  We propose two frequency-domain filters to analyze ringdown signals of binary
black hole mergers. The first rational filter is constructed based on a set of
(arbitrary) quasi-normal modes (QNMs) of the remnant black holes, whereas the
second full filter comes from the transmissivity of the remnant black holes.
The two filters can remove corresponding QNMs from original time-domain
ringdowns, while changing early inspiral signals in a trivial way - merely a
time and phase shift. After filtering out dominant QNMs, we can visualize the
existence of various subdominant effects. For example, by applying our filters
to a GW150914-like numerical relativity (NR) waveform, we find second-order
effects in the (l = 4, m = 4), (l = 5, m = 4) and (l = 5, m = 5) harmonics; the
spherical-spheroidal mixing mode in the (l = 2,m = 2) harmonic; and a mixing
mode in the (l = 2,m = 1) harmonic due to a gravitational recoil. In another NR
simulation where two component spins are anti-aligned with the orbital angular
momentum, we also find retrograde modes. The filters are sensitive to the
remnant properties (i.e., mass and spin) and thus have a potential application
to future data analyses and parameter estimations. We also investigate the
stability of the full filter. Its connection to the instability of QNM spectra
is discussed.
