Acoustic emissions as a term sometimes has a very broad meaning given "scales" of observation/ mesurements and subject of interest stimulation method/source.
Say for simplicity it is a small earthquake induced in a nondestructive or even destruvtive manner.
So you create several small eathquake defects or microcracks and so on. They are "transmitted" signal sources, which are recorded what you call acquired waveform signals.
Very impotant point is to understand what is your sensor recording in fact and that the acquired numbers are realistic, and in what ways they may get modulated? The information that you seek from numbers is encoded in the data in a collective sense.
You need to extract and describe the information of variability in strength, compitence and morpology of your subject against spatio-temporally constrained
description of "continuum anomalies" distribution in your subject/field.
You have to consider 2 aspects: the time series you got from measurement and its spectral analysis.
From the first one, you will decide a threshold and extract time dependent parameters such as time of hit, maximum amplitude, time of rise, number of hits, duration, signal intensity,... all of them are usually performed by commercial software.
Then you will have to perform a spectral analysis in order to detect the frequencies best represented in your signal. This may give interesting results if your sensors are wide-band. The simplest way to perform spectral analysis is to compute a Fourier transform, and look at the modulus (square).
Which are the main parameters... depends on your application and can't be decided a priori. What you can do is compute a all set of parameters and then compute a principal component analysis to detect the most relevant parameters.
Here is the link to "Damage assessment of carbon-epoxy composites with and without resin flow channels": https://www.sciencedirect.com/science/article/pii/S0263822318308857
In my opinion, most important characteristics in acoustic signals are distinct frequency spectral and amplitude distribution. The shapes of the amplitude distribution at the high amplitude are generally more sporadic in nature, reflecting the statistical variability in fracture process.