We present a method for efficiently searching long-duration gravitational wave signals from compact binary coalescences (CBCs). The approach exploits the smooth frequency-domain behavior of ratios between neighboring waveform templates. The matched-filter signal-to-noise ratio (SNR) time series of a data segment is first computed for a reference template, and the SNRs of nearby templates are then reconstructed by convolving this reference SNR time series with the ratio waveforms, defined as the frequency-domain ratios between the reference and neighboring templates. The computational speedup arises because the ratio waveforms can be safely truncated: they are significant only over a short interval approximately equal to the duration difference between the templates. Storing these truncated ratio waveforms is practical and enables additional efficiency gains, in contrast to storing full templates, which is generally infeasible for long-duration low-mass signals. We demonstrate the efficacy of the method with mock nonspinning CBC injections in the $1-3M_{\odot }$ range. The reconstructed SNR time series agrees with that obtained from standard matched filtering to an accuracy of $\mathcal{O}({10}^{-4})$, while the relative computational cost is reduced by $\gtrsim 25\%$. With a truncation threshold of ${10}^{-3}$ applied to the ratio waveform amplitudes, the storage requirement is reduced by a factor of $\sim 60$ relative to storing the full template bank.

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• Gravitational waves