Non-Stationary Signal Noise Removal Using Wavelet Transform in MATLAB

In this article, we explore how to perform non-stationary signal noise removal using wavelet transform in MATLAB. Non-stationary signal denoising is a crucial task in digital signal processing, as noise can significantly impact signal quality and affect subsequent analysis and processing. To mitigate this impact, we employ wavelet transform techniques to reduce noise. Wavelet transform is one of the most widely used techniques in digital signal processing, capable of decomposing signals into frequency bands at different scales and processing each band individually to achieve non-stationary signal denoising.

The implementation in MATLAB typically involves several key steps: First, we use the wavedec function to perform wavelet decomposition, which breaks down the signal into approximation and detail coefficients. Then, we apply thresholding techniques (such as soft or hard thresholding) to the detail coefficients using functions like wthresh to remove noise components. Common threshold selection methods include Rigorous SURE threshold and universal threshold, which can be implemented via MATLAB's thselect function. Finally, we reconstruct the denoised signal using the waverec function. The article will introduce the fundamental principles of wavelet transform and their MATLAB implementation methods, helping readers better understand how to utilize wavelet transform for effective non-stationary signal noise removal.

Key MATLAB functions for wavelet denoising include wden for automatic denoising, wdenoise for enhanced denoising capabilities (available in newer versions), and wpdencmp for wavelet packet denoising. The choice of wavelet basis functions (such as Daubechies, Symlets, or Coiflets) and decomposition levels significantly affects denoising performance, which we will demonstrate through practical code examples.