  The high planetary multiplicity revealed by Kepler implies that Transit Time
Variations (TTVs) are intrinsically common. The usual procedure for detecting
these TTVs is biased to long-period, deep transit planets whereas most
transiting planets have short periods and shallow transits. Here we introduce
the Spectral Approach to TTVs technique that allows expanding the TTVs catalog
towards lower TTV amplitude, shorter orbital period, and shallower transit
depth. In the Spectral Approach we assume that a sinusoidal TTV exists in the
data and then calculate the improvement to $\chi^2$ this model allows over that
of linear ephemeris model. This enables detection of TTVs even in cases where
the transits are too shallow so individual transits cannot be timed. The
Spectral Approach is more sensitive due to the reduced number of free
parameters in its model. Using the Spectral Approach, we: (a) detect 131 new
periodic TTVs in Kepler data (an increase of ~2/3 over a previous TTV catalog);
(b) Constrain the TTV periods of 34 long-period TTVs and reduce amplitude
errors of known TTVs; (c) Identify cases of multi-periodic TTVs, for which
absolute planetary mass determination may be possible. We further extend our
analysis by using perturbation theory assuming small TTV amplitude at the
detection stage, which greatly speeds up our detection (to a level of few
seconds per star). Our extended TTVs sample shows no deficit of short period or
low amplitude transits, in contrast to previous surveys in which the detection
schemes were significantly biased against such systems.
