improves readout fidelity. A common baseline for dispersive readout uses a boxcar averager to compute a uniformly weighted average over a fixed window, followed by threshold-based state assignment. In this paper, we evaluated an adaptive finite-impulse-response (FIR) filter trained in real time using the least-mean-squares (LMS) algorithm on a field-programmable gate array (FPGA) quantum controller. We also analyzed measured readout shots offline to compare the frozen filter with boxcar averaging and to evaluate per-sample weighting and sequential detection. For the fixed FIR filters tested, we show summing the filtered samples gives the boxcar sum multiplied by one complex number, apart from a small edge correction. We call this the kernel collapse. The multiplication scales the state separation and noise equally without improving state discrimination, and we call this the boxcar limit. The frozen LMS filter reduces trace noise, but same-shot offline comparisons show no resolved improvement in readout fidelity at the tested operating points. On a 2D transmon, tuning the integration window accounts for much of the observed improvement over full-window integration, highlighting the importance of an optimized boxcar baseline when evaluating per-sample weighting. We then examine how changing the decision method can reduce calibration effort and decision time. On a higher-fidelity 3D ancilla readout, model-based template estimation reaches the same fidelity target as direct averaging with about 30 rather than 300 labeled shots per state. Offline sequential replay assigns most shots before the acquisition window ends, with contrast fidelity within an absolute +/-0.5% tolerance of the boxcar on the primary…