The SIFO Operator: A Full-Spectrum Complex Mathematical Foundations and Signal Processing Sliding Filter

This document formalizes the Sliding Interpolated Forecasting Operator (SIFO) as a full-spectrum complex filter. By leveraging an asymmetric exponential amplification core coupled with a π-scaled hyperbolic phase accumulator, SIFO bridges the gap between aggressive momentum detection and phase-stable oscillatory tracking. We define the operator, analyze its spectral properties, and provide the necessary numerical stabilization techniques for implementation in sliding window capacities