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.

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Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition

Recently, there has been a growing attention on fractional Fourier transform (FrFT) for time-frequency analysis In this investigation, an FrFT-based signal decomposition algorithm is utilized to decompose ultrasonic signals into a linear combination of signal components As a transformation tool, FrFT is employed to estimate an optimal transform order, which leads to the maximum amplitude response, or the highest kurtosis value in the fractional transform domain Furthermore, a signal component is obtained by applying a window in the fractional domain and inverse FrFT In an iterative manner, ultrasonic signals are decomposed into the signal components until a predefined stop criterion is satisfied Analytical and simulation results show that FrFT is an alternative method to perform high-resolution analysis of nonstationary ultrasonic signals

Performance evaluation of fractional Fourier transform(FrFT) for time-frequency analysis of ultrasonic signals in NDE applications

Since decades, the fractional Fourier transform (FrFT) has attracted researchers from various domains such as signal and image processing applications. These applications have been essentially demanding the requirement of low computational complexity of FrFT. In this paper, FrFT is simplified to reduce the complexity, and further an efficient CORDIC-based architecture for computing discrete fractional Fourier transform (DFrFT) is proposed which brings down the computational complexity and hardware requirements and provides the flexibility to change the user defined fractional angles to compute DFrFT on-the-fly. Architectural design and working method of proposed architecture along with its constituent blocks are discussed. The hardware complexity and throughput of the proposed architecture are illustrated as well. Finally, the architecture of DFrFT of the order sixteen is implemented using Verilog HDL and synthesized targeting an FPGA device ”XLV5LX110T”. The hardware simulation is performed for functional verification, which is compared with the MATLAB simulation results. Further, the physical implementation result of the proposed design shows that the design can be operated at a maximum frequency of 154 MHz with the latency of 63-clock cycles.

An Efficient VLSI Architecture for Computation of Discrete Fractional Fourier Transform

In this study, a Fractional Fourier transform-based signal decomposition (FrFT-SD) algorithm is utilized to analyze ultrasonic signals for NDE applications. FrFT, as a transform tool, enables signal decomposition by rotating the signal with an optimal transform order. The search of optimal transform order is conducted by searching the highest kurtosis value of the signal in the transformed domain. Simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter. Furthermore, parameter estimation is applied to the decomposed components (i.e., chirplets) for echo characterization. Simulations and experimental results show that FrFT-SD not only reconstructs signal successfully, but also estimates parameters accurately. Therefore, FrFT-SD could be an effective tool for analysis of ultrasonic signals.

Analysis of fractional fourier transform for ultrasonic NDE Applications

In this investigation, an adaptive filter algorithm using Fractional Fourier transform (FrFT) has been developed for enhancement of targets in microstructure noise. In particular, the FrFT is introduced as a transformation tool to prepare ultrasonic signals for a more compact support. It also reduces the non-stationarity of signals. Furthermore, a normalized least mean square (NLMS) filter is applied on the transformed signal to suppress the grain noise. In order to evaluate the performance of the algorithm, various experimental ultrasonic data sets are acquired from a large grained specimen with embedded defects. A 5-MHz broadband transducer is utilized for data acquisition. The proposed algorithm is applied to discriminate defects in presence of high grain scattering noise. The experimental study shows that the algorithm greatly reduces grain noise and improves the signal-to-grain-noise ratio by about 12 dB. With the help of FrFT and the NLMS filter, the algorithm successfully identifies defects embedded in grain noise. This type of study can broaden the scope of applying adaptive filter in material evaluation and target detection.

Adaptive filtering and Fractional Fourier transform for ultrasonic signal processsing and flaw detection

The fractional Fourier transform (FrFT), which is a generalized form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications including radar involving the use and detection of chirp signals, pattern recognition and Synthetic Aperture Radar (SAR) image processing. The Chirp Scaling Algorithm (CSA) is one of the most important and well-known radar imaging algorithms. It is attractive because of its excellent focusing ability and implementation simplicity. Benefiting from the inherent structure of the FrFT for non- stationary digital signal processing and analysis, especially for chirped-type signals, a new version of the CSA based on the Fractional Fourier Transform (FrFT) is developed. The introduced Fractional Chirp Scaling Algorithm (FrCSA) applied the Fast Fourier Transform (FFT) instead of the fractional Fourier transform (FrFT) in the azimuth direction for the analytical development tractability purposes only as it numerically tractable in both dimensions. To demonstrate the resolution and focusing enhancement in the azimuth dimension using the FrCSA and also to be able to perform azimuth fractional filtering, noise removal and flight path nonlinearity compensation, a closed form expression for the azimuth fractional transformation is required. In this talk we present the mathematical derivation for a closed- form expression of the azimuth-fractional Fourier transform of the new FrCSA with application to high resolution imaging. Results to real SAR data images will show significantly enhanced features using the FrFT-based azimuth expression instead of the classical FFT-based one within the fractional chirp scaling algorithm or any other chirped-type SAR imaging algorithm.

A.S. Amein

Papers

The fractional Fourier transform and its application to high resolution SAR imaging