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The pulse is probably doable but difficult, at least on an iPhone. The noise in the accelerometer data from just holding it is pretty substantial.

Pulse is pretty trivial with another sensor on pretty much every smart phone out there: the camera

I've been using pulse apps for probably at least a decade

I’ve compared iPhone pulse apps to my Polartec H10 chest strap and they are wildly different many times. More than 10% difference easily.