Personally, for signal processing, I use Oppenheim & Schafer.

For sound radiation specifically, Fourier Acoustics by Williams is a good introduction.

For signal processing try 'Bendat and Piersol' 2010 edition. For acoustics 'Bies and Hanson' is a good back and has some simple signal processing in the appendix. 

I'd suggest   Handbook of Signal Processing in Acoustics

Editors: Havelock, David, Kuwano, Sonoko, Vorländer, Michael (Eds.) , Springer.

Not sure if you have found something readable already. Personally I can recommend the book from Grosse and Ohtsu "Acosutic emission analysis" published by Springer.

Also, if you want my personal opinion, you may also want to look into my PhD-thesis, which contains further reading regarding composite materials AE found on my profile for free download.

I recommend the book "Acosutic emission Testing" published by Springer. Personaly, for AE signal analysis, I think Fast Fourier Transform, Short-time Fourier Transform and wavelet transform are the effective tools.

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 Situ Monitoring of Fiber-Reinforced Composites Theory, Basic Concepts, Methods, and Applications

https://www.springer.com/gp/book/9783319309538