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Why is in some cases that the messaged received from the demodulation process has slightly more amplitude then the original message?

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Your question is not at all clear. What do you mean by "message"?

IF you are asking about the peak-to-peak or RMS amplitude of a demodulated FM signal - the absolute amplitude of the modulating signal is not a captured or encoded in an FM signal. The recovered (demodulated) signal has the same relative amplitudes between loud and soft passages, but the absolute signal amplitude in volts is not modulated onto the carrier.

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In AM super heterodyne radio theory, the AGC or automatic gain control circuit will increase the amplification of the RF antenna amplifier that is fed to the heterodyne mixer. Thus the amplitude of the detected audio signal can be greater, depending on the gain in the AGC circuit.

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