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DTIC ADP010920: A Family of Complex Wavelets for the Characterizati... |
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by Defense Technical Information Center |
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In the presence of oscillating singularities the standard |
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Wavelet Transfrom Modulus Maxima (WTMM) method gives |
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irrelevant information on the Hoelder regularity of the |
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function. In general, two exponents h,beta are necessary |
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to describe the singular behavior of a function f(x), |
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namely the Hoelder exponent h and the oscillation |
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exponent beta describing the local power law divergence |
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of the instantaneous frequency. If f(x) contains |
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oscillating singularities the regularity of the primitive |
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of f(x) depends on beta. In this case the Hoelder |
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exponent does not increase by 1 as in the case of a cusp |
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singularity but by beta + 1. Thus, the singularity |
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spectrum of general functions depends on both exponents, |
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D(h,beta). In order to extract Hoelder exponents and to |
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quantify at the same time the oscillating behavior we |
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propose to use a family of complex progressive wavelets |
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?psi sub n! with an increasing number of vanishing |
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moments. |
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Date Published: 2015-10-29 12:55:56 |
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Identifier: DTIC_ADP010920 |
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Item Size: 1794571 |
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Language: english |
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Media Type: texts |
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# Topics |
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DTIC Archive; Haase, Maria; STUTTGART... |
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@chris85 |
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