  There have been many efforts to correct systematic effects in astronomical
light curves to improve the detection and characterization of planetary
transits and astrophysical variability. Algorithms like the Trend Filtering
Algorithm (TFA) use simultaneously-observed stars to remove systematic effects,
and binning is used to reduce high-frequency random noise. We present TFAW, a
wavelet-based modified version of TFA. TFAW aims to increase the periodic
signal detection and to return a detrended and denoised signal without
modifying its intrinsic characteristics. We modify TFA's frequency analysis
step adding a Stationary Wavelet Transform filter to perform an initial noise
and outlier removal and increase the detection of variable signals. A wavelet
filter is added to TFA's signal reconstruction to perform an adaptive
characterization of the noise- and trend-free signal and the noise contribution
at each iteration while preserving astrophysical signals. We carried out tests
over simulated sinusoidal and transit-like signals to assess the effectiveness
of the method and applied TFAW to real light curves from TFRM. We also studied
TFAW's application to simulated multiperiodic signals, improving their
characterization. TFAW improves the signal detection rate by increasing the
signal detection efficiency (SDE) up to a factor ~2.5x for low SNR light
curves. For simulated transits, the transit detection rate improves by a factor
~2-5x in the low-SNR regime compared to TFA. TFAW signal approximation performs
up to a factor ~2x better than bin averaging for planetary transits. The
standard deviations of simulated and real TFAW light curves are ~40x better
than TFA. TFAW yields better MCMC posterior distributions and returns lower
uncertainties, less biased transit parameters and narrower (~10x) credibility
intervals for simulated transits. We present a newly-discovered variable star
from TFRM.
