LFM Signal Detection Method Based on Fractional Fourier Transform

Abstract

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.

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“…As a generalized form of Fourier transform, Namias [ 37 ] redefined the concept of FrFT in a purely mathematical way from the perspective of eigenvalues and eigenfunctions, and gave a high-order differential form of FrFT in 1980. After Almeida [ 38 ] pointed out that FrFT can be understood as the rotation of the time–frequency plane, and Ozaktas [ 39 ] proposed a discrete algorithm with a calculation amount equivalent to FFT, more scholars have begun applying FrFT to the signal processing field [ 40 , 41 ]. The p -order fractional Fourier transform of a one-dimensional signal is defined as follows [ 42 ]: where is the kernel function, and its expression is where is the rotation angle, p is the order of the FrFT, and δ is the impulse function.…”

“…Sensors 2023, 23, x FOR PEER REVIEW 3 of 17 scholars have begun applying FrFT to the signal processing field [40,41]. The p-order fractional Fourier transform of a one-dimensional signal is defined as follows [42]:…”