Beyond FINDCHIRP: Breaking the memory wall and optimal FFTs for Gravitational-Wave Matched-Filter Searches with Ratio-Filter Dechirping

A primary bottleneck in modern FFT-based matched-filter searches for gravitational waves from compact binary coalescences is not raw processor throughput, but available memory bandwidth. Standard frequency-domain implementations, such as the FINDCHIRP algorithm, rely on streaming long template waveforms and data from main memory, which leads to significant processor stalling when template durations exceed cache capacities. In this work, we introduce \textit{Ratio-Filter Dechirping} as a solution, an algorithmic restructuring of the matched filter that transforms the operation from a memory-bound Fast Fourier Transform (FFT) into a cache-efficient, compute-bound Finite Impulse Response (FIR) convolution. By utilizing a reference template to remove common orbital phase evolution, we produce slowly changing frequency-domain ratios that can be accurately implemented as short FIR filters. This method delivers a measured speedup of $8\times$ for the core filtering loop used in offline searches and should enable $>10\times$ for low-latency analysis. We find that this approach generalizes to a variety of searches that include physical features such as finite size effects, eccentricity, and precession. By dramatically reducing the computational cost of matched filtering, this approach enables the expansion of searches into dense or high-dimensional parameter spaces, such as those for eccentric or subsolar-mass signals, that are already limited by available computing budgets. Furthermore, this framework provides a natural path for hardware acceleration on GPU architectures.