General approach for obtaining joint representations in signal analysis and an application to scale

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Abstract
A general approach for obtaining joint representations in signal analysis is presented. The method is applied to scale representations. We define a new scale operator and show that it leads to joint representations of the Altes and Marinovic type and we also define joint representations with inverse frequency and show that it leads to Bertrand-Bertrand type distributions. We derive the uncertainty principle for scale and obtain the minimum time-scale uncertainty signal.

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