Hilbert Envelope Extraction from Real Discrete Finite Signals Considering the Nonlocality of Hilbert Transform

Methods of determining the envelope (instantaneous amplitude) of a real signal for continuous and discrete cases are investigated. The analysis of advantages and disadvantages of existing methods for extraction the envelope of a real signal for continuous and discrete cases are given. The efficiency of the choice of determining the conjugate signal by Hilbert transform method is substantiated. The problem of determining Hilbert envelope for real, discrete and finite signals by the methods of discrete Fourier transform (DFT) and discrete-time Fourier transform (DTFT) is considered. The reason for the large relative errors in the measurement of Hilbert envelopes by DFT method is revealed. A new effective method and an effective method for measuring the envelope of a real, discrete, finite signal is developed, which reduces the relative error of its measurement by an order of magnitude and reduces by an order of magnitude the computational cost and the necessary memory for implementing the method as well. The theoretical results obtained in the work are confirmed by the results of numerical modeling.