Figure 3

State-space recurrence analysis for a periodic signal. Demonstration of results of time-delayed state-space recurrence analysis applied to a perfectly periodic signal (a) created by taking a single cycle (period k = 134 samples) from a speech signal and repeating it end-to-end many times. The signal was normalised to the range [-1, 1]. (b) All values of P(T) are zero except for P(133) = 0.1354 and P(134) = 0.8646 so that P(T) is properly normalised. This analysis is also applied to (c) a synthesised, uniform i.i.d. random signal on the range [-1, 1], for which (d) the density P(T) is fairly uniform. For clarity only a small section of the time series (1000 samples) and the recurrence time (1000 samples) is shown. Here, T _max = 1000. The length of both signals was 18088 samples. The optimal values of the recurrence analysis parameters were found at r = 0.12, m = 4 and τ = 35.