5-Level Decomposition of Simulated Signals Using DB4 Wavelet

The DB4 wavelet is a commonly used discrete wavelet basis function belonging to the Daubechies wavelet family, characterized by its 4-order vanishing moment property. In signal processing applications, it is widely employed for signal decomposition and reconstruction tasks, particularly suitable for handling signals with local abrupt changes or non-stationary characteristics. In MATLAB implementations, the DB4 wavelet can be accessed using the 'db4' identifier in wavelet transform functions.

Performing a 5-level decomposition on simulated signals involves breaking down the original signal into different frequency subbands through wavelet transformation. Each decomposition level generates approximation coefficients (low-frequency components) and detail coefficients (high-frequency components). As the decomposition depth increases, the low-frequency components of the signal become progressively refined, while high-frequency noise becomes separated into different levels of detail coefficients. The wavelet decomposition process can be implemented using functions like wavedec() in MATLAB, which returns the decomposition vector and corresponding bookkeeping matrix.

In noise reduction applications, commonly used thresholding methods include hard thresholding and soft thresholding. Hard thresholding sets signal amplitudes below the threshold directly to zero, while soft thresholding sets sub-threshold values to zero and applies shrinkage to values above the threshold. Additionally, improved thresholding techniques such as adaptive thresholding and statistically-based threshold selection methods can optimize denoising performance for different noise distributions. These can be implemented using wthresh() function with appropriate threshold calculation methods like universal threshold (thselect) or minimax threshold.

Through DB4 wavelet decomposition combined with appropriate threshold processing, noise in simulated signals can be effectively suppressed while preserving critical signal features, thereby enhancing the signal-to-noise ratio and improving the accuracy of subsequent analysis. The complete workflow typically involves signal decomposition, threshold application using wdencmp() or similar functions, and signal reconstruction using waverec().