Digital Signal Processing: From Complex Numbers to the Hilbert Transform

We present a bottom up review of complex numbers through analytical functions commonly used in digital signal processing. Standard practice uses complex exponential functions for engineering and physics problems including differential equations, electrical engineering, analog and digital signal processing, control systems, mechanical vibrations, and wave propagation. We often use these methods by rote. In this paper, we review complex math and aim to fill common knowledge gaps in digital signal processing.