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Given a BPSK-modulated carrier what would happen to the phase changes in the signal after the carrier is moved to baseband?

Would the time intervals between the phase transitions in the time domain remain the same?

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There is no change - the complex envelope of the signal (magnitude and phase) at any given carrier frequency is no different from when that carrier frequency = 0 (DC, at baseband). To hold this equivalence the baseband signal must be complex (often represented with I and Q data paths) unless the signal is completely on the real axis... for example If the BPSK Signal at the carrier has a 10 degree phase offset (such that the carrier frequency is toggling between 10 degrees and 190 degrees), the baseband signal will do the same as long as it is allowed to be complex.

For this reason it usually doesn’t make sense to actually model a sinusoidal carrier when doing simulations but work directly with the complex baseband signal.

The further details given on upconversion and downconversion in this post may help provide further insight: Frequency shifting of a quadrature mixed signal

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