Ridge and Phase Identification in the Frequency Analysis of Transient Signals by Harmonic Wavelets

1999 ◽  
Vol 121 (2) ◽  
pp. 149-155 ◽  
Author(s):  
D. E. Newland
Keyword(s):  
Frequency Analysis ◽  
Phase Identification ◽  
Computational Algorithms ◽  
High Definition ◽  
Diagnostic Features ◽  
Transient Signals ◽  
Phase Gradient ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Harmonic Wavelet

It is difficult to generate high-definition time-frequency maps for rapidly changing transient signals. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition. Features of these algorithms include the use of ridge identification and phase gradient as diagnostic features.

scholarly journals Application of Time-Frequency Analysis to Transient Data from Centrifuge Earthquake Testing

2000 ◽  
Vol 7 (4) ◽  
pp. 195-202 ◽  
Author(s):  
David E. Newland ◽  
Gary D. Butler
Keyword(s):  
Frequency Analysis ◽  
Good Method ◽  
Centrifuge Modeling ◽  
Transient Vibration ◽  
Time Frequency Analysis ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Vibration Data ◽  
Harmonic Wavelet ◽  
Detailed Interpretation

Centrifuge model experiments have generated complex transient vibration data. New algorithms for time-frequency analysis using harmonic wavelets provide a good method of analyzing these data. We describe how the experimental data have been collected and show typical time-frequency maps obtained by the harmonic wavelet algorithm. Some preliminary comments on the interpretation of these maps are given in terms of the physics of the underlying model. Important features of the motion that are not otherwise apparent emerge from the analysis. Later papers will deal with their more detailed interpretation and their implications for centrifuge modeling.

Practical Signal Analysis: Do Wavelets Make Any Difference?

1997 ◽  
Author(s):  
David E. Newland
Keyword(s):  
Signal Analysis ◽  
Simple Structure ◽  
Essential Element ◽  
Signal Decomposition ◽  
High Definition ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
Harmonic Wavelet ◽  
Short Time ◽  
Better Than

Abstract Signal decomposition by time-frequency and time-scale mapping is an essential element of most diagnostic signal analysis. Is the wavelet method of decomposition any better than the short-time Fourier transform and Wigner-Ville methods? This paper explores the effectiveness of wavelets for diagnostic signal analysis. The author has found that harmonic wavelets are particularly suitable because of their simple structure in the frequency domain, but it is still difficult to produce high-definition time-frequency maps. New details of the theory of harmonic wavelet analysis are described which provide the basis for computational algorithms designed to improve map definition.

Linear Multi-Degree-of-Freedom System Stochastic Response by Using the Harmonic Wavelet Transform

2003 ◽  
Vol 70 (5) ◽  
pp. 724-731 ◽  
Author(s):  
P. Tratskas ◽  
P. D. Spanos
Keyword(s):  
Wavelet Transform ◽  
Linear System ◽  
Spectral Characteristics ◽  
Degree Of Freedom ◽  
Harmonic Wavelets ◽  
Time Frequency ◽  
The Family ◽  
Harmonic Wavelet ◽  
The Time Domain ◽  
System Frequency

The wavelet transform is used to capture localized features in either the time domain or the frequency domain of the response of a multi-degree-of-freedom linear system subject to a nonstationary stochastic excitation. The family of the harmonic wavelets is used due to the convenient spectral characteristics of its basis functions. A wavelet-based system representation is derived by converting the system frequency response matrix into a time-frequency wavelet “tensor.” Excitation-response relationships are obtained for the wavelet-based representation which involve linear system theory, spectral representation of the excitation and of the response vectors, and the wavelet transfer tensor of the system. Numerical results demonstrate the usefulness of the developed analytical procedure.

Joint Time-Frequency Analysis of Small Scale Ocean Storms via the Harmonic Wavelet Transform

2017 ◽  
Author(s):  
Valentina Laface ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Ketson Roberto Maximiano dos Santos
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Sea Surface ◽  
Surface Elevation ◽  
Scale Model ◽  
Small Scale ◽  
Ocean Engineering ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Harmonic Wavelet

The paper focuses on utilizing the Harmonic Wavelet Transform (HWT) for estimating the evolutionary power spectrum (EPS) of sea storms. A sea storm is considered herein as a non-stationary stochastic process with a time duration of the order of days. The storm evolution can be represented in three stages: the growth, the peak and the decay. Specifically, during growth the intensity of the wave increases with time until reaching the apex, and then decreases. The analysis is carried out by processing the time series of the free surface elevation recorded at the Natural Ocean Engineering Laboratory of Reggio Calabria, Italy. A peculiarity of the NOEL lab is that a local wind from NNW often generates sea states consisting of pure wind waves that represent a small scale model, in Froude similarity, of ocean storms (www.noel.unirc.it). The main focus of the paper is, first, to acquire a joint time-frequency representation of the storm via estimating the associated EPS, and second, to explore the variability in time of the spectrum and of the dominant frequencies of the storm. The EPS is estimated by utilizing a non-stationary record of the sea surface elevation during a storm recorded at NOEL lab. Further, in this paper, the standard representation of sea storms is also considered. That is, the non-stationary process is represented as a sequence of stationary processes (sea states or buoy records), each of them characterized by an intensity defined by a significant wave height Hs and by a duration Δt. During the time interval Δt the sea surface elevation is considered stationary and the frequency spectrum may be computed via the Fast Fourier Transform (FFT). Results obtained following this procedure, which can be considered essentially as a brute-force application of the short-time FT, are compared with those obtained via a HWT based joint time-frequency analysis.

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