I think the author does a good job of looking at some of the practical aspects of IQ data but I see the question of "Why IQ" quite differently. When I started

I think the author does a good job of looking at some of the practical aspects of IQ data but I see the question of "Why IQ" quite differently. When I started with SDR and wrote some Fourier Transform code I wanted to know why if I fed it a sine wave at frequency X, I got two peaks in the transform. Experts said, "Well that is because you have a real signal only, if you add the quadrature component you'll see just one peak." Which is true, if you do that you see one peak, but WHY was my question. The answer to that question was that there is a difference between discrete mathematics and continuous mathematics. And more specifically, when you operate using discrete mathematics, you need to understand both the slope and the magnitude of the the function you are working with. A discrete version of sin(ωt) (where ω = 2πf) that is "real only" as some would say, has zero values in the quadrature side. That happens when the signal is the sum of two signals that are the complex conjugate of each other (their quadrature (or imaginary) parts differ only in sign). The discrete Fourier transform correctly picks up both of those signals and identifies them as +f and -f.