How can I start learning about pitch detection?
i have to disagree with


  Calculation of the AMDF is less computationally expensive than the ACF due to the lack of multiplication operations (Niesler and Robinson ).


i don't think the cost of a multiplication is considered particularly more expensive than an absolute value.  (you might have a multiplier hanging around in your FPGA anyway.)

but this:



is new to me.  so they are looking for the value of $\tau$ that maximizes $f(\tau)$.

it looks interesting, but i don't see how it does better regarding the octave problem.  you could have a tone at A-440 that sounds like A-440 and then add to that a teeny-weeny (like -40 dB) amount of subharmonic at A-220.  the maximum $f(\tau)$ is might happen at $\tau = \frac{f_\mathrm{s}}{220 \text{Hz}}$ when you want it to happen at $\tau = \frac{f_\mathrm{s}}{440 \text{Hz}}$.

but i wonder what dividing by one plus the AMDF does to help.  it's something i hadn't thought about before.  i have to think about it a little.