Fig. 3.

Relationship between low- and high-pass filters in the time domain. A: in response to a step input (gray line), an HPF responds (thick black line) with an initial step, followed by an exponential decay with a time constant of 1 s. B: since an integrator followed by an HPF is equivalent to a low-pass filter (LPF), we show that an LPF responds (thick black line) to a step input (gray) with an exponential rise with a time constant of 1 s. C: when an HPF is combined with a leaky integrator with a time constant of 30 s, a leaky LPF (thick dashed black line) results. It has a response that differs little from the LPF (thick black solid line) for the first second or two.