Temporal Envelope Fit of Transient Audio Signals

Abstract

We address the problem of temporal envelope modeling for transient audio signals. We propose the Gamma distribution function (GDF) as a suitable candidate for modeling the envelope keeping in view some of its interesting properties such as asymmetry, causality, near-optimal time-bandwidth product, controllability of rise and decay, etc. The problem of finding the parameters of the GDF becomes a nonlinear regression problem. We overcome the hurdle by using a logarithmic envelope fit, which reduces the problem to one of linear regression. The logarithmic transformation also has the feature of dynamic range compression. Since temporal envelopes of audio signals are not uniformly distributed, in order to compute the amplitude, we investigate the importance of various loss functions for regression. Based on synthesized data experiments, wherein we have a ground truth, and realworld signals, we observe that the least-squares technique gives reasonably accurate amplitude estimates compared with other loss functions.

Research of the indirect friction sensor for prediction of contact stress by improved inverse method in strip rolling

“…According to this phenomenon, the envelope fitting method [30] is used for obtaining the trend terms (mean envelope curves) of reconstructed stresses by old inverse method. Firstly, the reconstructed contact stresses are established by appropriately increasing the truncation point.…”

Piecewise-defined function for effectively implementing the audio volume automation

“…within relation (1), and expressions ( 16)-( 18), respectively, one eventually figures out the procedure needed for fade shaping over a certain interval [𝑡 , 𝑡 ], 𝑖 ≥ 0. More specifically, one derives:…”

“…Audio volume automation is mostly carried out in application software such as digital audio workstations (DAWs) by allowing the user to place various control points with the purpose of generating an amplitude envelope [1]- [7]. Since a control point simply indicates the expected audio volume at a certain playback position, adjustable fades (fade-up and/or fade-down audio effects) have to be implemented to automate the volume between each two control points that are placed successively [2]- [8].…”

An improved inverse method by envelope fitting for prediction of contact stresses in strip rolling

“…In this paper, considering the consistent convergence of the Fourier (power) series which is used in inverse method, the envelope fitting [14] has been proposed to improve the inverse method for prediction of the contact stresses. Through comparisons of the simulation data with theoretical results predicted by different inverse methods, it can be found that the improved inverse method by envelope fitting has a better predictive effect than the old method, in particular for the friction stress.…”