A Signal Theoretic Approach for Envelope Analysis of Real-Valued Signals

Analytic envelope is the most prevalent definition of envelopes of real-valued signals. However, analytic signals are not adopted by some envelope detectors in application. This paper investigates the envelopes of real-valued signals from a signal processing perspective. We show that the upper and lower envelopes of signals can be obtained by signal reconstruction after extrema sampling on signals. We prove that extrema sampling is a sub-Nyquist sampling. We then conclude that the envelopes of real-valued signals contain two parts, some low-frequency components of the original signal and some new components generated by sub-Nyquist extrema samplings. Some examples are presented to compare with the analytic envelope of signals.