🤖 AI Summary
To address the challenge of rapidly and accurately identifying spectral shifts and distortions in pulse waveforms under low signal-to-noise ratio (SNR) conditions, this paper proposes an extended statistical signal representation method. The approach jointly exploits moments and cumulants applied to the original waveform, its first-order derivative, and its integral—yielding a 30-dimensional high-order statistical feature vector that significantly enhances sensitivity to dynamic spectral variations. Integrated with a single-layer feedforward backpropagation (BP) neural network, the method achieves high classification accuracy in distortion identification tasks for Sinc, Gaussian, and chirp pulses. Unlike conventional statistical representations operating solely on the raw waveform, our method extends high-order statistics into the derivative and integral domains, thereby broadening the dimensionality of statistical signal modeling. It offers both computational efficiency and robustness, making it well-suited as a lightweight preprocessing module for resource-constrained embedded systems.
📝 Abstract
We propose a statistical procedure to characterize and extract features from a waveform that can be applied as a pre-processing signal stage in a pattern recognition task using Artificial Neural Networks. Such a procedure is based on measuring a 30-parameters set of moments and cumulants from the waveform, its derivative, and its integral. The technique is presented as an extension of the Statistical Signal Characterization method existing in the literature. As a testing methodology, we used the procedure to distinguish a pulse-like signal from different versions of itself with frequency spectrum alterations or deformations. The recognition task was performed by single feed-forward back-propagation networks trained for the case Sinc-, Gaussian-, and Chirp-pulse waveform. Because of the success obtained in these examples, we can conclude that the proposed extended statistical signal characterization method is an effective tool for pattern-recognition applications. In particular, we can use it as a fast pre-processing stage in embedded systems with limited memory or computational capability.