Critical data length for period estimation
Srikanth Venkata Tenneti, Palghat P. Vaidyanathan · 2016
We address the following question in this paper: Given that the period of a discrete time periodic signal belongs to a set P = {P1, P2,..., Pκ}, what is the minimum duration of the signal necessary to identify its period? It will be shown that the following number of samples is both necessary and sufficient: max Pi+ Pj- gcd (Pi, Pj), where gcd is the greatest common divisor, and the maximization is over all pairs Pi, Pj ∈ P. Sufficiency is shown via a constructive proof, leading to a new period estimation algorithm.