(1) Fundamental frequency trajectories
(2) Periodic average representations of fundamental frequencies of fed-back and produced speech (phonation).
(3) The coherency of each variation frequency component.
(4) The loop transfer function of fed-back-to-produced interactions with confidence intervals.
(5) The minimum AIC estimations of AR parameters of the fundamental frequency trajetories for natural feedback conditions without artificial manipulations.
(6) Decomposition of the estimated response into two dominant components.
Representations from (2), (3) and (4) are averaged over separate measurements of the same conditions and illustrated. In addition mathematical descriptions and calculation procedures of all statistical values are given in detail. This allows us to estimate impulse and step responses to auditory stimulations. New findings using this set of procedures include (1) a strong but slow response around the 0.5Hz region and (2) the possible existence of the same response for natural speech. The first finding is due to a new decomposition algorithm. The validness of this decomposition is demonstrated by the fact that introducing about a 500ms delay into the artificial auditory feedback path makes the pitch contour very unstable.