A Musical Use for the Haar Function Wavelet

2005 ◽  
Author(s):  
Daryl Caswell
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Near Field ◽  
French Horn ◽  
Sound Analysis ◽  
Concert Hall ◽  
Analysis Techniques ◽  
Haar Function ◽  
Musical Tone ◽  
The Time Domain

The utility of the Haar function wavelet has long been dismissed due to its inability to transpose between the time domain and the frequency domain. However, the Haar function possesses attributes that make it an ideal wavelet for certain applications. In this paper, we explore the use of the Haar function as a means to expose aspects of musical tone that are not available through other sound analysis techniques. Specifically, the method presented here was used to identify the differences in the tone of the French Horn created by different acoustically reflective surfaces placed in the near field of the horn bell. The fundamentals of the Haar function wavelet are described and its use as a signal analyzer is explained. Results are shown that demonstrate the effect of two different kinds of sound reflectors constructed for a major North American concert hall.

scholarly journals Scattering of an Impact Wave by a Crack in a Composite Plate

1992 ◽  
Vol 59 (3) ◽  
pp. 596-603 ◽  
Author(s):  
S. K. Datta ◽  
T. H. Ju ◽  
A. H. Shah
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Impact Load ◽  
Near Field ◽  
Boundary Integral ◽  
Transition Elements ◽  
Element Discretization ◽  
Crack Tips ◽  
Time Domain Response ◽  
The Time Domain

The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate containing a horizontal crack is investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour completely enclosing the crack. This combined method leads to a set of linear unsymmetric complex matrix equations, which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time-domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high-order finite elements have been used. Also, both the six-node singular elements and eight-node transition elements are used around the crack tips to model the crack-tip singularity. From the numerical results for surface responses it seems possible to clearly identify both the depth and length of this crack.

Time-Domain Approach for Acoustic Scattering of Rotorcraft Noise

2012 ◽  
Vol 57 (4) ◽  
pp. 1-12 ◽  
Author(s):  
Seongkyu Lee ◽  
Kenneth S. Brentner ◽  
Philip J. Morris
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Impulsive Noise ◽  
Near Field ◽  
Acoustic Scattering ◽  
Frequency Domain Analysis ◽  
Computational Time ◽  
Computationally Efficient ◽  
Time Saving ◽  
The Time Domain

This paper addresses acoustic scattering of rotorcraft noise in the time domain. A time-domain equivalent source method is used since it is considered to be a computationally efficient method to solve acoustic scattering. In addition, the time-domain method provides a solution for all frequencies of interest in a single computation and is able to predict the acoustic scattering of aperiodic signals. The prediction is validated against exact solutions for a monopole source. The numerical method is then used to predict acoustic scattering of noise from a BO105 tail rotor by a representative fuselage. Complex directivity patterns are seen in the near field, and a large scattering effect is observed in the far field to the side of the fuselage. The time-domain code results of sound pressure level are validated against the results obtained by a frequency-domain analysis. Finally, acoustic scattering for an impulsive noise source is investigated to simulate main rotor blade–vortex interaction noise. The scattered pressure has a comparable amplitude as that of the incident pressure so that the total pressure is dramatically changed compared to the incident pressure. For the impulsive noise, a large computational time saving is achieved compared to the frequency-domain approach, in which the computation must be repeated for each frequency.

Time domain finite element method for metamaterial-based low frequency near field systems

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zhi Gong ◽  
Shiyou Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Frequency Domain ◽  
Time Domain ◽  
Near Field ◽  
Low Frequency ◽  
Electromagnetic Properties ◽  
Content Type ◽  
The Time Domain ◽  
Element Method

Purpose The purpose of this work is to develop a computational paradigm for performance analysis of low-frequency electromagnetic devices containing both magnetic metamaterials (MTMs) and natural media. Design/methodology/approach A time domain finite element method (TDFEM) is proposed. The electromagnetic properties of the MTMs are modeled by a nonstandard Lorentz model. The time domain governing equation is derived by converting the one from the frequency domain into the time domain based on the Laplace transform and convolution. The backward difference is used for the temporal discretization. An auxiliary variable is introduced to derive the recursive formula. Findings The numerical results show good agreements between the time domain solutions and the frequency domain solutions. The error convergence trajectory of the proposed TDFEM conforms to the first-order accuracy. Originality/value To the best knowledge of the authors, the presented work is the first one focusing on TDFEMs for low-frequency near fields computations of MTMs. Consequently, the proposed TDFEM greatly benefits the future explorations and performance evaluations of MTM-based near field devices and systems in low-frequency electrical and electronic engineering.

