The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification
This work addresses the problem of signal classification under random displacements for researchers in signal processing, presenting an incremental extension of an existing transform.
The paper introduces the Signed Cumulative Distribution Transform, a new mathematical signal transform for analyzing non-rigid signal displacements, and demonstrates its application in classifying signals under random displacements.
This paper presents a new mathematical signal transform that is especially suitable for decoding information related to non-rigid signal displacements. We provide a measure theoretic framework to extend the existing Cumulative Distribution Transform [ACHA 45 (2018), no. 3, 616-641] to arbitrary (signed) signals on $\overline{\mathbb{R}}$. We present both forward (analysis) and inverse (synthesis) formulas for the transform, and describe several of its properties including translation, scaling, convexity, linear separability and others. Finally, we describe a metric in transform space, and demonstrate the application of the transform in classifying (detecting) signals under random displacements.