Signal Decomposition

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Jafar Saniie - One of the best experts on this subject based on the ideXlab platform.

  • Chirplet Signal Decomposition: analysis, algorithms and applications
    2020
    Co-Authors: Jafar Saniie, Yufeng Lu
    Abstract:

    In ultrasonic imaging applications, the detected echoes contain important information pertaining to the physical properties of the propagation path. These echoes often interfere with each other due to the limited resolution of the transducer and may also be corrupted by noise and/or undesired scattering echoes. Consequently, isolating ultrasonic echoes becomes a challenging problem and conventional Signal analysis techniques fail to unravel the desire Signal information. In this study, chirplet Signal Decomposition algorithms have been studied by decomposing highly convoluted ultrasonic Signals into a linear expansion of chirplets. For Signal parameter estimation, two different Decomposition techniques are investigated: chirplet Signal Decomposition based on the chirplet transform (CTSD), and the matching pursuit Signal Decomposition (MPSD) using statistical estimation methods (i.e., Maximum Likelihood and Maximum a Posteriori). In CTSD algorithm, the parameter vector of chirplets is estimated based on chirplet transform of the ultrasonic Signal. By localizing the dominant echo in the chirplet transform of the Signal, we can estimate the time-of-arrival, center frequency and amplitude of the dominant echo, then successively estimate the remaining parameters. In an iterative manner, the residual Signal is obtained by subtracting the estimated dominant echo from the Signal. The Decomposition process is repeated until the energy of residual Signal becomes below a pre-defined reconstruction condition. As an alternative, in the MPSD algorithm, statistical methods are utilized to iteratively optimize the parameters of chirplets to match the Signal and achieve high resolution Decomposition. Computer simulations and experimental analysis show that both algorithms provide efficient parameter estimation and robust chirplet Signal Decomposition. Furthermore, an FPGA-based hardware/software co-design for a fast CTSD algorithm has been successfully developed on Xilinx FPGA platform for real-time applications. This type of study addresses a broad range applications including target detection, deconvolution, object classification, velocity measurement, and ranging system.

  • NDE applications of compressed sensing, Signal Decomposition and echo estimation
    2014 IEEE International Ultrasonics Symposium, 2014
    Co-Authors: Yufeng Lu, Ramazan Demirli, Jafar Saniie
    Abstract:

    In this investigation, a compressed sensing (CS) sampling scheme is closely incorporated into ultrasound Signal Decomposition. The CS is used to exploit the sparsity of ultrasound echo Signals and thereby significantly reduce the sampling rate with 20-30 times lower than the Nyquist rate. Furthermore, the time-of-arrivals (TOAs) of dominant echoes are estimated with the sparse sampling. The estimated TOAs along with a priori information of the transducers are used for model-based Signal Decomposition on the incomplete ultrasonic data, where Gaussian Chirplet (GC), a commonly used echo model, is adopted. Parameters of GC echoes are estimated for pattern recognition and defect characterization in the presence of noise with SNR as low as -5 dB. Through an experimental study, the Decomposition results and estimated parameters confirm the robustness and effectiveness of the proposed technique. The study has a broad range of application in Signal analysis including sparse representation, parameter estimation, and defect detection.

  • Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition
    Advances in Acoustics and Vibration, 2012
    Co-Authors: Yufeng Lu, Alireza Kasaeifard, Erdal Oruklu, Jafar Saniie
    Abstract:

    A fractional fourier transform (FrFT) based chirplet Signal Decomposition (FrFT-CSD) algorithm is proposed to analyze ultrasonic Signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in Signal Decomposition and parameter estimation. FrFT rotates the Signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the Signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs Signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in Signal detection, estimation, and pattern recognition.

  • Ultrasonic chirplet Signal Decomposition for defect evaluation and pattern recognition
    2009 IEEE International Ultrasonics Symposium, 2009
    Co-Authors: Yufeng Lu, Erdal Oruklu, Jafar Saniie
    Abstract:

    In this study, a quantitative method using chirplet Signal Decomposition (CSD) is presented for pattern recognition and defect characterization. The CSD algorithm is utilized to decompose the ultrasonic Signal into a linear combination of chirplets, and efficiently estimate the echo parameters. These parameters can be correlated to the structure of defects. For experimental studies, planar and focused transducers with different center frequencies have been used for testing the embedded defects in specimen at normal or oblique refracted angles. It has been shown that the CSD successfully associates the estimated chirplets and their parameters as a quantitative method to characterize defects.

