I recommend Prandoni & Vetterli's coursera class on Signal processing[1].
They have really made an effort to teach this in an intuitive manner
instead of just throwing equations at you. This was the course where
I finally really understood Fourier transforms in a visual way.
The other course I recommend is the Audio Signal processing class by Xavier Serra[2]
This is a practical class with lots of hands on programming examples and introduction
to useful open-source software tools.
Nice write-up. The pragmatic title is certainly accurate.
From first principles my favorite is Oppenheim / Schafer's 1989 version of 'Discrete-Time Signal Processing'. Its falling apart from all the use over the years.
That’s like the gold standard when it comes to the theory, though I like Richard Lyons book better, as it shows many tricks. Most DSP guys have a bag (trash bag sized) full of tricks.
the green-tea-press book called 'think dsp', available here: http://greenteapress.com/thinkdsp/thinkdsp.pdf is also pretty good introduction on the topic. but, as others have remarked, nothing beats oppenheim's seminal text 'Discrete-Time Signal Processing'
The book also has an accompanying active MOOC on Coursera platform.