Hero III. Shift and scale invariant detection

Dierent signal realizations generated from a given source may not appear the same. Time shifts, fre-quency shifts, and scales are among the signal varia-tions commonly encountered. Time-frequency distribu-tions (TFDs) covariant to time and frequency shifts and scale changes re ect these variations in a predictable manner. Based on such TFDs, representations invari-ant to these signal distortions are possible. Presented here are two approaches for discriminating between sig-nal classes where within class translation and scale vari-ation occur. The rst method uses an auto-correlation followed by a scale transform to achieve the invari-ances. The second method treats the TFD as a two-dimensional probability density function and applies a transformation that removes the mean and variance to provide the shift and scale invariance. Each method employs discrimination mechanisms to yield powerful results. 1