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Major components of scale-space theory are Gaussian filtering, and the use of zero-crossing thresholders and Laplacian operators. Properties of scale-space filtering may be useful for data analysis in multiresolution machine-sensing systems. However, these systems typically violate the Gaussian filter assumption, and often the data analyses used (e.g. trend analysis and classification) are not consistent with zero-crossing thresholders and Laplacian operators. The authors extend the results of scale-space theory to include these more general conditions. In particular, it is shown that relaxing the requirement of linear scaling allows filters to have non-Gaussian spatial characteristics, and that relaxing of the scale requirements ( s→0) of the impulse response allows the use of scale-space filters with limited frequency support (i.e. bandlimited filters). Bandlimited scale-space filters represent an important extension of scale-space analysis for machine sensing