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For a digital lock-in amplifier (synchronous demodulator) I have a sinusoidal reference signal in the range of 10-15kHz, the amplitude and phase I want to observe changes very slowly <10Hz.

My question is do I gain any benefit by oversampling the input signal, or is twice the reference frequency enough, i.e ~30kHz in my case?

I ask because the A/D converted signal is mixed with the reference oscillator and low-passed filtered to almost DC.

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Oversampling here would be extremely easy, so do it!

The benefits are of a noise nature (which is probably why you're doing the whole lock-in amplifier dance in the first place); you get a part of your oversampling factor as SNR gain.

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