12. Things to Try

The chapter is dense; absorb it in stages. A few hands-on experiments that pay back the math:

1. Listen to AM and FM on a basic radio. Notice that AM stations fade gradually with distance, with hiss creeping in. FM stations sound clean until they abruptly drop into noise. That cliff is the FM threshold. Drive your car out of range of an FM broadcast slowly and you can pinpoint the threshold to within a kilometer.
2. Build an envelope detector. A 1N4148 diode, 1 nF cap, 100 kΩ resistor. Drive with an AM signal from a function generator (most sig gens have an AM mode; set $f_c = 100$ kHz, $f_m = 1$ kHz, $\mu = 0.5$). Probe before and after the detector. You should see the carrier on input, audio envelope on output. Then crank $\mu$ past 1 and watch the output distort.
3. Run an SDR. An RTL-SDR dongle ($30) and free software (gqrx, SDR#, Cubic SDR) lets you tune across the entire spectrum from ~25 MHz to ~1.7 GHz. Watch the spectrum as you tune. AM stations look like a tall carrier with side-fuzz; FM looks like a wider spread with no carrier line; SSB looks like a one-sided fuzz. Decode them with the appropriate demodulator setting and listen.
4. Synthesize and demodulate FM in Python (the code above). Vary $\beta$ from 0.1 to 10 and watch the Bessel-comb spectrum spread. Try recovering the message with the analytic-signal method. Observe what happens when you add Gaussian noise with SNR below 10 dB: clicks and dropouts appear, the threshold effect made visible.
5. Record a TEMPEST signal. With an SDR and a small loop antenna near a CRT or older LCD monitor, scan a few MHz to tens of MHz and look for harmonics that change pattern when the screen content changes. Demodulating these can reveal text or images on the screen. (Many countries restrict aggressive TEMPEST research; respect local law and only use displays you own.)