Wavelet Analysis of Signals: Decomposition, Reconstruction and Filtering Procedures

When performing wavelet analysis on signals, the process involves systematic steps of wavelet decomposition and reconstruction, along with wavelet-based filtering operations. The first critical step is selecting an appropriate wavelet basis function (such as 'db4' for Daubechies wavelets or 'sym8' for Symlets) and determining the decomposition level through functions like wmaxlev() in MATLAB to ensure optimal frequency resolution. Next, wavelet decomposition is performed using functions like wavedec(), which breaks down the signal into approximation coefficients (low-frequency components) and detail coefficients (high-frequency components) across multiple resolution levels. Following decomposition, coefficient filtering can be applied using thresholding techniques (e.g., ddencmp() and wdencmp() for denoising) to remove or emphasize specific frequency components through hard or soft thresholding algorithms. After filtering, wavelet reconstruction is executed using waverec() to synthesize the modified coefficients back into a reconstructed signal. These comprehensive steps enable detailed wavelet analysis, providing enhanced time-frequency localization and more accurate signal processing results compared to traditional Fourier methods.