CHIRPLET SIGNAL DECOMPOSITION AND PARAMETER ESTIMATION ALGORITHMS FOR ULTRASONIC SIGNAL ANALYSIS
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In ultrasonic imaging systems, shape, size and orientation of the reflectors and the physical properties of the propagation path govern the patterns of backscattered echoes. However, the backscattered echoes often interfere with each other due to closed locations, orientations and size of reflectors and may be corrupted by noise. Hence, signal modeling and parameter estimation of the ultrasonic echoes are essential for image analysis, detection, classification and diagnosis. Certain important information like position, shape and size of the reflectors can be represented by chirplet signal parameters. Similarly, in other important application area of signal modeling such as radar, sonar and speech, chirplet signal parameters are also critical. The objective of this study is to analyze the pattern of ultrasonic echoes using chirplet signal decomposition and parameter estimation techniques. Signal processing method for decomposing multiple interfering ultrasonic echoes is a major and challenging problem. The chirplet signal decomposition algorithms designed and analyzed in this investigation are based on the Fractional Fourier Transform (FrFT) and elliptic template matching applied to time-frequency distributions of ultrasonic signals. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition. Fractional Fourier Transform 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 xi 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. To accelerate echo estimation algorithm, we present a novel method for estimating the parameters of chirp echo by means of ellipse fitting in the Time-Frequency (TF) domain. Wigner-Ville Distribution (WVD) and Short-Time Fourier Transform (STFT) of chirplets are in the form of concentric ellipses in the TF plane. The elements of ellipse such as long axis, short axis and the slope of the ellipse correspond to the chirplet parameters and this can be used for parameter estimation. To demonstrate the parameter estimation performance of ellipse fitting method, the algorithm is used to decompose an ultrasonic experimental signal consisting of many interfering echoes acquired in nondestructive testing of a steel block. The comparison between the reconstructed signal and the experimental result shows that the decomposition has been successfully performed in the presence of measurement noise and interference from microstructure scattering echoes. The Ellipse Fitting Method (EFM) employs short-time Fourier transform as the main computational load of the algorithm that makes it a good candidate for real-time applications using FFT hardware accelerators. In this study we also present a Field-Programmable Gate-Array (FPGA) implementation that is able to perform chirplet signal decomposition using EFM. The EFM algorithm has been implemented as a system-on-chip consisting hardware architecture and software code on a Xilinx Virtex-5 FPGA. The xii designed hardware architecture is a combination of an embedded Microblaze processor, IP cores, communication buses, and I/Os. The software component represents a portion of the estimation algorithm that runs on the Microblaze processor. The EFM algorithm is used to decompose an ultrasonic experimental signal consisting of many interfering echoes.. The profiling analysis shows the major portion of the execution time (i.e., 94%) is for the FFT computations. By adding and interfacing the FFT IP-core accelerator to Microblaze, the estimation time for each chirp echo is reduced by 85% (i.e. from 550 ms to 82 ms). This reduction in echo estimation is highly desirable and makes the real-time parameteric signal analysis practical.