Wavelet Analysis for Signal Processing 1) Computing Wavelet Transform of Signals

Wavelet analysis for signal processing represents a crucial technique in modern signal analysis. When performing wavelet transformation, one can compute the wavelet transform of signals using functions like pywt.wavedec() in Python or wavedec() in MATLAB, which decomposes signals into different frequency components while preserving temporal information. During extreme point analysis, modulus maxima curves can be extracted by tracking local maxima across scales in the wavelet coefficient matrix, revealing oscillation patterns and singularity locations in the signal. Furthermore, the Lipschitz exponents for two singular points can be calculated through the scaling behavior of wavelet modulus maxima, implementing algorithms that examine the logarithmic decay of wavelet coefficients across scales to quantify local signal regularity. In summary, wavelet analysis for signal processing constitutes a sophisticated yet highly valuable technique that enables deeper understanding of signal characteristics through multi-resolution analysis and singularity detection.