The extinction pulse method has been proven to be a suitable method for radar target discrimination using the natural resonance annihilation concept. The standard procedure for extinction pulse (E-pulse) construction is based on an expansion on subsectional polynomials. In this paper it is proposed a new formalism for E-pulse construction using beta-splines. This formalism allows the E-pulse polynomial basis expansion to be treated in a unified theoretical framework and leads to a simplification of the original problem due to the linear nature of all the involved parameters. This new formulation has been also used to impose new conditions over the spectral contents of the E-pulses. These E-pulses constructed using the new conditions annihilate better the natural modes in the late-time radar target response, and provide a better discrimination rates than the classical scheme
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