High-Order Bi-orthogonal Fourier Transform and Its Applications in Non-stability Signal Analysis

Abstract

This paper presents a novel signal analysis algorithm, named High-order Bi-orthogonal Fourier Transform (HBFT), which can be seen as an expansion of Fourier transform. The HBFT formula and discrete HBFT formula are derived, some of their main characteristics are briefly discusses. This paper also uses HBFT to analyze the multi-LFM signals, obtain the modulate rate parameters, analyze the high dynamic signals, and obtain the accelerated and varying accelerated motion parameters. The result proves that HBFT is suitable for analysis of the non-stability signals with high-order components.