MATLAB Implementation of Continuous Wavelet Transform

Continuous Wavelet Transform (CWT) is a fundamental signal processing technique that decomposes signals into frequency subbands while maintaining temporal information. The implementation typically involves MATLAB's wavelet toolbox functions such as cwt() which computes the transform using complex Morlet wavelets by default. Key parameters include scales (determining frequency resolution) and the mother wavelet selection affecting time-frequency localization. The provided data.mat file contains sample signals for practical experimentation, allowing users to visualize scalograms (time-scale representations) using imageSC() and analyze coefficient magnitudes. This technique finds extensive applications in image processing (edge detection), audio analysis (pitch tracking), and data compression (energy compaction). Mastery of CWT enables sophisticated multiresolution analysis through functions like wavedec() for decomposition and waverec() for reconstruction, providing solutions for real-world signal characterization problems. Implementation considerations include proper scaling parameter selection and handling boundary effects using symmetric padding modes. A typical workflow involves loading signals with load('data.mat'), performing CWT analysis, and interpreting the resulting coefficient matrix for feature extraction.