Hanning Window Function Interpolation Algorithm

This document provides an in-depth exploration of the Hanning window function interpolation algorithm, a spectral analysis technique designed to precisely calculate amplitude, phase, and frequency parameters of multiple harmonic signals. The algorithm implementation typically involves applying a Hanning window to reduce spectral leakage, followed by interpolation between spectral bins to achieve higher frequency resolution than standard FFT analysis. Through this algorithm, we can achieve more accurate characterization and interpretation of harmonic signal features, with common implementations involving peak detection in the frequency domain and parabolic interpolation around detected peaks. The application scope spans multiple domains including audio processing (where it improves pitch detection accuracy), image processing (for frequency-domain analysis), and general signal processing systems. The algorithm's core principle leverages the Hanning window's known spectral characteristics to correct amplitude and phase measurements, while frequency interpolation uses ratio-based methods between adjacent FFT bins. Implementation considerations include selecting appropriate FFT sizes, handling closely-spaced harmonics, and managing computational complexity through optimized interpolation routines. Further research into the algorithm's implementation methods remains valuable for practical engineering applications, particularly in real-time systems requiring high-accuracy spectral measurements. In summary, the Hanning window interpolation algorithm serves as a crucial tool for comprehensive analysis of multi-harmonic signals, bridging the gap between standard FFT resolution limits and precise parameter estimation requirements.