RELAX Algorithm for Harmonic Detection

In this text, we introduce the RELAX algorithm for harmonic detection, which offers significant advantages over traditional FFT methods. The algorithm effectively estimates signal amplitude, frequency, and phase parameters, playing a crucial role in signal processing and analysis. Through iterative refinement techniques, the RELAX algorithm employs a relaxation-based approach that sequentially estimates and removes dominant harmonic components, allowing for more accurate parameter extraction even in noisy environments. By implementing the RELAX algorithm, we can achieve more precise characterization of signal features and enhance signal processing and interpretation capabilities. The core implementation typically involves nested optimization loops where frequency estimation is performed using nonlinear least-squares methods, followed by amplitude and phase estimation through linear regression. This makes the RELAX algorithm for harmonic detection a valuable tool that enables deeper understanding and investigation of signal properties, particularly useful in applications requiring high-resolution spectral analysis beyond FFT limitations.