Spectral Analysis of Wavelet Filters

This project focuses on spectral analysis of wavelet filters using the Mallat decomposition method to achieve signal reconstruction. The implementation involves performing wavelet decomposition on signals to extract spectral information, which is then utilized to reconstruct the original signals. In code implementation, this typically involves applying discrete wavelet transform (DWT) through filter banks, where high-pass and low-pass filters separate signal components at different scales. The spectral analysis of wavelet filters plays a crucial role in signal processing applications, enabling better understanding of signal frequency characteristics. Key functions include wavelet coefficient computation and inverse wavelet transform for reconstruction. This technique finds extensive applications in image processing for denoising and compression, audio processing for feature extraction, and other signal analysis domains. Mastering Mallat decomposition and wavelet filter spectral analysis is therefore essential for signal processing engineers, particularly when implementing efficient multi-resolution analysis algorithms in practical systems.