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The Symmetry Characteristic and Parameter Estimation of FRFT Modular Function of LFM Signal

Haiyan Guo

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Abstract

By means of mathematical derivation,a conclusion is obtained that the modular function of fractional Fourier transform(FRFT) of infinite time LFM signal is symmetrical,unilateral and strictly monotone.Through analyzing,this feature is also suitable for time limited LFM signal.Based on this conclusion,a new method using two-step search for time limited LFM signal detection and parameter estimation based on FRFT is proposed.The effect of FRFT algorithm error on the symmetry and monotonicity of the FRFT modular function of LFM signal is overcome in this method.The computational complexity is decreased effectively and the precision of parameter estimation is improved.Simulation results show its effectivity.

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What this paper is about

By means of mathematical derivation,a conclusion is obtained that the modular function of fractional Fourier transform(FRFT) of infinite time LFM signal is symmetrical,unilateral and strictly monotone.Through analyzing,this feature is also suitable for time limited LFM signal.Based on this conclusion,a new method using two-step search for time limited LFM signal detection and parameter estimation based on FRFT is proposed.The effect of FRFT algorithm error on the symmetry and monotonicity of the FRFT modular function of LFM signal is overcome in this method.The computational complexity is decreased effectively and the precision of parameter estimation is improved.Simulation results show its effectivity.

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Available abstract

By means of mathematical derivation,a conclusion is obtained that the modular function of fractional Fourier transform(FRFT) of infinite time LFM signal is symmetrical,unilateral and strictly monotone.Through analyzing,this feature is also suitable for time limited LFM signal.Based on this conclusion,a new method using two-step search for time limited LFM signal detection and parameter estimation based on FRFT is proposed.The effect of FRFT algorithm error on the symmetry and monotonicity of the FRFT modular function of LFM signal is overcome in this method.The computational complexity is decreased effectively and the precision of parameter estimation is improved.Simulation results show its effectivity.

Key concepts: SIGNAL (programming language), Modular design, Function (biology), Monotonic function, Algorithm, Fractional Fourier transform, Fourier transform, Estimation theory

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