  • ACM Great Lakes Symposium on VLSI - Fpga-based hardware/software co-design for chirplet Signal Decomposition
    Proceedings of the 18th ACM Great Lakes symposium on VLSI - GLSVLSI '08, 2008
    Co-Authors: Yufeng Lu, Erdal Oruklu, Jafar Saniie
    Abstract:

    In various Signal processing applications, Decomposition and analysis of non-stationary Signals is a challenging problem. In this work, we present a computationally efficient method, fast chirplet Signal Decomposition (FCSD) algorithm, for decomposing highly convoluted Signals into a linear expansion of chirplets, and successively estimates the chirplet parameters. These parameters are capable of representing a broad range of echo shapes, including the broad-band, narrow-band, symmetric, skewed, nondispersive or dispersive, and have significant physical interpretations for radar, sonar, and ultrasonic imaging applications. For the real-time implementation of chirplet Signal Decomposition algorithm, an FPGA-based hardware/software co-design is developed on Xilinx Virtex II Pro FPGA platform. In this study, based on the balance among the system constraints, cost, and the efficiency of estimations, the performance of different algorithm implementation schemes have been explored. The developed system successfully exhibits the robustness in the chirplet Signal Decomposition of experimental Signals. This type of study addresses a broad range of applications including velocity measurement, target detection, deconvolution, object classification, data compression, and pattern recognition.

Yufeng Lu - One of the best experts on this subject based on the ideXlab platform.

  • Chirplet Signal Decomposition: analysis, algorithms and applications
    2020
    Co-Authors: Jafar Saniie, Yufeng Lu
    Abstract:

    In ultrasonic imaging applications, the detected echoes contain important information pertaining to the physical properties of the propagation path. These echoes often interfere with each other due to the limited resolution of the transducer and may also be corrupted by noise and/or undesired scattering echoes. Consequently, isolating ultrasonic echoes becomes a challenging problem and conventional Signal analysis techniques fail to unravel the desire Signal information. In this study, chirplet Signal Decomposition algorithms have been studied by decomposing highly convoluted ultrasonic Signals into a linear expansion of chirplets. For Signal parameter estimation, two different Decomposition techniques are investigated: chirplet Signal Decomposition based on the chirplet transform (CTSD), and the matching pursuit Signal Decomposition (MPSD) using statistical estimation methods (i.e., Maximum Likelihood and Maximum a Posteriori). In CTSD algorithm, the parameter vector of chirplets is estimated based on chirplet transform of the ultrasonic Signal. By localizing the dominant echo in the chirplet transform of the Signal, we can estimate the time-of-arrival, center frequency and amplitude of the dominant echo, then successively estimate the remaining parameters. In an iterative manner, the residual Signal is obtained by subtracting the estimated dominant echo from the Signal. The Decomposition process is repeated until the energy of residual Signal becomes below a pre-defined reconstruction condition. As an alternative, in the MPSD algorithm, statistical methods are utilized to iteratively optimize the parameters of chirplets to match the Signal and achieve high resolution Decomposition. Computer simulations and experimental analysis show that both algorithms provide efficient parameter estimation and robust chirplet Signal Decomposition. Furthermore, an FPGA-based hardware/software co-design for a fast CTSD algorithm has been successfully developed on Xilinx FPGA platform for real-time applications. This type of study addresses a broad range applications including target detection, deconvolution, object classification, velocity measurement, and ranging system.

  • NDE applications of compressed sensing, Signal Decomposition and echo estimation
    2014 IEEE International Ultrasonics Symposium, 2014
    Co-Authors: Yufeng Lu, Ramazan Demirli, Jafar Saniie
    Abstract:

    In this investigation, a compressed sensing (CS) sampling scheme is closely incorporated into ultrasound Signal Decomposition. The CS is used to exploit the sparsity of ultrasound echo Signals and thereby significantly reduce the sampling rate with 20-30 times lower than the Nyquist rate. Furthermore, the time-of-arrivals (TOAs) of dominant echoes are estimated with the sparse sampling. The estimated TOAs along with a priori information of the transducers are used for model-based Signal Decomposition on the incomplete ultrasonic data, where Gaussian Chirplet (GC), a commonly used echo model, is adopted. Parameters of GC echoes are estimated for pattern recognition and defect characterization in the presence of noise with SNR as low as -5 dB. Through an experimental study, the Decomposition results and estimated parameters confirm the robustness and effectiveness of the proposed technique. The study has a broad range of application in Signal analysis including sparse representation, parameter estimation, and defect detection.

  • Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition
    Advances in Acoustics and Vibration, 2012
    Co-Authors: Yufeng Lu, Alireza Kasaeifard, Erdal Oruklu, Jafar Saniie
    Abstract:

    A fractional fourier transform (FrFT) based chirplet Signal Decomposition (FrFT-CSD) algorithm is proposed to analyze ultrasonic Signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in Signal Decomposition and parameter estimation. FrFT rotates the Signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the Signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs Signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in Signal detection, estimation, and pattern recognition.

