This paper describes a parametric representation of ultra-wideband radar signatures and its physical interpretation. Under the scattering theory of electromagnetic waves, a transfer function of radar scattering is factorized into three elementary parts and a radar signature with three parameters is derived. To use these parameters for radar target classification and identification, the relation between them and the response waveform is analytically revealed and numerically checked. The result indicates that distortion of the response waveform is sensitive to these parameters, and thus they can be expected to be used as features for radar target classification and identification.