Signal Detection Program Using Wavelet Transform Modulus Maxima Method

This signal detection program implements an advanced methodology combining wavelet transforms and modulus maxima analysis. The algorithm performs multi-resolution analysis by decomposing signals into different frequency components using wavelet basis functions. The modulus maxima detection module identifies local extrema in the wavelet coefficients across multiple scales, which correspond to significant signal features and discontinuities. In practical implementation, the program typically utilizes functions like continuous wavelet transform (CWT) or discrete wavelet transform (DWT) for decomposition, followed by peak detection algorithms that track local maxima through scale-space representations. This combined approach enables precise identification of signal characteristics such as sharp transitions, singularities, and transient events. The program's architecture includes wavelet coefficient computation, modulus calculation, maxima tracking across scales, and threshold-based feature extraction. By integrating these mathematical techniques, the system provides a robust framework for signal analysis that supports various applications including anomaly detection, feature extraction, and pattern recognition in both research and practical implementations.