  • Ultrasonic chirplet Signal Decomposition for defect evaluation and pattern recognition
    2009 IEEE International Ultrasonics Symposium, 2009
    Co-Authors: Yufeng Lu, Erdal Oruklu, Jafar Saniie
    Abstract:

    In this study, a quantitative method using chirplet Signal Decomposition (CSD) is presented for pattern recognition and defect characterization. The CSD algorithm is utilized to decompose the ultrasonic Signal into a linear combination of chirplets, and efficiently estimate the echo parameters. These parameters can be correlated to the structure of defects. For experimental studies, planar and focused transducers with different center frequencies have been used for testing the embedded defects in specimen at normal or oblique refracted angles. It has been shown that the CSD successfully associates the estimated chirplets and their parameters as a quantitative method to characterize defects.

  • ACM Great Lakes Symposium on VLSI - Fpga-based hardware/software co-design for chirplet Signal Decomposition
    Proceedings of the 18th ACM Great Lakes symposium on VLSI - GLSVLSI '08, 2008
    Co-Authors: Yufeng Lu, Erdal Oruklu, Jafar Saniie
    Abstract:

    In various Signal processing applications, Decomposition and analysis of non-stationary Signals is a challenging problem. In this work, we present a computationally efficient method, fast chirplet Signal Decomposition (FCSD) algorithm, for decomposing highly convoluted Signals into a linear expansion of chirplets, and successively estimates the chirplet parameters. These parameters are capable of representing a broad range of echo shapes, including the broad-band, narrow-band, symmetric, skewed, nondispersive or dispersive, and have significant physical interpretations for radar, sonar, and ultrasonic imaging applications. For the real-time implementation of chirplet Signal Decomposition algorithm, an FPGA-based hardware/software co-design is developed on Xilinx Virtex II Pro FPGA platform. In this study, based on the balance among the system constraints, cost, and the efficiency of estimations, the performance of different algorithm implementation schemes have been explored. The developed system successfully exhibits the robustness in the chirplet Signal Decomposition of experimental Signals. This type of study addresses a broad range of applications including velocity measurement, target detection, deconvolution, object classification, data compression, and pattern recognition.

W. Fitzgerald - One of the best experts on this subject based on the ideXlab platform.

  • Time-frequency Signal Decomposition using energy mixture models
    2000 IEEE International Conference on Acoustics Speech and Signal Processing. Proceedings (Cat. No.00CH37100), 2000
    Co-Authors: M. Coates, W. Fitzgerald
    Abstract:

    We address the problem of Signal Decomposition. We specify Signal components by the property that their energies are localised and disjoint in the time-frequency plane. Rather than modelling the Signal directly, we represent the time-frequency energy of the Signal using a finite mixture model. This model is used to develop a partitioning of the time-frequency plane, allowing the application of time-frequency filtering to isolate components. Modelling energy rather than specifying a dictionary of allowable waveforms imposes fewer constraints on what a component may be. We demonstrate how the approach can be applied in the context of vibration analysis, where we wish to isolate the structure of individual bending waves travelling through a beam.

Dejie Yu - One of the best experts on this subject based on the ideXlab platform.

  • sparse Signal Decomposition method based on multi scale chirplet and its application to the fault diagnosis of gearboxes
    Mechanical Systems and Signal Processing, 2011
    Co-Authors: Fuqiang Peng, Dejie Yu
    Abstract:

    Abstract Based on the chirplet path pursuit and the sparse Signal Decomposition method, a new sparse Signal Decomposition method based on multi-scale chirplet is proposed and applied to the Decomposition of vibration Signals from gearboxes in fault diagnosis. An over-complete dictionary with multi-scale chirplets as its atoms is constructed using the method. Because of the multi-scale character, this method is superior to the traditional sparse Signal Decomposition method wherein only a single scale is adopted, and is more applicable to the Decomposition of non-stationary Signals with multi-components whose frequencies are time-varying. When there are faults in a gearbox, the vibration Signals collected are usually AM–FM Signals with multiple components whose frequencies vary with the rotational speed of the shaft. The meshing frequency and modulating frequency, which vary with time, can be derived by the proposed method and can be used in gearbox fault diagnosis under time-varying shaft-rotation speed conditions, where the traditional Signal processing methods are always blocked. Both simulations and experiments validate the effectiveness of the proposed method.

Alexander M. Krot - One of the best experts on this subject based on the ideXlab platform.