The ampmodem object implements an analog amplitude modulation (AM) modulator/demodulator pair. Two basic transmission schemes are available: single side-band (SSB), and double side-band (DSB). For an input message signal , the double side-band transmitted signal is where is the carrier frequency, and is the modulation index.

http://liquidsdr.org/doc/ampmodem/

This tutorial explains how to write and simulate a phase-locked loop in the C programming language.

http://liquidsdr.org/blog/pll-howto/