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The message I need to modulate is sinusoidal and centered around 0V, exactly like in the above document. But from what I've gathered, PSoC I/Os cannot accept or output a negative voltage. Is this correct? If so, how could it be possible to do AM as the application note shows?
There, you will see an explanation of adding an offset to the input 'message' signal, prior to hitting the GPIO pin.
What's not shown in app note (nor video), is how to add this offset voltage to the message signal. For this, you'll have to do some research applicable to your project. Generally, it's done with an op-amp.