Demodulating a signal generated by IR LED/ phototransistor pair
I've done exactly what you are trying to do (for photoplethysmography). The demodulation is easily done with a sample-and-hold type circuit.

To see why, just think about how the blood modulates the pulses of the carrier signal. It effectively scales the amplitude of the pulses (hence it is amplitude modulation) according to the heart beat waveform. Then the S/H circuit samples the amplitude of each pulse, recovering the heart waveform itself.



Here's a working implementation of the circuit. You simply close the switch for a period when the IR LED is on, then keep it open and it will hold the value sampled until the next IR LED pulse.