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A new method of radar target discrimination and identification is presented. This new method is based on the natural frequencies of the target. It consists of synthesizing aspect-independent discriminant signals, called extinction-pulses (E-pulses) and single-mode extraction signals which, when convolved numerically with the late-time transient response of an expected target, lead to zero or single-mode responses. When the synthesized, discriminant signals for an expected target are convolved with the radar return from a different target, the resulting signal will be significantly different from the expected zero or single-mode responses, thus, the differing targets can be discriminated. Theoretical synthesis of discriminant signals from known target natural frequencies and experimental synthesis of them for a complex target from its measured pulse response are presented. The scheme has been tested with measured responses of various targets in the laboratory.