evolutionary timescales $\tau_{\rm gas}$ and $\tau_{\rm gw}$ are both much longer than the observational period of LISA, $f$ is almost a constant in our model. In this case the computation of the inner product $\left<h_1|h_2\right>$ can be performed in the time domain and the calculation of the FF can be simplified. First, the noise curve $S_n(f)$ can be taken out of the integration because of the small variation of $f$, so that $$\left<h_{1} | h_{2}\right>\approx \frac{2}{S_n} \int_{0}^{\infty} [\tilde{h}_{1}^{*}(f) \tilde{h}_{2}(f)+\tilde{h}_{1}(f) \tilde{h}_{2}^{*}(f)] d f.$$ Second, using Parseval’s theorem, we further derive $$\left <h_{1} | h_{2}\right >\approx \frac{4}{S}\int_{0}^{\infty} h_{1}(t) h_{2}(t)d t.$$ Finally, the FF can be written as $${\rm FF}=\frac{\int_{0}^{\infty} h_{1}(t) h_{2}(t)d t}{\sqrt{\int_{0}^{\infty} h_{1}(t) h_{1}(t)d t\int_{0}^{\infty} h_{2}(t) h_{2}(t)d t}}.$$ Note that there is no more dependence on $d_L$, $Q(\theta, \varphi, \psi,
\iota)$, or $S_n(f)$, because they all cancel out. Given $h_1$, i.e., the signal, we want to find a template $h_2$ that maximizes the FF. The parameter space in which we conduct this search is $({\cal M}_c,\,q,\,\phi)$, where $\phi$ is the initial phase.

Examples {#sec:examp}
--------

Figure \[fig:heatmap\] shows one example of our search. The signal is generated using a BBH with ${\cal M}_c=8.7\,M_\odot$, $q=0.7$, and a hydrodynamical timescale of $\tau_{\rm gas}=10^3$ years. 