function angle = popvecangle(phases, rates)
% estimate population vector
vecs = zeros(2, length(phases));
norm = sum(rates);
vecs(1, :) = rates.*cos(2*pi*phases/180.0)/norm;
vecs(2, :) = rates.*sin(2*pi*phases/180.0)/norm;
mvec = mean(vecs, 2);
angle = atan2(mvec(2), mvec(1));
angle = angle/2/pi*180.0;
if angle < 0
    angle = angle + 180.0;
end
end