Function Approximation Using BP Algorithm and Sigmoid Function

We can achieve a series of functions by implementing wavelet transform, including wavelet filtering and wavelet denoising. Wavelet transform serves as a powerful signal processing tool that enables analysis and processing of various signal types. Through wavelet filtering implementation (typically involving convolution operations with wavelet coefficients), we can perform noise reduction and interference removal to extract desired signal components. These functionalities can be implemented using algorithms like Discrete Wavelet Transform (DWT) with decomposition and reconstruction steps, utilizing functions such as wavedec and waverec in signal processing libraries. The practical applications span multiple domains including image processing (using 2D wavelet transforms), audio processing, and biomedical engineering. Therefore, mastering wavelet transform technology is crucial for in-depth research and applications in signal processing, particularly when combined with optimization techniques like thresholding in denoising algorithms.