High-precision Parameter Estimation For LFM Signal Based On Fractional Fourier Transform

With the rapid development of industrialization in China, nondestructive testingtechnology is widely used to ensure the high quality of the products. Among the five mostcommonly used nondestructive testing technologies, the ultrasonic testing technology iswidely applied to industrial inspection, medical testing and so on, because of its simpleequipment, flexible operation, strong penetrability and harmless to the human body. Alongwith the rapid development of sensor technology, DSP technology and computer technology,the digital and intelligent trend of ultrasonic detection system is becoming more and moreobvious.Most traditional ultrasonic testing systems take the pulse with little time-bandwidth astheir transmitting signal, which results in the poor anti-noise ability, low detecting precision,high residual error rate and so on. According to the Shannon theorem, we can improve theanti-noise ability by increasing the time-bandwidth. So we propose to transmit the linearfrequency modulation (LFM) signal instead, which has a large time-bandwidth. Based on this,several parameter estimation algorithms for LFM signal is proposed.The main research results in this paper include:1. With the analysis of the received signal, we establish the signal model and theFRFT to detect and estimate the parameters of the LFM signals. By the mathematicalderivation of the optimal order FRFT power spectral, the relational expression betweenspectral pick value and the LFM parameters is deduced. And a LFM signal parameterestimation algorithm based on FRFT is proposed: DIRECT-FRFT.2. We find that the discrete signal FRFT spectral peak is not always consistent with thereal one, thus there will be a discrete error in the result of DIRECT-FRFT. In order to solvethis problem, two high-precision algorithms (FRFT-TELS1&FRFT-TELS2), based on theTaylor expansion and the least square method, are proposed in this paper. We also do someperformance simulation among these three algorithms. And from the simulation results we seethat the two improved algorithms do have a higher performance. 3. Combining the previous research results, we set up a digital ultrasonic testingsystem based on LFM signal and FRFT. And we also use this system to inspect a steel platewhich has a defect inside. The estimate values of the steel plate’s length and the defect’sdistance are nearly the same with the real one. As we see, our ultrasonic testing system worksvery well in the steel plate inspection experiment.