Multi-Level Signal Decomposition Using Harmonic Wavelets

In this context, harmonic wavelets can be employed to perform multi-level decomposition of signals. By extracting characteristic features from the signals, we can conduct more detailed analyses that help better understand signal properties and characteristics, leading to more accurate judgments and decisions. The implementation typically involves a wavelet decomposition algorithm that recursively applies high-pass and low-pass filters to separate signal components across different frequency bands. Through multi-level decomposition, we can observe signals from various frequency and scale perspectives, further revealing hidden information and patterns within the signal data. This approach often utilizes a pyramidal algorithm structure where each decomposition level produces approximation coefficients (low-frequency components) and detail coefficients (high-frequency components). The harmonic wavelet transform is particularly effective for this purpose as it provides excellent frequency localization properties. Therefore, using harmonic wavelets for multi-level signal decomposition represents an effective methodology that delivers richer and more comprehensive signal analysis results. The process can be implemented using numerical computing environments with wavelet toolbox functions for decomposition and reconstruction operations, allowing researchers to extract meaningful features like energy distribution, frequency content, and transient characteristics across different resolution levels.