillatory System

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