Signal Recognition Program Using AR Model Coefficients and LM Neural Network for Weak Signal Detection

This program implements precise weak signal recognition by integrating AutoRegressive (AR) modeling with Levenberg-Marquardt (LM) neural network algorithms. The approach is particularly effective in low signal-to-noise ratio scenarios, such as biomedical signal processing or industrial equipment monitoring applications.

The program workflow consists of two core computational stages:

First, feature extraction is performed using AR modeling on raw signals. The AR model establishes linear relationships between current signal values and historical data points, effectively capturing statistical characteristics through AR coefficient computation. The program implements algorithms like the Yule-Walker equations or Burg's method to calculate optimal AR coefficients, which serve as compact feature representations. Compared to using raw signal data directly, this method better highlights key characteristics of weak signals while reducing dimensionality.

Second, the extracted AR coefficients are fed as input features into an LM neural network for training and classification. The LM algorithm operates as a hybrid optimization technique combining Gauss-Newton and gradient descent methods, featuring rapid convergence and excellent stability for nonlinear problems. The neural network architecture incorporates carefully designed hidden layers and activation functions to learn recognition patterns from AR features. Implementation includes functions for Jacobian matrix calculation and damping parameter adjustment to balance convergence speed and stability.

The complete pipeline provides end-to-end weak signal recognition: from raw signal input through AR feature extraction to neural network classification. This integrated approach demonstrates superior noise resistance and recognition accuracy compared to traditional methods, particularly excelling in low-SNR environments. The program incorporates computational efficiency optimizations through vectorized operations and parallel processing where applicable, ensuring rapid response times for practical applications.