Improved estimation of the amplitude envelope of time-domain signals using true envelope cepstral smoothing

The amplitude modulations of musical instrument sounds and speech are important perceptual cues. Accurate estimation of the amplitude, or equivalently energy, envelope of a time-domain signal (waveform) is not a trivial task, though. Ideally, the amplitude envelope should outline the waveform connecting the main peaks and avoiding over fitting. In this work we propose a method to obtain a smooth function that approximately matches the main peaks of the waveform using true envelope estimation, dubbed true amplitude envelope. True envelope is a cepstral smoothing technique that has been shown to outperform traditional envelope estimation techniques both in accuracy of estimation and ease of order selection. True amplitude envelope gives a reliable estimation that follows closely sudden variations in amplitude and avoids ripples in more stable regions with near optimal order selection depending on the fundamental frequency of the signal.