Fractional Fourier Transform of Ultrasonic Chirp Signal for Range Measurement

Ultrasonic range measurement system send out ultrasonic chirp signal, the reflected echo signal is received by the system and transferred into electrical signal by piezoelectric sensor; time of difference between sending and receiving signal is used to calculate the distance. But there is multi-reflections and noise in the echo ultrasonic wave that affect the quality of the received signal, which occurs overlapping phenomenon, thus make the reading wrong or instability. This study proposes a method to separate the time-overlapping chirp signal, first the echo signal is processed by fractional Fourier transform, then filtered out by a rectangular window, and finally the original signal is restored by inverse fractional Fourier transform. The proposed signal separation method is verified by application to a simulation of a composite chirp signal, the result show that each component signal can be recovered with little spectral error.