8 March 2002 Two-dimensional Zernike wavelets for one-dimensional complex signal identification
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We present an approach to complex signal identification that uses a non-linear transformation into a 2-D (image) domain as a fundamental first step. Motivating this approach is the observation that many complex signals of interest have characteristic complex--plane behaviors when viewed under certain invariance rules, e.g., rotation and/or scaling in the complex--plane. Orthonormal bases in 2D that exhibit special properties may be employed to some advantage for 1D classification. Specifically, we use the Zernike transform to yield rotationally invariant features of complex 1D signals. These features may be furthered projected into a low dimensional subspace via a standard Fisher analysis in the context of a specific data set. Using a small data set consisting of six different sources the method is shown to perform well and exhibit a high level of noise robustness. The resulting feature vector is of low dimensionality and has reasonable computational cost.
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Anthony Teolis, Anthony Teolis, "Two-dimensional Zernike wavelets for one-dimensional complex signal identification", Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); doi: 10.1117/12.458756; https://doi.org/10.1117/12.458756

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