Digital signal processing is the art of ... processing signals to come out as you need them or get the the needed information from them. You have 2 views ,perspective points too see a signal:
  1. the time domain( a plot of the air pressure,intensity,tension over time,a plot)
  2. the frequency domain(a signal at any point in its time domain can be considered  a sum of simple signals)
Diving in to this domain automatically takes you through math,computer programming and physics. 
I present to you DSP guide ,it leaves the math at the end chapters.It explains eveything in a simple way:

Free e-book:

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