Envelope of a Real Discrete Signal on a Finite Interval and Methods for Its Determination

Abstract

Methods of determining the envelopes (instantaneous amplitudes) of an actual signal are studied, both for a continuous and a discrete case. The representation of a real continuous and discrete signal in the time and frequency domains is considered. It is shown that the application of one or another representation of the signal is determined by the area of application of the signal processing method. The analysis of the advantages and disadvantages of existing methods for determining the envelope (instantaneous amplitude) of the actual signal for a continuous and discrete case is given. The efficiency of the choice of determining the conjugate signal by the Hilbert transform method is substantiated. The problem of determining the Hilbert envelope for real, discrete, finite signals by the methods of discrete Fourier transform and discrete - time Fourier transform is considered. The main reason for the large relative errors in the measurement of Hilbert envelopes by the discrete Fourier transform method is revealed. A new effective and efficient method has been developed for measuring the envelope of a real, discrete, finite signal, which reduces the relative error of its measurement by an order of magnitude, reduces computational costs and the necessary memory for implementing the method. The theoretical results obtained in the work are confirmed by the results of numerical simulation of measuring the envelope of a real, discrete, finite signal by the existing and proposed method.