Goal
Connect amplitude, phase and instantaneous frequency to the transmitted message.
Prerequisites: Parts 02, 07–09.
Future lessons
- AM, DSB and SSB: envelope, carrier and sidebands.
- PM and FM: phase and frequency modulation, the derivative of phase, and constant envelope.
- Polar form z = A·exp(jφ), phase unwrapping (unwrap) and behavior near zero amplitude.
- Polar transmitter: separate amplitude and phase chains, their bandwidths and the matching of their delays.
Lab plan
- For AM, FM and SSB, plot I/Q, the envelope, the unwrapped phase and the instantaneous frequency.
- Split SSB into amplitude and phase, put it back together and measure the error.
- Add different delays and band limits to the two chains; measure the spectral spreading.
We do the experiments in Python with NumPy, SciPy and Matplotlib. We keep the parameters, units and plots. The base models use float64 and complex128; we add bit-depth limits in separate experiments.
Completion criteria
- I can explain why the SSB envelope usually changes.
- I take into account that the phase is undefined at zero amplitude, and the matching of the two chains.
Result for the main project
A polar transmitter model and an experiment with chain mismatch.