JOINT INTERPRETATION OF AIRBORNE ELECTROMAGNETIC DATA IN THE TIME DOMAIN AND FREQUENCY DOMAIN

2018 ◽  
Vol 12 (7-8) ◽  
pp. 76-83
Author(s):  
E. V. KARSHAKOV ◽  
J. MOILANEN
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Frequency Interval ◽  
Single Spectrum ◽  
Simultaneous Inversion ◽  
Homogeneous Half Space ◽  
Time Domain Data ◽  
The Time Domain

Тhe advantage of combine processing of frequency domain and time domain data provided by the EQUATOR system is discussed. The heliborne complex has a towed transmitter, and, raised above it on the same cable a towed receiver. The excitation signal contains both pulsed and harmonic components. In fact, there are two independent transmitters operate in the system: one of them is a normal pulsed domain transmitter, with a half-sinusoidal pulse and a small "cut" on the falling edge, and the other one is a classical frequency domain transmitter at several specially selected frequencies. The received signal is first processed to a direct Fourier transform with high Q-factor detection at all significant frequencies. After that, in the spectral region, operations of converting the spectra of two sounding signals to a single spectrum of an ideal transmitter are performed. Than we do an inverse Fourier transform and return to the time domain. The detection of spectral components is done at a frequency band of several Hz, the receiver has the ability to perfectly suppress all sorts of extra-band noise. The detection bandwidth is several dozen times less the frequency interval between the harmonics, it turns out thatto achieve the same measurement quality of ground response without using out-of-band suppression you need several dozen times higher moment of airborne transmitting system. The data obtained from the model of a homogeneous half-space, a two-layered model, and a model of a horizontally layered medium is considered. A time-domain data makes it easier to detect a conductor in a relative insulator at greater depths. The data in the frequency domain gives more detailed information about subsurface. These conclusions are illustrated by the example of processing the survey data of the Republic of Rwanda in 2017. The simultaneous inversion of data in frequency domain and time domain can significantly improve the quality of interpretation.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

A Multiple Harmonic Open-Loop Controller for Hydro/Aerodynamic Force Measurements in Rotating Machinery Using Magnetic Bearings

2002 ◽  
Vol 124 (4) ◽  
pp. 827-834 ◽  
Author(s):  
D. O. Baun ◽  
E. H. Maslen ◽  
C. R. Knospe ◽  
R. D. Flack
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Open Loop ◽  
Rotating Machinery ◽  
Operating Conditions ◽  
Rotor Vibration ◽  
Aerodynamic Forces ◽  
Analog Input ◽  
Input And Output ◽  
The Time Domain

Inherent in the construction of many experimental apparatus designed to measure the hydro/aerodynamic forces of rotating machinery are features that contribute undesirable parasitic forces to the measured or test forces. Typically, these parasitic forces are due to seals, drive couplings, and hydraulic and/or inertial unbalance. To obtain accurate and sensitive measurement of the hydro/aerodynamic forces in these situations, it is necessary to subtract the parasitic forces from the test forces. In general, both the test forces and the parasitic forces will be dependent on the system operating conditions including the specific motion of the rotor. Therefore, to properly remove the parasitic forces the vibration orbits and operating conditions must be the same in tests for determining the hydro/aerodynamic forces and tests for determining the parasitic forces. This, in turn, necessitates a means by which the test rotor’s motion can be accurately controlled to an arbitrarily defined trajectory. Here in, an interrupt-driven multiple harmonic open-loop controller was developed and implemented on a laboratory centrifugal pump rotor supported in magnetic bearings (active load cells) for this purpose. This allowed the simultaneous control of subharmonic, synchronous, and superharmonic rotor vibration frequencies with each frequency independently forced to some user defined orbital path. The open-loop controller was implemented on a standard PC using commercially available analog input and output cards. All analog input and output functions, transformation of the position signals from the time domain to the frequency domain, and transformation of the open-loop control signals from the frequency domain to the time domain were performed in an interrupt service routine. Rotor vibration was attenuated to the noise floor, vibration amplitude ≈0.2 μm, or forced to a user specified orbital trajectory. Between the whirl frequencies of 14 and 2 times running speed, the orbit semi-major and semi-minor axis magnitudes were controlled to within 0.5% of the requested axis magnitudes. The ellipse angles and amplitude phase angles of the imposed orbits were within 0.3 deg and 1.0 deg, respectively, of their requested counterparts.

