Code for QMF Filter Bank Design and Simulation with Algorithm Implementation

This documentation presents a MATLAB-based implementation for designing and simulating Quadrature Mirror Filter (QMF) banks, which are fundamental components in digital signal processing systems, particularly in audio/image compression applications. The code architecture employs modular functions for filter coefficient calculation, perfect reconstruction analysis, and multi-rate signal processing simulations. The core functionality enables automated QMF bank design through configurable parameters including subband count (typically powers of 2), filter length specifications, and prototype filter types (e.g., Kaiser window-based FIR designs). The algorithm implements polyphase decomposition structures for computational efficiency, with built-in validation checks for alias cancellation and phase linearity conditions. A key feature is the interactive GUI framework built using MATLAB's App Designer, which provides real-time visualization of filter bank structures through block diagrams and frequency domain plots. The code includes analytical modules for characterizing magnitude response (using fft-based calculations), phase response (with group delay analysis), and reconstruction error metrics through signal flow simulations. The implementation incorporates comprehensive documentation with theoretical background on QMF design principles, including spectral factorization methods and power complementary filter constraints. Example scripts demonstrate practical applications such as subband coding simulations and comparative analysis with tree-structured filter banks. The codebase utilizes object-oriented programming for filter bank configuration management, ensuring reproducible results across different design specifications. This resource serves both educational and research purposes, offering validated reference implementations for academic studies and practical system development. The modular architecture allows easy extension to modified filter structures like cosine-modulated filter banks, with built-in benchmarking capabilities for performance evaluation against theoretical bounds.