scholarly journals Time Reversal and Fractional Fourier Transform-Based Method for LFM Signal Detection in Underwater Multi-Path Channel

2021 ◽  
Vol 11 (2) ◽  
pp. 583
Author(s):  
Zhichen Zhang ◽  
Haiyan Wang ◽  
Haiyang Yao
Keyword(s):  
Fourier Transform ◽  
Signal Detection ◽  
Time Reversal ◽  
Fractional Fourier Transform ◽  
Simulated Data ◽  
Detection Performance ◽  
Performance Curves ◽  
Novel Method ◽  
The Difference ◽  
Peak Value

Fractional Fourier transform (FrFT) is a useful tool to detect linear frequency modulated (LFM) signal. However, the detection performance of the FrFT-based method will deteriorate drastically in underwater multi-path environment. This paper proposes a novel method based on time-reversal and fractional Fourier transform (TR-FrFT) to solve this problem. We make use of the focusing ability of time-reversal to mitigate the influence of multi-path, and then improve the detection performance of FrFT. Simulated results show that, compared to FrFT, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 8.75 dB. Lake experiments results indicate that, the difference between peak value and maximum pseudo-peak value of the signal processed by TR-FrFT is improved by 7.6 dB. The detection performance curves of FrFT and TR-FrFT detectors with simulated data and lake experiments data verify the effectiveness of proposed method.

LFM Signal Detection Method Based on Fractional Fourier Transform

2014 ◽  
Vol 989-994 ◽  
pp. 4001-4004 ◽  
Author(s):  
Yan Jun Wu ◽  
Gang Fu ◽  
Yu Ming Zhu
Keyword(s):  
Fourier Transform ◽  
Signal Detection ◽  
Frequency Analysis ◽  
Experimental Analysis ◽  
Fractional Fourier Transform ◽  
Detection Method ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Frequency Information ◽  
Strong Impulse

As a generalization of Fourier transform, the fractional Fourier Transform (FRFT) contains simultaneity the time-frequency information of the signal, and it is considered a new tool for time-frequency analysis. This paper discusses some steps of FRFT in signal detection based on the decomposition of FRFT. With the help of the property that a LFM signal can produce a strong impulse in the FRFT domain, the signal can be detected conveniently. Experimental analysis shows that the proposed method is effective in detecting LFM signals.

scholarly journals Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials

2018 ◽  
Vol 9 ◽  
pp. 1828-1833 ◽  
Author(s):  
Daniela Dragoman
Keyword(s):  
Wave Function ◽  
Fourier Transform ◽  
Fractional Fourier Transform ◽  
Berry Phase ◽  
Wave Functions ◽  
Electron Propagation ◽  
One Step ◽  
The Difference ◽  
Integrated Logic ◽  
The Fourier Transform

A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction transverse to that of electron propagation. The difference between the propagation lengths necessary to obtain a fractional Fourier transform of a given order in these two cases could be seen as a manifestation of the Berry phase. The Fourier transform of the electron wave function is a particular case of the fractional Fourier transform. If the input and output wave functions are discretized, this configuration implements in one step the discrete fractional Fourier transform, in particular the discrete Fourier transform, and thus can act as a coprocessor in integrated logic circuits.

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