  Given set of functions $y_i(t)$ and $x(t)$ such that $y_i(t) = a_i
x\left[h_i(t)\right]$ with $a_i$ being an unknown amplitude with low changes in
time (or $\frac{\Delta a_i}{a^2_i} << 1$) and $h_i(t)$ an unknown warping
function, the paper shows that $h_i(t)$ can be described using a non-linear
differential equation. The differential equation then can be utilized to
estimate the warping function $h_i(t)$ using a nonlinear least-squares
optimization. This differential equation can also be useful for reducing and
analyzing phase variability in data sequences. Results, obtained on synthetic
curves, showed that the proposed method is effective in aligning the curves.
The obtained aligned curves exhibit variation only in amplitude, and phase
variation can be removed efficiently.
