scholarly journals Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Yufeng Lu ◽  
Alireza Kasaeifard ◽  
Erdal Oruklu ◽  
Jafar Saniie
Keyword(s):  
Experimental Data ◽  
Pattern Recognition ◽  
Fourier Transform ◽  
Parameter Estimation ◽  
Fractional Fourier Transform ◽  
Signal Decomposition ◽  
Chirp Rate ◽  
Rate Parameter ◽  
Ultrasonic Signals ◽  
The Relationship

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.

Performance Analysis of LFM Signal Parameter Estimation through FrFT Transform

2012 ◽  
Vol 195-196 ◽  
pp. 80-83
Author(s):  
Ze Zhong Wang ◽  
Yu Huang ◽  
Feng Liu
Keyword(s):  
Fourier Transform ◽  
Parameter Estimation ◽  
Fractional Fourier Transform ◽  
Frequency Estimation ◽  
Parameters Estimation ◽  
Chirp Rate ◽  
Signal Parameter ◽  
Central Frequency ◽  
Simulation Results ◽  
Radar Signals

The fractional Fourier transform (FrFT) used to process linearly frequency modulated (LFM) signals is applied in the differentiation and parameters estimation of LFM radar signals. The performance of the LFM signals detection and parameters estimation through FrFT are studied when the signal-noise ratio (SNR) is low. The situation is set and the demonstration routine through simulations is made so that the performance on the chirp rate estimation and the central frequency estimation of LFM signals through FrFT is tested, the time used to obtain parameter estimation results through computer simulations is compared. The simulation results demonstrate that the method through FrFT could be used to differentiate LFM radar signals and to estimate parameters of LFM radar signals when the SNR is low.

Detection and Parameter Estimation of Chirp Signal Based on Time-Frequency Analysis

2014 ◽  
Vol 989-994 ◽  
pp. 3989-3992
Author(s):  
Guang Zhi Wu ◽  
Gang Fu ◽  
Yan Jun Wu
Keyword(s):  
Fourier Transform ◽  
Parameter Estimation ◽  
Fractional Fourier Transform ◽  
Chirp Signal ◽  
Wigner Transform ◽  
Time Frequency ◽  
The Relationship ◽  
Generic Time ◽  
Time Frequency Distribution ◽  
Better Than

Based on the relationship between the Radon-Wigner transform and fractional Fourier transform and the time frequency distribution, using the property that Radon-Wigner transform has better performance in time and frequency domain, detection and parameter estimation of Chirp signal have been done by Radon-Wigner transform or fractiona1 Fourier transform. The theoretica1 analysis and simulation prove that two techniques are better than generic time-frequency transform, such as Wigner-Ville transform.

scholarly journals The Solvability of a Class of Convolution Equations Associated with 2D FRFT

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1928
Author(s):  
Zhen-Wei Li ◽  
Wen-Biao Gao ◽  
Bing-Zhao Li
Keyword(s):  
Fourier Transform ◽  
Convolution Operator ◽  
Fractional Fourier Transform ◽  
Hankel Transform ◽  
Polar Coordinates ◽  
Two Dimensional ◽  
Spatial Shift ◽  
Fractional Hankel Transform ◽  
The Relationship ◽  
Convolution Equations

In this paper, the solvability of a class of convolution equations is discussed by using two-dimensional (2D) fractional Fourier transform (FRFT) in polar coordinates. Firstly, we generalize the 2D FRFT to the polar coordinates setting. The relationship between 2D FRFT and fractional Hankel transform (FRHT) is derived. Secondly, the spatial shift and multiplication theorems for 2D FRFT are proposed by using this relationship. Thirdly, in order to analyze the solvability of the convolution equations, a novel convolution operator for 2D FRFT is proposed, and the corresponding convolution theorem is investigated. Finally, based on the proposed theorems, the solvability of the convolution equations is studied.

scholarly journals Nyquist Zone Index and Chirp Rate Estimation of LFM Signal Intercepted by Nyquist Folding Receiver Based on Random Sample Consensus and Fractional Fourier Transform

Sensors ◽  
2019 ◽  
Vol 19 (6) ◽  
pp. 1477 ◽  
Author(s):  
Xinqun Liu ◽  
Tao Li ◽  
Xiaolei Fan ◽  
Zengping Chen
Keyword(s):  
Fourier Transform ◽  
Random Sample ◽  
Fractional Fourier Transform ◽  
Estimation Method ◽  
Ultra Wideband ◽  
Estimation Methods ◽  
Radar Signal ◽  
Chirp Rate ◽  
Time Frequency ◽  
Random Sample Consensus

The Nyquist folding receiver (NYFR) can achieve a high-probability interception of an ultra-wideband (UWB) signal with fewer devices, while the output of the NYFR is converted into a hybrid modulated signal of the local oscillator (LO) and the received signal, which requires the matching parameter estimation methods. The linear frequency modulation (LFM) signal is a typical low probability of intercept (LPI) radar signal. In this paper, an estimation method of both the Nyquist Zone (NZ) index and the chirp rate for the LFM signal intercepted by NYFR was proposed. First, according to the time-frequency characteristics of the LFM signal, the accurate NZ and the rough chirp rate was estimated based on least squares (LS) and random sample consensus (RANSAC). Then, the information of the LO was removed from the hybrid modulated signal by the known NZ, and the precise chirp rate was obtained by using the fractional Fourier transform (FrFT). Moreover, a fast search method of FrFT optimal order was presented, which could obviously reduce the computational complexity. The simulation demonstrated that the proposed method could precisely estimate the parameters of the hybrid modulated output signal of the NYFR.

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