Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: In this article, the free vibration analysis of composite laminated conical, cylindrical shells and annular plates with various boundary conditions based on the first order shear deformation theory, using the Haar wavelet discretization method, is presented.
82 citations
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TL;DR: Application of the method for the identification of the CRS A465 industrial robot proves the validity of the proposed approach to the parameterization of robot excitation trajectories based on a combined Fourier series and polynomial functions.
Abstract: This paper describes a new approach to the parameterization of robot excitation trajectories for optimal robot identification The trajectory parameterization is based on a combined Fourier series and polynomial functions The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the d-optimality criterion, taking into account motion constraints in joint and Cartesian space This parameterization satisfies both the guarantees of convergence by adding terms and the matching of the boundary conditions Application of the method for the identification of the CRS A465 industrial robot proves the validity of the proposed approach
82 citations
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TL;DR: In this paper, it was shown that the simulated random processes are asymptotically Gaussian processes as the number of terms, N, of sine or cosine functions approaches infinity.
82 citations
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TL;DR: In this paper, the Paley-Wiener type constant for nonharmonic Fourier series and wavelet Riesz basis was improved to 1/4 for orthonormal basis.
Abstract: In this paper we present two applications of a Stability Theorem of Hilbert frames to nonharmonic Fourier series and wavelet Riesz basis. The first result is an enhancement of the Paley-Wiener type constant for nonharmonic series given by Duffin and Schaefer in [6] and used recently in some applications (see [3]). In the case of an orthonormal basis, our estimate reduces to Kadec’ optimal 1/4 result. The second application proves that a phenomenon discovered by Daubechies and Tchamitchian [4] for the orthonormal Meyer wavelet basis (stability of the Riesz basis property under small changes of the translation parameter) actually holds for a large class of wavelet Riesz bases.
82 citations
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TL;DR: In this article, the Fourier decomposition method (FDM) was proposed for the analysis of nonlinear (i.e. data generated by nonlinear systems) and nonstationary time series.
Abstract: Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data In this paper, we propose a Fourier Decomposition Method (FDM) and demonstrate its efficacy for the analysis of nonlinear (ie data generated by nonlinear systems) and nonstationary time series The proposed FDM decomposes any data into a small number of `Fourier intrinsic band functions' (FIBFs) The FDM presents a generalized Fourier expansion with variable amplitudes and frequencies of a time series by the Fourier method itself We propose an idea of zero-phase filter bank based multivariate FDM (MFDM) algorithm, for the analysis of multivariate nonlinear and nonstationary time series, from the FDM We also present an algorithm to obtain cutoff frequencies for MFDM The MFDM algorithm is generating finite number of band limited multivariate FIBFs (MFIBFs) The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency The proposed methods produce the results in a time-frequency-energy distribution that reveal the intrinsic structures of a data Simulations have been carried out and comparison is made with the Empirical Mode Decomposition (EMD) methods in the analysis of various simulated as well as real life time series, and results show that the proposed methods are powerful tools for analyzing and obtaining the time-frequency-energy representation of any data
82 citations