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

IDENTIFICATION OF INTERHARMONICS BASED ON WAVELET PACKET TRANSFORM

2021 ◽  
Vol 3 (1) ◽  
pp. 031-036
Author(s):  
S. A. GOROVOY ◽  
◽  
V. I. SKOROKHODOV ◽  
D. I. PLOTNIKOV ◽  
◽  
...  
Keyword(s):  
Fourier Transform ◽  
Simulation Model ◽  
Frequency Domain ◽  
Time Domain ◽  
Wavelet Packet ◽  
High Accuracy ◽  
Wavelet Packet Transform ◽  
Mathematical Apparatus ◽  
Nonlinear Load ◽  
The Time Domain

This paper deals with the analysis of interharmonics, which are due to the presence of a nonlinear load. The tool for the analysis was a mathematical apparatus - wavelet packet transform. Which has a number of advantages over the traditional Fourier transform. A simulation model was developed in Simulink to simulate a non-stationary non-sinusoidal mode. The use of the wavelet packet transform will allow to determine the mode parameters with high accuracy from the obtained wavelet coefficients. It also makes it possible to obtain information, both in the frequency domain of the signal and in the time domain.

scholarly journals A research on fiber-optic vibration pattern recognition based on time-frequency characteristics

2018 ◽  
Vol 10 (12) ◽  
pp. 168781401881346 ◽  
Author(s):  
Tabi Fouda Bernard Marie ◽  
Dezhi Han ◽  
Bowen An ◽  
Jingyun Li
Keyword(s):  
Pattern Recognition ◽  
Frequency Domain ◽  
Time Domain ◽  
Fiber Optic ◽  
Pattern Recognition Method ◽  
Recognition Method ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Vibration Pattern ◽  
The Time Domain

To detect and recognize any type of events over the perimeter security system, this article proposes a fiber-optic vibration pattern recognition method based on the combination of time-domain features and time-frequency domain features. The performance parameters (event recognition, event location, and event classification) are very important and describe the validity of this article. The pattern recognition method is precisely based on the empirical mode decomposition of time-frequency entropy and center-of-gravity frequency. It implements the function of identifying and classifying the event (intrusions or non-intrusion) over the perimeter to secure. To achieve this method, the first-level prejudgment is performed according to the time-domain features of the vibration signal, and the second-level prediction is carried out through time-frequency analysis. The time-frequency distribution of the signal is obtained by empirical mode decomposition and Hilbert transform and then the time-frequency entropy and center-of-gravity frequency are used to form the time-frequency domain features, that is, combined with the time-domain features to form feature vectors. Multiple types of probabilistic neural networks are identified to determine whether there are intrusions and the intrusion types. The experimental results demonstrate that the proposed method is effective and reliable in identifying and classifying the type of event.

scholarly journals Comparison of machine learning models based on time domain and frequency domain features for faults diagnosis in rotating machines

2018 ◽  
Vol 211 ◽  
pp. 17009
Author(s):  
Natalia Espinoza Sepulveda ◽  
Jyoti Sinha
Keyword(s):  
Machine Learning ◽  
Frequency Domain ◽  
Time Domain ◽  
Intelligent Systems ◽  
Learning Models ◽  
Machine Vibration ◽  
Vibration Data ◽  
Machine Learning Model ◽  
The Time Domain ◽  
Machine Learning Models

The development of technologies for the maintenance industry has taken an important role to meet the demanding challenges. One of the important challenges is to predict the defects, if any, in machines as early as possible to manage the machines downtime. The vibration-based condition monitoring (VCM) is well-known for this purpose but requires the human experience and expertise. The machine learning models using the intelligent systems and pattern recognition seem to be the future avenue for machine fault detection without the human expertise. Several such studies are published in the literature. This paper is also on the machine learning model for the different machine faults classification and detection. Here the time domain and frequency domain features derived from the measured machine vibration data are used separated in the development of the machine learning models using the artificial neutral network method. The effectiveness of both the time and frequency domain features based models are compared when they are applied to an experimental rig. The paper presents the proposed machine learning models and their performance in terms of the observations and results.

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