Lebesgue functions of rational interpolations of non-band-limited functions

2017 ◽  
Author(s):  
Margit Pap ◽  
Akos Pilgermajer
Keyword(s):  
Band Limited ◽  
Lebesgue Functions

Method of estimation of hidden correlation of narrowband noise signals

2019 ◽  
pp. 34-39 ◽  
Author(s):  
E.I. Chernov ◽  
N.E. Sobolev ◽  
A.A. Bondarchuk ◽  
L.E. Aristarhova
Keyword(s):  
Signal Processing ◽  
Digital Signal Processing ◽  
New Technology ◽  
Digital Signal ◽  
Measuring Instruments ◽  
Central Frequency ◽  
Pearson Criterion ◽  
Useful Signal ◽  
Band Limited ◽  
Narrowband Noise

The concept of hidden correlation of noise signals is introduced. The existence of a hidden correlation between narrowband noise signals isolated simultaneously from broadband band-limited noise is theoretically proved. A method for estimating the latent correlation of narrowband noise signals has been developed and experimentally investigated. As a result of the experiment, where a time frag ent of band-limited noise, the basis of which is shot noise, is used as the studied signal, it is established: when applying the Pearson criterion, there is practically no correlation between the signal at the Central frequency and the sum of signals at mirror frequencies; when applying the proposed method for the analysis of the same signals, a strong hidden correlation is found. The proposed method is useful for researchers, engineers and metrologists engaged in digital signal processing, as well as developers of measuring instruments using a new technology for isolating a useful signal from noise – the method of mirror noise images.

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

scholarly journals Low-Frequency Signal Sampling Method Implemented in a PLC Controller Dedicated to Applications in the Monitoring of Selected Electrical Devices

Electronics ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 442
Author(s):  
Marcin Jaraczewski ◽  
Ryszard Mielnik ◽  
Tomasz Gębarowski ◽  
Maciej Sułowicz
Keyword(s):  
Power System ◽  
Reactive Power ◽  
Low Frequency ◽  
Sampling Frequency ◽  
Electrical Signal ◽  
Distortion Factor ◽  
Electrical Devices ◽  
Frequency Sampling ◽  
Sampled Signal ◽  
Band Limited

High requirements for power systems, and hence for electrical devices used in industrial processes, make it necessary to ensure adequate power quality. The main parameters of the power system include the rms-values of the current, voltage, and active and reactive power consumed by the loads. In previous articles, the authors investigated the use of low-frequency sampling to measure these parameters of the power system, showing that the method can be easily implemented in simple microcontrollers and PLCs. This article discusses the methods of measuring electrical quantities by devices with low computational efficiency and low sampling frequency up to 1 kHz. It is not obvious that the signal of 50–500 Hz can be processed using the sampling frequency of fs = 47.619 Hz because it defies the Nyquist–Shannon sampling theorem. This theorem states that a reconstruction of a sampled signal is only guaranteed possible for a bandlimit fmax < fs, where fmax is the maximum frequency of a sampled signal. Therefore, theoretically, neither 50 nor 500 Hz can be identified by such a low-frequency sampling. Although, it turns out that if we have a longer period of a stable multi-harmonic signal, which is band-limited (from the bottom and top), it allows us to map this band to the lower frequencies, thus it is possible to use the lower sampling ratio and still get enough precise information of its harmonics and rms value. The use of aliasing for measurement purposes is not often used because it is considered a harmful phenomenon. In our work, it has been used for measurement purposes with good results. The main advantage of this new method is that it achieves a balance between PLC processing power (which is moderate or low) and accuracy in calculating the most important electrical signal indicators such as power, RMS value and sinusoidal-signal distortion factor (e.g., THD). It can be achieved despite an aliasing effect that causes different frequencies to become indistinguishable. The result of the research is a proposal of error reduction in the low-frequency measurement method implemented on compact PLCs. Laboratory tests carried out on a Mitsubishi FX5 compact PLC controller confirmed the correctness of the proposed method of reducing the measurement error.

Classical Sampling Series of Band Limited Functions: Oversampling and Non-existence

2016 ◽  
Vol 15 (1) ◽  
pp. 131-138
Author(s):  
B. A. Bailey ◽  
W. R. Madych
Keyword(s):  
Sampling Series ◽  
Band Limited

scholarly journals Propagation of Narrow Band‐Limited Noise in a Layered Wave Guide

1959 ◽  
Vol 31 (6) ◽  
pp. 838-838
Author(s):  
C. S. Clay
Keyword(s):  
Narrow Band ◽  
Wave Guide ◽  
Band Limited

Model‐based calibration of band‐limited impedance data: Hoover Field

2002 ◽  
Author(s):  
Olivier Burtz ◽  
Gianni Matteucci ◽  
William Meyer
Keyword(s):  
Model Based ◽  
Impedance Data ◽  
Band Limited

n-Widths and Optimal Interpolation of Time- and Band-Limited Functions II

1985 ◽  
Vol 16 (4) ◽  
pp. 803-813 ◽  
Author(s):  
Avraham A. Melkman
Keyword(s):  
Optimal Interpolation ◽  
Band Limited

Existence and uniqueness of band-limited, positive semidefinite extrapolations

1990 ◽  
Vol 38 (3) ◽  
pp. 547-549 ◽  
Author(s):  
K.S. Arun ◽  
L.C. Potter
Keyword(s):  
Existence And Uniqueness ◽  
Positive Semidefinite ◽  
Band Limited
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