MATLAB Implementation of Energy Operator with Detailed Algorithm

This document presents a MATLAB implementation of the energy operator algorithm along with its detailed computational methodology, which finds applications in envelope demodulation and instantaneous frequency calculation. The implementation begins with defining the core energy operator calculation method, involving key signal processing steps such as signal sampling and digital filtering operations. The algorithm typically employs Teager-Kaiser energy operator or similar approaches to track signal energy variations. The program structure includes: - Signal preprocessing routines for input validation and normalization - Energy operator calculation using difference equations: ψ[x(n)] = x²(n) - x(n-1)x(n+1) - Envelope demodulation functionality that analyzes amplitude variations by computing the signal's energy trajectory - Instantaneous frequency estimation module that derives frequency-time information through energy operator derivatives For envelope demodulation applications, the code implements Hilbert-transform-free envelope extraction by computing the square root of the energy operator output. The instantaneous frequency calculation employs differentiation and normalization operations on the energy operator results to obtain frequency versus time characteristics. This MATLAB implementation utilizes vectorized operations for computational efficiency and includes optional visualization functions for plotting time-domain signals, energy profiles, and frequency variations. The program features configurable parameters for sampling rates, filter coefficients, and analysis windows, making it suitable for various signal processing and spectral analysis applications in engineering and research domains.