This video goes through an overview of what you would learn in a discrete time signals (or digital signal processing) course. Sampling, digital filters, the z-transform, and the applications of these are some of the things included. I had to over simplify a lot to barely keep this video under 30 minutes but hopefully it gives you an idea of how this type of math is used in the real world.
Pole/Zero plot and digital filter modeler used in video:
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