scholarly journals Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1050
Author(s):  
Zhihua Zhang
Keyword(s):  
Frequency Domain ◽  
Multiresolution Analysis ◽  
Background Noise ◽  
Sparse Reconstruction ◽  
Time Frequency ◽  
Processing Data ◽  
Narrowband Signal ◽  
Frequency Domains ◽  
Frame Multiresolution Analysis

Framelets have been widely used in narrowband signal processing, data analysis, and sampling theory, due to their resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information. The well-known approach to construct framelets with useful properties is through frame multiresolution analysis (FMRA). In this article, we characterize the frequency domain of bandlimited FMRAs: there exists a bandlimited FMRA with the support of frequency domain G if and only if G satisfies G⊂2G, ⋃m2mG≅Rd, and G\G2⋂G2+2πν≅∅(ν∈Zd).

Two-Stage Adaptive Line Enhancer and Sliced Wigner Trispectrum for the Characterization of Faults from Gear Box Vibration Data

1999 ◽  
Vol 121 (4) ◽  
pp. 488-494 ◽  
Author(s):  
S. K. Lee ◽  
P. R. White
Keyword(s):  
Background Noise ◽  
Two Stage ◽  
Vibration Signals ◽  
Time Frequency ◽  
Vibration Data ◽  
Frequency Representation ◽  
Frequency Domains ◽  
Adaptive Line Enhancer ◽  
Gear Fault

Impulsive sound and vibration signals in gears are often associated with faults which result from impacting and as such these impulsive signals can be used as indicators of faults. However it is often difficult to make objective measurements of impulsive signals because of background noise signals. In order to ease the measurement of impulsive sounds embedded in background noise, it is proposed that the impulsive signals are enhanced, via a two stage ALE (Adaptive Line Enhancer), and that these enhanced signals are then analyzed in the time and frequency domains using a Wigner higher order time-frequency representation. The effectiveness of this technique is demonstrated by application to gear fault data.

scholarly journals Splitting of Framelets and Framelet Packets

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 697
Author(s):  
Zhihua Zhang
Keyword(s):  
Background Noise ◽  
Data Science ◽  
Scaling Function ◽  
Frame Theory ◽  
The Other ◽  
Sparse Reconstruction ◽  
Integer Number ◽  
Time Frequency ◽  
Novel Approaches ◽  
Frame Multiresolution Analysis

Due to resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information, the frame theory is becoming a dynamic forefront topic in data science. In this study, we overcome the disadvantages in the construction of traditional framelet packets derived by frame multiresolution analysis and square iterative matrices. We propose two novel approaches: One is to directly split known framelets again and again; the other approach is based on a generalized scaling function whose shifts are not a frame of some space. In these two approaches, the iterative matrices used are not square and the number of rows in the iterative matrix can be any integer number.

scholarly journals Recurrent Neural Networks for Narrowband Signal Detection in the Time-Frequency Domain

2004 ◽  
Vol 213 ◽  
pp. 483-486
Author(s):  
David Brodrick ◽  
Douglas Taylor ◽  
Joachim Diederich
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Signal Detection ◽  
Frequency Domain ◽  
Recurrent Neural Networks ◽  
Radio Frequency Interference ◽  
Recurrent Networks ◽  
Time Frequency ◽  
Narrowband Signal ◽  
Radio Signals

A recurrent neural network was trained to detect the time-frequency domain signature of narrowband radio signals against a background of astronomical noise. The objective was to investigate the use of recurrent networks for signal detection in the Search for Extra-Terrestrial Intelligence, though the problem is closely analogous to the detection of some classes of Radio Frequency Interference in radio astronomy.

Design of Adaptive Filter for Health Monitoring on a Gearbox

2006 ◽  
Vol 321-323 ◽  
pp. 1237-1240
Author(s):  
Sang Kwon Lee ◽  
Jung Soo Lee
Keyword(s):  
Signal Processing ◽  
Frequency Domain ◽  
Adaptive Filter ◽  
Health Monitoring ◽  
Background Noise ◽  
Adaptive Signal Processing ◽  
Vibration Signals ◽  
Time Frequency ◽  
Frequency Representation ◽  
Adaptive Signal

Impulsive vibration signals in gearbox are often associated with faults, which lead to due to irregular impacting. Thus these impulsive vibration signals can be used as indicators of machinery faults. However it is often difficult to make objective measurement of impulsive signals because of background noise signals. In order to ease the measurement of impulsive signal embedded in background noise, we enhance the impulsive signals using adaptive signal processing and then analyze them in time and frequency domain by using time-frequency representation. This technique is applied to the diagnosis of faults within laboratory gearbox.

scholarly journals Spillover effects from news to travel and leisure stocks during the COVID-19 pandemic: Evidence from the time and frequency domains

2021 ◽  
pp. 135481662110584
Author(s):  
Ying Wang ◽  
Hongwei Zhang ◽  
Wang Gao ◽  
Cai Yang
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Spillover Effects ◽  
Short Term ◽  
Time Frequency ◽  
Frequency Domains ◽  
Media Hype ◽  
The Time Domain ◽  
The Impact

The impact of the COVID-19 pandemic on tourism has received general attention in the literature, while the role of news during the pandemic has been ignored. Using a time-frequency connectedness approach, this paper focuses on the spillover effects of COVID-19-related news on the return and volatility of four regional travel and leisure (T&L) stocks. The results in the time domain reveal significant spillovers from news to T&L stocks. Specifically, in the return system, T&L stocks are mainly affected by media hype, while in the volatility system, they are mainly affected by panic sentiment. This paper also finds two risk contagion paths. The contagion index and Global T&L stock are the sources of these paths. The results in the frequency domain indicate that the shocks in the T&L industry are mainly driven by short-term fluctuations. The spillovers from news to T&L stocks and among these T&L stocks are stronger within 1 month.

