Digital Signal Processing 101

CHAPTER 2Complex Numbers and Exponentials

Complex numbers are among those things many of us were taught a long time ago and have long since forgotten. Unfortunately, they are important in digital communications and DSP, so we need to resurrect them.

What we were taught—and some of us vaguely remember—is that a complex number has a “real” and an “imaginary” part, and the imaginary part is the square root of a negative number, which is really a nonexistent number. This explanation right away sounds fishy, and while it’s technically true, there is a much more intuitive way of looking at it.

The whole reason for complex numbers is that we are going to need a two-dimensional number plane to understand DSP. The traditional number line extends from ...