scholarly journals The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1922
Author(s):  
Donnacha Daly ◽  
Didier Sornette
Keyword(s):  
Scale Invariant ◽  
Vanishing Moments ◽  
Physical Systems ◽  
Time Frequency ◽  
Multi Resolution Analysis ◽  
Chirplet Transform ◽  
Resolution Analysis ◽  
Self Similar ◽  
Short Time ◽  
Discrete Scale

This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.

Voltage Flicker Extraction Based on Wavelet Analysis

2013 ◽  
Vol 385-386 ◽  
pp. 1389-1393 ◽  
Author(s):  
Lin Chai ◽  
Jun Ru Sun
Keyword(s):  
Low Frequency ◽  
Matlab Simulation ◽  
Time Frequency ◽  
Multi Resolution Analysis ◽  
Voltage Signal ◽  
Time Frequency Localization ◽  
Resolution Analysis ◽  
Modulus Maximum ◽  
Voltage Flicker ◽  
Non Stationary Signal

Extracting voltage flicker from the sampling voltage signal is a precondition for management of flicker. Voltage flicker signal is a low frequency time-varying non-stationary signal. The traditional fourier transform has great limitations when analyze the non-stationary signal for not having the time resolution. As wavelet transform has good property of time-frequency localization, it become a powerful tool for analyze this kind of signal. This paper adopts multi-resolution analysis of wavelet to extract voltage flicker signal. Furthermore, according to the characteristics of wavelet function, this paper selects Daubechies wavelet to accomplish the multi-level decomposition and reconstruction of signal, in order to get the frequency and amplitude of voltage flicker signals. Based on the principle of modulus maximum, it can be determined what time the voltage flicker happen and over. The results of MATLAB simulation indicate that voltage flicker signal can be effectively extracted by wavelet multi-resolution analysis. Wavelet multi-resolution analysis is considerably ideal for voltage flicker extraction.

ECG Signal Denoising Algorithm Based on Optimization Wavelet Transform

2013 ◽  
Vol 706-708 ◽  
pp. 785-788
Author(s):  
Guo Shun Yuan ◽  
Li Qing Geng
Keyword(s):  
Wavelet Transform ◽  
Median Filter ◽  
Noise Removal ◽  
Signal Denoising ◽  
Time Frequency ◽  
Multi Resolution Analysis ◽  
Signal Characteristics ◽  
Eigen Values ◽  
Resolution Analysis ◽  
Ecg Noise Removal

Wavelet transform algorithm with its unique multi-resolution analysis and it is in the time - frequency domain has the advantage of the ability to characterize the local signal characteristics, let it has been widely used in signal detection, noise removal, feature extraction, image compression and so on. In this paper, on the basis of already wavelet transform ECG noise removal, proposed a median filter optimization algorithm, enables ECG noise removal effect is more obvious, also for the Eigen values detection of ECG lay a better foundation.

scholarly journals Time-frequency Analysis of Multicomponent LFM signal based on Hough and Chirplet Transform

2018 ◽  
Vol 173 ◽  
pp. 03054
Author(s):  
Xueqin Zhang ◽  
Ruolun Liu
Keyword(s):  
Fourier Transform ◽  
Line Detection ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Chirplet Transform ◽  
Frequency Map ◽  
Linear Frequency Modulated Signal ◽  
Short Time

The Chirplet Transform (CT) is effective in the characterization of IF for mono-component linear-frequency-modulated signal. However, During the initialization process, using the peak of the time-frequency map of the short-time Fourier transform to fit the line is greatly affected by noise. For the multi-component signals, it is more difficult to distinguish and fit different IF lines. Since the Hough is good at a common algorithm for the line detection, the ridge edge fitting is replaced by the Hough transform in this paper. The experiment results show significant improvement in the obtained time-frequency representation.

scholarly journals Time-frequency super-resolution with superlets

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Vasile V. Moca ◽  
Harald Bârzan ◽  
Adriana Nagy-Dăbâcan ◽  
Raul C. Mureșan
Keyword(s):  
High Frequency ◽  
Synthetic Data ◽  
Super Resolution ◽  
Frequency Resolution ◽  
Scale Free ◽  
Time Frequency ◽  
Brain Signals ◽  
Self Similar ◽  
Short Time ◽  
Spectral Estimator