Frequency domain of weakly translation invariant frame MRAs

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Signal Processing ◽  
Data Analysis ◽  
Frequency Domain ◽  
Scaling Function ◽  
Narrow Band ◽  
Scaling Functions ◽  
Translation Invariant ◽  
Frequency Domains ◽  
Band Signal

Frequency domain of bandlimited frame multiresolution analyses (MRAs) plays a key role when derived framelets are applied into narrow-band signal processing and data analysis. In this study, we give a characterization of frequency domain of weakly translation invariant frame scaling functions [Formula: see text] with frequency domain [Formula: see text]. Based on it, we further study convex and ball-shaped frequency domains. If frequency domain of bandlimited frame scaling function [Formula: see text] is convex and completely symmetric about the origin, then it must be weakly invariant and [Formula: see text]. If [Formula: see text] has a ball-shaped frequency domain, the ball radius must be bounded by [Formula: see text]. These frequency domain characters are owned uniquely by frame scaling functions and not by orthogonal scaling functions.

scholarly journals Time-Frequency Characterization of Rotating Instabilities in a Centrifugal Pump with a Vaned Diffuser

2008 ◽  
Vol 2008 ◽  
pp. 1-10 ◽  
Author(s):  
G. Pavesi ◽  
G. Cavazzini ◽  
G. Ardizzon
Keyword(s):  
Large Scale ◽  
Pressure Fluctuations ◽  
Computer Code ◽  
Design Flow ◽  
Vaned Diffuser ◽  
Time Frequency ◽  
Ansys Cfx ◽  
Frequency Domains ◽  
Radial Pump

This paper presents acoustic and flowdynamic investigations of large-scale instabilities in a radial pump with a vaned diffuser. Pressure fluctuations were measured with transducers placed flush at the inlet duct, at the impeller discharge, and in the vane diffuser walls. Two impeller rotation speeds were analyzed in the study, at design, and at off-design flow rates. A spectral analysis was carried out on the pressure signals in frequency and in time-frequency domains to identified precursors, inception, and evolution of the pressure instabilities. The results highlighted the existence of a rotating pressure structure at the impeller discharge, having a fluid-dynamical origin and propagating both in the radial direction and inside the impeller. The experimental data were then compared with the results obtained with help of ANSYS CFX computer code; focusing on the changing flow field at part load. Turbulence was reproduced by DES model.

scholarly journals Application of Correlation Analysis for Assessment of Infrasound Signals Emission by Wind Turbines

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6891
Author(s):  
Tomasz Boczar ◽  
Dariusz Zmarzły ◽  
Michał Kozioł ◽  
Daria Wotzka
Keyword(s):  
Correlation Analysis ◽  
Frequency Domain ◽  
Coherence Function ◽  
Wind Farms ◽  
Wavelet Coherence ◽  
Technical Parameters ◽  
Time Frequency ◽  
Frequency Domains ◽  
Frequency Transformations ◽  
The Time Domain

The study reported in this paper is concerned with areas related to developing methods of measuring, processing and analyzing infrasound noise caused by operation of wind farms. The paper contains the results of the correlation analysis of infrasound signals generated by a wind turbine with a rated capacity of 2 MW recorded by three independent measurement setups comprising identical components and characterized by the same technical parameters. The measurements of infrasound signals utilized a dedicated measurement system called INFRA, which was developed and built by KFB ACOUSTICS Sp. z o.o. In particular, the scope of the paper includes the results of correlation analysis in the time domain, which was carried out using the autocovariance function separately for each of the three measuring setups. Moreover, the courses of the cross-correlation function were calculated separately for each of the potential combinations of infrasound range recorded by the three measuring setups. In the second stage, a correlation analysis of the recorded infrasound signals in the frequency domain was performed, using the coherence function. In the next step, infrasound signals recorded in three setups were subjected to time-frequency transformations. In this part, the waveforms of the scalograms were determined by means of continuous wavelet transform. Wavelet coherence waveforms were calculated in order to determine the level of the correlation of the obtained dependencies in the time-frequency domain. The summary contains the results derived from using correlation analysis methods in the time, frequency and time-frequency domains.

scholarly journals Frame Multiresolution Analysis on Local Fields of Positive Characteristic

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Firdous A. Shah
Keyword(s):  
Multiresolution Analysis ◽  
Positive Characteristic ◽  
Scaling Function ◽  
Local Fields ◽  
Wavelet Frames ◽  
Shift Invariant Spaces ◽  
Frame Multiresolution Analysis ◽  
Invariant Spaces ◽  
The Scaling Function

We present a notion of frame multiresolution analysis on local fields of positive characteristic based on the theory of shift-invariant spaces. In contrast to the standard setting, the associated subspace V0 of L2(K) has a frame, a collection of translates of the scaling function φ of the form φ(·-u(k)):k∈N0, where N0 is the set of nonnegative integers. We investigate certain properties of multiresolution subspaces which provides the quantitative criteria for the construction of frame multiresolution analysis (FMRA) on local fields of positive characteristic. Finally, we provide a characterization of wavelet frames associated with FMRA on local field K of positive characteristic using the shift-invariant space theory.

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