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One way to demodulate an amplitude modulated signal from its carrier is to build a peak-follower. This could be a simple RC filter with a diode at the input. The voltage across the capacitor would charge to the peak value of the carrier (envelope), and then discharge through the resistor. The time constant would be selected so that the capacitor would have no "trouble" following the envelope. Since the typical ratio of signal to carrier frequency is quite high, i.e. 20kHz signal vs 1MHz carrier, the time constant can be quite short.

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