Parabolic Lagrange Interpolation Filter Implementation with MATLAB Code

This documentation provides a comprehensive explanation of how to implement a parabolic Lagrange interpolation filter, accompanied by corresponding MATLAB program examples. The parabolic Lagrange interpolation filter represents a widely-used signal processing technique employed for signal reconstruction and smoothing applications. By utilizing this filter, you can enhance your data processing and analysis capabilities while achieving more accurate results. This article will cover the fundamental algorithm principles and implementation steps, supplemented with detailed MATLAB code that demonstrates key functions such as lagrange interpolation polynomial calculation and filtering operations. The implementation approach involves constructing second-order Lagrange basis polynomials to approximate signal values between known data points. The provided code includes functions for handling interpolation coefficients, managing signal windows, and applying the filter to discrete signal sequences. We will examine critical implementation details including the interpolation formula derivation, matrix operations for efficient computation, and practical considerations for real-time signal processing. This documentation aims to facilitate your understanding and application of parabolic Lagrange interpolation filters in your own projects, with code examples that can be readily adapted to various signal processing scenarios.