Dierent 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 reect 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 rst method uses an auto-correlation followed by a scale transform to achieve the invariances. The second method treats the TFD as a twodimensional 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.
The scale transform introduced by Cohen 111 is a special case of the Mellin transform. The scale transform has mathematical properties desirable for comparison of signals for which scale variation occurs. In addition to the scale invariance property of the Mellin transform many properties specific to the scale transform have been pree;ented [l]. A procedure is presented in this paper for complete implementation of the scale transformation for discrete signals. This complements discrete Mellin transforms and delineates steps whose implementation are specific to the scale transform.
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