Yes I thought of that but then dividing by 2 to recover the carrier frequency has phase ambiguity.A possible solution is double carrier frequency by a full wave rectifier. This eliminates 180 degree phase jump on modulation polarity change. Then apply bandpass filter.
The carrier extracted from input signal has same ambiguity unless you combine it with modulation signal, as it's e.g. achieved in Costas loop.but then dividing by 2 to recover the carrier frequency has phase ambiguity.
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