Introduction to Signal Processing

I think their treatment of the subject is more 'modern'. Classical signal processing is the stuff that you will find in Orfanidis's book in the OP and other classics such as Lyons, Oppenheim/Shafer, etc. Modern signal processing involves more harmonic analysis. There has been a lot of work, since the late 80s in the areas of wavelets, dictionary learning, etc. which you won't find in 'classical texts' on signal processing. In some universities these topics are taught in 'advanced' signal processing courses, at honors or graduate level. I hesitate to call this kind as 'advanced' signal processing, because I feel you need the same kind of prerequisites for 'classical' and 'modern' signal processing: linear algebra, Fourier analysis, basic probability, 'random processes', etc. In fact, I think 'modern' signal processing taught at the undergrad level also has the added benefit of being a gentle application-oriented introduction to real analysis for EE students.