  Numerical relativists can now produce gravitational waveforms with memory
effects routinely and accurately. The gravitational-wave memory effect contains
very low-frequency components, including a persistent offset. The presence of
these components violates basic assumptions about time-shift behavior
underpinning standard data-analysis techniques in gravitational-wave astronomy.
This poses a challenge to the analysis of waveform spectra: How to preserve the
low-frequency characteristics when transforming a time-domain waveform to the
frequency domain. To tackle this challenge, we revisit the preprocessing
procedures applied to the waveforms that contain memory effects. We find
inconsistency between the zero-frequency limit of displacement memory and the
low- frequency spectrum of the same memory preprocessed using the common scheme
in literature. To resolve the inconsistency, we propose a new robust
preprocessing scheme that produces the spectra of memory waveforms more
faithfully. Using this new scheme, we inspect several characteristics of the
spectrum of a memory waveform. In particular, we find a discernible beating
pattern formed by the dominant oscillatory mode and the displacement memory.
This pattern is absent in the spectrum of a waveform without memory. The
difference between the memory and no-memory waveforms is too small to be
observed by current-generation detectors in a single binary-black-hole event.
Detecting the memory in a single event is likely to occur in the era of
next-generation detectors.
