Wavelet analysis represents a sophisticated branch of signal processing where wavelet transforms enable critical applications including image compression, vibration signal decomposition and reconstruction. Compared to Fourier transforms, wavelet transformations operate as local transforms in both spatial and frequency domains, allowing efficient information extraction from signals. Through fundamental operations like scaling and translation, wavelet transforms achieve multi-scale signal decomposition and reconstruction, effectively overcoming many limitations of Fourier analysis. As a new mathematical discipline, wavelet analysis synthesizes functional analysis, Fourier analysis, and numerical analysis, serving as a powerful "time-scale" analysis and multi-resolution analysis technique with extensive applications across signal processing, speech synthesis, image compression, and pattern recognition.
MATLAB
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