Wavelet-Based Numerical Methods for Signal Processing

Abstract

Modern signal processing makes great use of wavelet transforms since they provide a flexible way to examine nonstationary signals both across time and frequency. This study looks at the optimization and use of several wavelet transforms include dual tree complex wavelet, stationary wavelet transforms (SWT), discrete wavelet transform (DWT), and continuous wavelet transform (CWT). For jobs including denoising, compression, feature extraction, and time frequency analysis, transform (DTCWT) is used. The paper looks at the tradeoffs between how fast it works, how good it is, and how reliable it is when choosing the right transform for various kinds of signals, including pictures, ECG, and speech. Important issues covered are the retention of high frequency components, edge integrity, and look into sophisticated approaches like synchro squeezed wavelet transforms (SSWT) for better frequency tracking and wavelet Galerkin feature stability across signal types. The study also examines techniques for resolving partial differential equations. Through performance evaluation using parameters such Signations Ratio (SNR), Peak Signations Ratio (PSNR), and Structural Similarity Index (SSIM), the research gives fresh perspective on the optimum methods for using wavelet transforms to address practical signal processing challenges.