Verification of Various Smoothing Algorithms

The document provides a detailed methodology for verifying various smoothing algorithms through both MATLAB implementations and comprehensive Word documentation. The verification process involved rigorous testing across multiple datasets using algorithmic approaches such as moving average filters, Savitzky-Golay filters, and exponential smoothing techniques. MATLAB scripts were developed to implement these algorithms with configurable parameters like window sizes (e.g., 5-point or 7-point moving windows) and polynomial orders for Savitzky-Golay filtering. Key functions utilized include smoothdata() for built-in MATLAB smoothing, custom implementations using conv() for convolution-based filtering, and sgolay() for polynomial smoothing. The analysis covers performance metrics including signal-to-noise ratio improvement, computational efficiency comparisons, and edge-case handling. Results demonstrate algorithm effectiveness under different noise conditions while documenting limitations such as phase delays in causal filters and boundary effects. The document concludes with recommendations for algorithm selection based on application requirements and suggests future enhancements like adaptive window sizing and real-time implementation approaches using circular buffers or streaming data processing techniques.