Abstract
Increased data acquisition by uncalibrated, heterogeneous digital sensor systems such as smartphones present new challenges. Binary metrics are proposed for the quantification of cyber-physical signal characteristics and features, and a standardized constant-Q variation of the Gabor atom is developed for use with wavelet transforms. Two different continuous wavelet transform (CWT) reconstruction formulas are presented and tested under different signal to noise ratio (SNR) conditions. A sparse superposition of Nth order Gabor atoms worked well against a synthetic blast transient using the wavelet entropy and an entropy-like parametrization of the SNR as the CWT coefficient-weighting functions. The proposed methods should be well suited for sparse feature extraction and dictionary-based machine learning across multiple sensor modalities.
Highlights
IntroductionTo the Gabor wavelet [2] and proposes binary metrics for signature characterization
This paper applies the constant-Q standardized Infrasonic Energy, Nth Octave (Inferno) framework [1]to the Gabor wavelet [2] and proposes binary metrics for signature characterization
This paper proposes a transition to binary metrics for digital data and introduces a standardized, quantized variation of the Gabor atoms with binary bases, optimal time-frequency resolution, and clear spectral energy containment
Summary
To the Gabor wavelet [2] and proposes binary metrics for signature characterization. If the signature characteristics are sufficiently unique and recognizable from those of ambient coherent and incoherent noise, they can be used to identify and classify an object or process. The transformation of diverse digital measurements into robust, scalable, and transportable representations is a prerequisite for signal detection, source localization, and machine learning applications for signature classification. The challenge at hand is to construct sparse signal representations that contain sufficient information for classification. Unambiguous classification can be elusive; measurement artifacts, unexpected signal variability, and non-stationary noise often conspire to add uncertainty to our classifiers. As will be discussed in this paper, information and uncertainty quantification can be substantially simplified when using standardized wavelets and binary metrics
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