How do I implement a simple AM and FM demodulator on an SDR platform for educational purposes?

Implementing a simple AM and FM demodulator on an SDR platform for educational purposes demonstrates the fundamental concepts of analog demodulation using software-defined radio hardware and GNU Radio or similar software. For AM demodulation: the SDR tunes to a broadcast AM station (530-1700 kHz); the received IQ (in-phase and quadrature) samples are: filtered to the channel bandwidth (approximately 10 kHz), then the envelope is computed by taking the magnitude of the complex signal: envelope = sqrt(I^2 + Q^2); this envelope is the demodulated audio signal; the DC component (carrier) is removed by a high-pass filter, and the result is sent to the sound card for playback. For FM demodulation: the SDR tunes to a broadcast FM station (88-108 MHz); the received IQ samples are: filtered to the channel bandwidth (200 kHz for wideband FM), then the instantaneous frequency is computed from the phase derivative: f_inst = (1/2pi) × d(arctan(Q/I))/dt; in discrete time: f_inst[n] = (1/2pi) × angle(x[n] × conj(x[n-1])) × f_sample; this gives the demodulated audio signal; after de-emphasis filtering (75 us time constant in the US), the audio is sent to the sound card. The SDR hardware needed: an RTL-SDR dongle ($20-30) covers 24-1766 MHz (adequate for FM; for AM, a direct-sampling modification or an upconverter is needed). Software: GNU Radio Companion (free, open-source) provides drag-and-drop signal processing blocks for both AM and FM demodulation.