I am about to start a new engineering job in the fields of signal processing and machine learning. I have a bachelor's degree in electrical engineering, but for the last two years I have been doing a master's in theoretical physics, so I have been away from the field of signal processing for a while.
In by bachelor's I learned continuous and discrete time signal processing from Lathi's text, and stochastic signal processing from a less known Swedish book.
Now that I am getting back to the field I am looking for something that is more compact and preferably to a higher mathematical standard than Lathi, but that still covers all the essentials. For example, I would now be comfortable with discussing the delta function as a distribution, proper discussion of convergence notions, and would prefer such an approach over the informal approach in Lathi.
My goals are twofold: to get back up to speed with the subject, and to get a deeper understanding.