Time-domain Approaches
In the time domain, a PDA typically estimates the period of a quasiperiodic signal, then inverts that value to give the frequency.
One simple approach would be to measure the distance between zero crossing points of the signal (i.e. the Zero-crossing rate). However, this does not work well with complex waveforms which are composed of multiple sine waves with differing periods. Nevertheless, there are cases in which zero-crossing can be a useful measure, e.g. in some speech applications where a single source is assumed. The algorithm's simplicity makes it "cheap" to implement.
More sophisticated approaches compare segments of the signal with other segments offset by a trial period to find a match. AMDF (average magnitude difference function), ASMDF (Average Squared Mean Difference Function), and other similar autocorrelation algorithms work this way. These algorithms can give quite accurate results for highly periodic signals. However, they have false detection problems (often "octave errors"), can sometimes cope badly with noisy signals (depending on the implementation), and - in their basic implementations - do not deal well with polyphonic sounds (which involve multiple musical notes of different pitches).
Current time-domain pitch detector algorithms tend to build upon the basic methods mentioned above, with additional refinements to bring the performance more in line with a human assessment of pitch. For example, the YIN algorithm and the MPM algorithm are both based upon autocorrelation.
Read more about this topic: Pitch Detection Algorithm
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