to the first post-Newtonian order: $$\begin{aligned}
\varphi_0 (t) &=& {16 \pi f_s\tau_0 \over 5} 
\left [ 1 - \left ({f\over f_s}\right )^{-5/3} \right] \nonumber,\\
\varphi_1(t)&=& 4 \pi f_s\tau_1 \left [ 1 - \left ( {f\over f_s} \right )^{-1} \right ]
\label {phaseN}\end{aligned}$$ where $f(t)$ is given implicitly by, $$t - t_s= \tau_0
\left [ 1 - \left ( {f \over f_s} \right )^{-8/3} \right ]+
\tau_1\left[1 - \left ( {f \over f_s} \right )^{-2} \right]
\label {frequencyN},$$ where $\tau_0$ and $\tau_1$ are constants having dimensions of time given by $$\begin{aligned}
\tau_0 &=& {5 \over 256} {\cal M}^{-5/3} (\pi f_s)^{-8/3},\nonumber\\
\tau_1 &=&  {5 \over 192\mu (\pi f_s)^2} \left ({743\over 336} + {11\over 4} \eta
\right ),
\label{NCT}\end{aligned}$$ where $\eta=\mu/M$, and $f_s$ is the instantaneous gravitational wave frequency of the signal at $t=t_s.$ The time elapsed starting from an epoch when the gravitational wave frequency is $f_s$ till the epoch when it becomes infinite will be referred to as the [*chirp time*]{} of the signal. In the quadrupole approximation $\tau_0$ is the chirp time whereas it is $\tau_0+\tau_1$ for the first post-Newtonian case [@Sat94]. The Newtonian part of the phase is characterised by three parameters: (i) the [*time of arrival*]{} $t_s$ when 