Clutter-free Doppler detection of signed velocity based on Legendre series expansion

A clutter-free velocimetry based on Legendre polynomial series expansion, which can fully utilize the unique low-frequency cut-off characteristic of the polynomial regression filter, is conceived. A set of complex I/Q Doppler signals, with a packet size of N, is expanded into a series of Legendre polynomials, obtaining expansion coefficients, L(n), (n=0, ..., N-1). Complex Legendre coefficients, C(±n), are then formed by linearly combining the Legendre coefficients as C(±n)=L(n-1)±jL(n) for an odd number of n and C(±n)=L(n)±jL(n-1) for an even number of n. The spectrum of the signed velocity can thereby be obtained from the absolute magnitudes of C(±n). The cut-off characteristic of the polynomial regression filter can be obtained by excluding C(±n) of small numbers of n.