Butterworth filtering to minimize various frequency components within luciferase fluctuations. (a) Raw luminescence data from tim-luc;cry+ antennae. (b) Result of applying a low pass filter to remove periodicities < 4 hours from the timecourse shown in (a), resulting in the smoother-appearing timecourse shown in (b). (c) Result of applying a high-pass filter to these data to remove periodicities > 72 hours, such that relatively high-frequency fluctuations remain. Note that the high pass removes the decreasing-slope trend (cf. Figure 4). (d) Result of applying a 72-hour low pass filter to highlight the overall temporal trend in these data, by virtue of removal in this case of nonlinear components (see text).