A method for constructing orthonormal basis functions with good time-frequency localization

Maximally localized Gabor orthonormal bases on locally compact Abelian groups

Aiming to monitor wear condition of milling cutters in time and provide tool change decisions to ensure manufacturing safety and product quality, a tool wear monitoring model based on Bagging-Gradient Boosting Decision Tree (Bagging-GBDT) is proposed. In order to avoid incomplete tool state information contained in a single domain feature parameter, a multi-domain combination method is used to extract candidate characteristic parameter sets from time domain, frequency domain, and time–frequency domain. Then top 21 significant features are screened by eXtreme Gradient Boosting selection method. Synthetic Minority Oversampling Technique technology is integrated during feature selection to overly sample feature vectors, so that wear condition categories can be well balanced. Bagging idea is then introduced for parallel calculation of the gradient boosting decision tree and to improve its generalization ability. A Bagging-GBDT milling cutter wear condition prediction model is constructed and verified by public ball-end milling data set. Experiments show that random features and training samples selection can effectively improve prediction performance and generalization ability of prediction model. Our Bagging-GBDT model gains F1 score of 0.99350, which is 0.2% and 13.2% higher than the random forest algorithm and basic GBDT model, respectively.

It has been shown that continuous-time orthonormal Wilson bases with good time-frequency localization can be constructed. We introduce and discuss discrete-time Wilson function sets and frames, and we show that Wilson sets and frames (potentially oversampled) can be derived from Weyl-Heisenberg sets and frames. We also show that discrete-time Wilson expansions correspond to a new class of cosine-modulated filter banks.

Pervasive computing has a great potential for many next-generation IT applications such as in e-learning. Pronunciation teaching is an essential part in Mandarin e-learning system. In this paper, tone analysis is made on the basis of wavelet transform (WT) which has good time-frequency localization as well as the advantage of being able to simulate the auditory property of ear. It has found its applications to exact pitch detection and accurate Mandarin tone recognition. By integrating the pervasive computing and tone analysis technology, a pervasive computing based Mandarin e-learning system is designed and implemented.

In this paper, we prove the existence of an orthonormal basis in at least one orbit of every generic irreducible representation of a simply connected and connected nilpotent Lie group. Our result has a wide-ranging impact, encompassing all irreducible representations of a nilpotent Lie group that are square-integrable modulo its center. This resolves a fundamental open problem in time-frequency analysis and frame theory, originally posed by Karlheinz Gröchenig. The implications of our findings are significant and far-reaching.

In hands-free telephone or video conference application, there exists an acoustic feedback coupling between the loudspeaker and microphone in an enclosed environment, which creates the acoustic echo. FIR filters are commonly used in acoustic echo cancellers because of their simple structure. However, in this paper, the Kautz and Laguerre filter structures are shown to be more efficient echo cancellers than the FIR filters, because they can describe accurately the acoustic echo system with fewer parameters. These filters are built from their respective orthonormal Kautz and Laguerre basis functions. The proposal is motivated by some theoretical and numerical results that the time-varying acoustic echo path is basically due to its time-varying zeros and not its time-invariant acoustical poles. Therefore, the poles of the Kautz and the Laguerre filters are estimated, and can be kept fixed or updated occasionally if required. The poles are estimated by a batch Gauss-Newton algorithm. Then, the coefficients of the Kautz and Laguerre filters can be estimated by most recursive algorithms that are suitable for linear regression models, e.g., the normalized LMS algorithm. Generally, it is shown that the proposed Kautz and Laguerre filters, as the filter structures in an acoustic echo canceller, have better convergence and tracking properties than the FIR and IIR filters.

In response to the urgent demand for the development of future radar application platforms from single radar functionality toward integrated multifunctional systems, we show an advanced microwave photonic waveform editing method that enables the editing of arbitrary radar waveforms, equipping them with the capability to perform spectrum sensing. This, in turn, expands single-function radar systems into joint radar and spectrum-sensing systems. We theoretically define and calculate the accumulation function of an arbitrary waveform after passing through a specific dispersive medium and utilize this accumulation function to further design a corresponding binary sequence for editing the waveform. After editing, the accumulation function of the edited waveform approximates that of a linearly frequency-modulated (LFM) signal matching the specific dispersive medium. Thus, the edited waveform can be compressed into a narrow pulse after passing through the dispersive medium, realizing the frequency-to-time mapping (FTTM) for achieving frequency measurement or time–frequency analysis. The concept is verified through both simulation and experiment. Using a dispersion-compensating fiber (DCF) with a total dispersion of −6817 ps/nm, arbitrary waveforms, including a 7-bit Barker phase-coded waveform, an LFM waveform, a nonlinearly frequency-modulated (NLFM) waveform, and a waveform with an “E” time–frequency diagram, are edited and further used for microwave frequency measurement and time–frequency analysis in an ultra-wide bandwidth of 36.8 GHz. The temporal resolution and frequency resolution are 2 ns and 0.86 GHz, respectively.

Investigation of optimal feature for milling chatter identification using supervised machine learning techniques

In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.

In this model, without dark matter, the flat rotation curves of galaxies and the mass-to-light ratios of clusters of galaxies are described quantitatively. The hypothesis is that the agent of gravitational force is propagated as if it were scattered with a mean free path of approximately 5 kiloparsecs. As a result, the force between moderately distant masses, separated by more than the mean free path, diminishes as the inverse first power of the distance, following diffusion equations, and describes the flat rotation curves of galaxies. The force between masses separated by <1 kiloparsec diminishes as the inverse square of distance. The excess gravitational force (ratio of 1/r:1/r2) increases with the scale of structures from galaxies to clusters of galaxies. However, there is reduced force at great distances because of the approximately 12 billion years that has been available for diffusion to occur. This model with a mean free path of approximately 5 kiloparsecs predicts a maximum excess force of a few hundredfold for objects the size of galactic clusters a few megaparsecs in size. With only a single free parameter, the predicted curve for excess gravitational force vs. size of structures fits reasonably well with observations from those for dwarf galaxies through galactic clusters. Under the diffusion model, no matter is proposed in addition to the observed baryons plus radiation and thus the proposed density of the universe is only a few percent of that required for closure.

Motivated by representingmultidimensional periodic nonlinear and non-stationary signals (functions), we study a class of orthonormal exponential basis for L2(Id) with I:= [0,1), whose exponential parts are piecewise linear spectral sequences with p-knots. It is widely applied in time-frequency analysis.

Presents a framework for fuzzy modeling of dynamic systems using orthonormal basis functions in the representation of the model input signals. The main objective of using orthonormal bases is to overcome the task of estimating the order and time delay of the process. The result is a nonlinear moving average fuzzy model which, consequently, has no feedback of prediction errors. Although any technique of fuzzy modeling can be used in the proposed framework, a relational approach is considered. The performance of fuzzy models with orthonormal basis functions is illustrated by examples and the results are compared with those provided by conventional fuzzy models and Volterra models.

A fuzzy clustering approach is developed to select pole locations for Orthonormal Basis Functions (OBFs), used for identification of Linear Parameter Varying (LPV) systems. The identification approach is based on interpolation of locally identified Linear Time Invariant (LTI) models, using globally fixed OBFs. Selection of the optimal OBF structure, that guarantees the least worst-case local modelling error in an asymptotic sense, is accomplished through the fusion of the Kolmogorov n-width (KnW) theory and Fuzzy c-Means (FcM) clustering of observed sample system poles.

The effect of grain size and deformation sub-structure on mechanical properties of polycrystalline aluminum

Cosine lobes for interactive direct lighting in dynamic scenes