An extended method for Statistical Signal Characterization using moments and cumulants, as a fast and accurate pre-processing stage of simple ANNs applied to the recognition of pattern alterations in pulse-like waveforms

TL;DR

This work addresses the need for fast, resource-efficient feature extraction for pulse-like waveform pattern recognition. It extends Hirsch's Statistical Signal Characterization by introducing a $30$-parameter ESSC feature set derived from the signal, its derivative, and its integral, enabling a lightweight pre-processing stage for simple ANNs. Evaluations on Sinc, Gaussian, and Chirp pulses show that an MLP using ESSC features can achieve roughly $90\%$ accuracy at SNRs above $20$ dB, with classification times about four times faster than a 1D-CNN, and with significantly lower architecture complexity. The findings suggest ESSC as a practical alternative to deep learning in low-resource settings, while maintaining competitive performance and enabling real-time pulse-pattern recognition.

Abstract

We propose a feature-extraction procedure based on the statistical characterization of waveforms, applied as a fast pre-processing stage in a pattern recognition task using simple artificial neural network models. This procedure involves measuring a set of 30 parameters, including moments and cumulants obtained from the waveform, its derivative, and its integral. The technique is presented as an extension of the Statistical Signal Characterization method, which is already established in the literature, and we referred to it as ESSC. As a testing methodology, we employed a procedure to distinguish a pulse-like signal from different versions of itself with altered or deformed frequency spectra, under various signal-to-noise ratio (SNR) conditions of Gaussian white noise. The recognition task was performed by machine learning networks using the proposed ESSC feature extraction method. Additionally, we compared the results with those obtained using raw data inputs in deep learning networks. The algorithms were trained and tested on cases involving Sinc-, Gaussian-, and Chirp-pulse waveforms. We measure accuracy and execution time for the different algorithms solving these pattern-recognition cases, and evaluate the architectural complexity of building such networks. We conclude that a simple multi-layer perceptron network using ESSC can achieve an accuracy of around 90%, comparable to that of deep learning algorithms, when solving pattern recognition tasks in practical scenarios with SNR above 20dB. Additionally, this approach offers an execution time approximately 4 times shorter and significantly lower network construction complexity, enabling its use in low-resource computational systems.

Figures (12)

• Figure 1: Examples of different mathematical methods to obtain auxiliary functions $g$ and characteristic parameters from an original function or signal $f(t_n)$ (the time $t$ is normalized to range between 0 and 1). a: weight function $g(t_n) = f(t_n)/\sum_n \left|f(t_n)\right|$; b: probability density function $g(t_n) = \left|f(t_n)\right|/\sum_n \left|f(t_n)\right|$; c: amplitud histogram $g(f)$ (with an interval width of around 1% of the whole amplitude range $[-0.22,1]$); d: $g[m] = (A_m, T_m)$ is the set of amplitud and time segments bounded by the extrema of the signal (SSC method developed by Hirsch).
• Figure 2: Schematic of the pre-processing algorithm of the artificial neural network for the pattern-recognition method.
• Figure 3: Deformation filters applied to a Sinc pulse. The original Sinc signal (a.1, no deformation) and its amplitude spectrum (a.2). It is shown the resulting signals (b.1, c.1, d.1, and e.1) and their corresponding amplitude spectra (solid blue line in b.2, c.2, d.2, and e.2) obtained by multiplying the original signal spectrum (a.2) times the deformation filter amplitude spectra (dotted green line in b.2, c.2, d.2, and e.2). The parameters for Gaussian and Low-Pass filters are the following, (b.2) ${\rm F_{G1}}$: $\nu_c = 0$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (c.2) ${\rm F_{G2}}$: $\nu_c = 3$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (d.2) ${\rm F_{LP1}}$: $\nu_c = 2$, ${\rm SR}_\nu = 0.5$; (e.2) ${\rm F_{LP2}}$: $\nu_c = 5$, ${\rm SR}_\nu = 0.5$.
• Figure 4: Deformation filters applied to a Gaussian pulse. The original Gaussian signal (a.1, no deformation) and its amplitude spectrum (a.2). It is shown the resulting signals (b.1, c.1, d.1, and e.1) and their corresponding amplitude spectra (solid blue line in b.2, c.2, d.2, and e.2) obtained by multiplying the original signal spectrum (a.2) times the deformation filter amplitude spectra (dotted green line in b.2, c.2, d.2, and e.2). The parameters for Gaussian and Low-Pass filters are the following, (b.2) ${\rm F_{G1}}$: $\nu_c = 0$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (c.2) ${\rm F_{G2}}$: $\nu_c = 3$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (d.2) ${\rm F_{LP1}}$: $\nu_c = 3$, ${\rm SR}_\nu = 0.5$; (e.2) ${\rm F_{LP2}}$: $\nu_c = 4$, ${\rm SR}_\nu = 0.5$.
• Figure 5: Deformation filters applied to a Chirp pulse. The original Chirp signal (a.1, no deformation) and its amplitude spectrum (a.2). It is shown the resulting signals (b.1, c.1, d.1, and e.1) and their corresponding amplitude spectra (solid blue line in b.2, c.2, d.2, and e.2) obtained by multiplying the original signal amplitude (a.2) times the deformation filter amplitude spectra (dotted green line in b.2, c.2, d.2, and e.2). The parameters for Gaussian and Low-Pass filters are the following, (b.2) ${\rm F_{G1}}$: $\nu_c = 0$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (c.2) ${\rm F_{G2}}$: $\nu_c = 3$, $\sigma_\nu = 2$, $\Delta_a = 0.4$; (d.2) ${\rm F_{LP1}}$: $\nu_c = 5$, ${\rm SR}_\nu = 0.5$; (e.2) ${\rm F_{LP2}}$: $\nu_c = 3$, ${\rm SR}_\nu = 0.5$.