Instantaneous Phase Method for Linear Frequency Modulated Signals with MATLAB Implementation

In this article, we conduct an in-depth investigation of instantaneous frequency extraction technology for linear frequency modulated (LFM) signals using the instantaneous phase method, accompanied by a MATLAB implementation program that demonstrates the practical application of this technique. The MATLAB code implements key algorithms including Hilbert transform for analytical signal generation, phase unwrapping techniques, and numerical differentiation methods for precise instantaneous frequency calculation. Additionally, we have identified a research paper that provides comprehensive explanations and discusses application domains of this technology. We will summarize and analyze this paper to help readers better understand the underlying mechanisms of the technique and its practical implementations in real-world scenarios. The implementation includes functions for signal generation, phase extraction, and frequency estimation with proper error handling and visualization capabilities.