AbstractDue to the Heisenberg–Gabor uncertainty principle, finite oscillation transients are difficult to localize simultaneously in both time and frequency. Classical estimators, like the short-time Fourier transform or the continuous-wavelet transform optimize either temporal or frequency resolution, or find a suboptimal tradeoff. Here, we introduce a spectral estimator enabling time-frequency super-resolution, called superlet, that uses sets of wavelets with increasingly constrained bandwidth. These are combined geometrically in order to maintain the good temporal resolution of single wavelets and gain frequency resolution in upper bands. The normalization of wavelets in the set facilitates exploration of data with scale-free, fractal nature, containing oscillation packets that are self-similar across frequencies. Superlets perform well on synthetic data and brain signals recorded in humans and rodents, resolving high frequency bursts with excellent precision. Importantly, they can reveal fast transient oscillation events in single trials that may be hidden in the averaged time-frequency spectrum by other methods.

Hurst Estimation of Scale Invariant Processes with Stationary Increments and Piecewise Linear Drift

2017 ◽  
Vol 16 (04) ◽  
pp. 1750036
Author(s):  
N. Modarresi ◽  
S. Rezakhah
Keyword(s):  
Piecewise Linear ◽  
Simulated Data ◽  
Fixed Number ◽  
Hurst Parameter ◽  
Scale Invariant ◽  
Stationary Increments ◽  
Linear Drift ◽  
Finite Dimensional ◽  
Self Similar ◽  
Discrete Scale

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first, we determine the scale intervals, their linear drifts and eliminate them. Then, a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion (fBm).

Wavelet Feature of Precipitation in Quzhou Jiuhua

2013 ◽  
Vol 438-439 ◽  
pp. 1286-1289
Author(s):  
Jun Ping Liu
Keyword(s):  
Wavelet Transform ◽  
Large Scale ◽  
Arithmetic Function ◽  
Small Scale ◽  
Time Frequency ◽  
Multi Scale ◽  
Multi Resolution Analysis ◽  
Resolution Analysis ◽  
Development And Management ◽  
Periodic Changes

Wavelet transform can carry on multi-scale and multi-resolution analysis of the signal through arithmetic function such as stretching and translation and so on .In this paper, applying Morlet complex wavelet performed wavelet transform of the month precipitation time sequence of Quzhou Jiuhua station, and analyzed period on different time scales. The future precipitation was analyzed based on main periods. The result showed that month precipitation has multi-scale characteristic and the main periods of month precipitation are 5-month, 11-month and 26-month. The periodic changes on large-scale nest the periodic changes on small-scale. The wavelet analysis can process signal in time frequency domain, which provide references for development and management of water resources.

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

scholarly journals Deep Learning Approach for Vibration Signals Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3929
Author(s):  
Han-Yun Chen ◽  
Ching-Hung Lee
Keyword(s):  
Surface Roughness ◽  
Tool Wear ◽  
Parameters Optimization ◽  
Frequency Spectra ◽  
Vibration Signals ◽  
Bearing Faults ◽  
Time Frequency ◽  
And Performance ◽  
The One ◽  
Short Time

This study discusses convolutional neural networks (CNNs) for vibration signals analysis, including applications in machining surface roughness estimation, bearing faults diagnosis, and tool wear detection. The one-dimensional CNNs (1DCNN) and two-dimensional CNNs (2DCNN) are applied for regression and classification applications using different types of inputs, e.g., raw signals, and time-frequency spectra images by short time Fourier transform. In the application of regression and the estimation of machining surface roughness, the 1DCNN is utilized and the corresponding CNN structure (hyper parameters) optimization is proposed by using uniform experimental design (UED), neural network, multiple regression, and particle swarm optimization. It demonstrates the effectiveness of the proposed approach to obtain a structure with better performance. In applications of classification, bearing faults and tool wear classification are carried out by vibration signals analysis and CNN. Finally, the experimental results are shown to demonstrate the effectiveness and performance of our approach.

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