in table 2 noting that u03c6 10 is the current phase u03c6 18 increase each of the u03c6 n excepting u03c6 10 by 0 89 u03c4 tt to compensate for the previous low pass filtering step 19 calculate a new instantaneous phase u03c6 inst as the angle to the center of gravity of n unit masses at polar coordinates of radius g n and angle u03c6 n revolutions 20 calculate the smallest signed difference u03b4 u03c6 inst between the phase estimated in the previous step and the current phase u03b4 u03c6 inst ue89e 1 u03b4 u03c6 inst u03c6 ue89e u03c6 inst u03c6 gt 0 5 u03b4 u03c6 inst ue89e u03c6 inst u03c6 1 ue89e u03c6 inst u03c6 lt 0 5 u03b4 u03c6 ue89e ue89e inst ue89e u03c6 inst u03c6 ue89e otherwise 21 derive a revised estimate u03b4 u03c6 rev equal to a weighted mean of the value calculated in the previous step and the average value u03b4 u03c6 i or u03b4 u03c6 e as appropriate u03b4 u03c6 ue89e 1 w ue89e u03b4 u03c6 i w ue89e ue89e u03b4 u03c6 inst ue89e 0 lt u03c6 lt 0 5 u03b4 u03c6 ue89e 1 w ue89e u03b4 u03c6 i w ue89e ue89e u03b4 u03c6 inst ue89e otherwise smaller values of w will cause better tracking of phase if the subject is breathing regularly and larger values will cause better tracking of phase if the subject is breathing irregularly 22 derive a blending fraction b such that the blending fraction is unity if the subject 39 s ventilation is well above v tgt zero if the subject is breathing near or below v tgt and increasing proportionally from zero to unity as the subject 39 s ventilation.