Harmonic Detection in Signals with Abrupt Changes Using Wavelet Transform

Applying wavelet transform to signals containing abrupt changes enables accurate harmonic detection and identification of signal transition moments. Harmonic detection serves as an effective methodology for identifying harmonic components within signals through frequency domain analysis. Wavelet transform operates as a mathematical instrument that decomposes signals into sub-signals across different frequency bands, facilitating enhanced characterization of signal features. Throughout this process, we leverage wavelet transform properties - particularly its multi-resolution analysis capability and modulus maxima detection at abrupt points - to precisely locate signal transitions. Implementation typically involves using wavelet families like Daubechies or Symlets through functions such as wavedec() for decomposition and wmaxlev() for determining optimal decomposition levels. This technique finds applications across diverse domains including power system harmonic analysis, where it detects harmonic distortions in electrical grids, and seismic signal processing for identifying earthquake onset times. Consequently, harmonic detection utilizing wavelet transform represents a highly valuable technical approach with robust implementation frameworks.