My understanding of lock-in used to be only that of an [analog lock-in amplifier][1].

Now, I am thinking about digital lock-in technique. 

Reading [this][1] has been helpful. 

However, I am having trouble identifying the digital lock-in's equivalent for the integration time found in the analog lock-in's [multiplier unit][2]. 

Is this not the right way to think about the more modern lock-in, which actually doesnt have a multiplier unit but achieves high SNR measurement with the use of a mixer and LPF.

I would like to apply 'the integration of the product of the reference signal and the input signal' picture to the modern lock-in if there is a way. (thinking about the LPF in the time domain may be the way to do exactly that but I can't exactly put my finger on it)
  


  [1]: https://electronics.stackexchange.com/questions/545046/how-exactly-does-the-low-pass-filtering-in-a-lock-in-amplifier-correspond-to-a-t
  [2]: https://wp.optics.arizona.edu/jpalmer/wp-content/uploads/sites/65/2018/11/Gesamttext.pdf