# Given 1 recording of my voice, how can I process it to sound like 2 independent recordings of my voice played in unison?

I have one recording of my voice $$x[n]$$ singing a song. One thing I could do is independently record me singing the song again to obtain $$y[n]$$. Then, $$z[n] = \frac{1}{2}\left(x[n] + y[n]\right)$$ would sound like a "chorus" of some sorts (assuming that both recordings were done in perfect sync).

My question is, without doing a bunch of independent recordings, is there some decent way to go straight from a single recording $$x[n]$$ to the 2-fold chorus $$z[n]$$? More generally, I'd like to be able to go to a $$k$$-fold chorus (equivalent to averaging $$k$$ independent recordings).

My gut tells me one could simulate independent recordings by randomizing the phase in $$x[n]$$'s STFT somehow, but I'm not sure of specifically what should be done. In this regard, the only relevant method I'm aware of is Paul stretching, which doesn't really fit the bill, I think.

Also, is there a standard name for this particular effect I'm trying to create?

• I absolutely appreciate being referenced to the nomenclature/tools to achieve the effect. But more importantly, I'm looking for the hard math that goes into making it happen. What are the actual DSP techniques/algorithms that go into making it happen, in terms of the original signal $x[n]$? – chausies Dec 30 '19 at 18:18
• @DanBoschen But I feel like an independent record $y[n]$ wouldn't simply have a different pitch/tempo than the original $x[n]$. It's more like, if $X[n, k]$ is the STFT of $x[n]$, then an independent recording $y[n]$ would have $Y[n, k]$ with the same frequency content but a randomly offset phase content (an offset that's somewhat randomized across each phoneme in the recording) – chausies Dec 30 '19 at 19:58