Shift and scale invariant detection

Different signal realizations generated from a given source may not appear the same. Time shifts, frequency shifts, and scales are among the signal variations commonly encountered. Time-frequency distributions (TFDs) covariant to time and frequency shifts and scale changes reflect these variations in a predictable manner. Based on such TFDs, representations invariant to these signal distortions are possible. Presented here are two approaches for discriminating between signal classes where within class translation and scale variation occur. The first method uses an auto-correlation followed by a scale transform to achieve the invariances. 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