Learn SDR 03a: Complex Numbers in SDR

Learn SDR with Professor Jason Gallicchio at Harvey Mudd College

Learn SDR Lesson 3: Complex numbers: adding (vector), multiplying components or magnitude+phase (math and simulation)

Complex numbers as 2D real / imaginary.

Adding component-wise is translation.

Multiplying component-wise by a real number is scaling

Euler's formula, multiplying as rotation

Multiplying complex exponentials is a lot cleaner and easier than trig identities:

cos(α + β) = cos(α) cos(β) – sin(α) sin(β)
cos(α – β) = cos(α) cos(β) + sin(α) sin(β)
2 cos(α) cos(β) = cos(α + β) + cos(α – β)
2 sin(α) sin(β) = cos(α – β) - cos(α + β)

Complex sinusoids as functions of time, both positive and negative.

Complex sinusoids as spirals

Show real and imaginary parts in time, constellation, and frequency plots

Show constellation plot rotating for slow signals.

HW: Generate a complex exponential. Add its complex conjugate to turn it into a real number. Show that the frequency power spectrum is symmetric.

https://gallicchio.github.io/learnSDR...

All GNURadio flowgraphs are at:
https://github.com/gallicchio/learnSDR

--- Learn SDR with Professor Jason Gallicchio