1. Introduction
2. The TFAW Algorithm
2.1. TFA Basics and Formulation
2.2. The Discrete Wavelet Transform and the Stationary Wavelet Transform
2.3. Wavelet Power Spectrum
2.4. TFAW: Application of the SWT
2.5. Outlier Removal Using the SWT
2.6. Signal and Noise Level Choice Criteria
2.7. Mother Wavelet Selection Criteria
3. TFAW Performance
3.1. TFAW vs TFA Transit Detection Efficiency
3.2. TFAW vs TFA Signal Reconstruction
3.3. Application to Multi-Periodic Signals
3.4. Wavelet Versus Bin Average Signal Approximation
3.5. Comparison of TFA and TFAW Transit Parameters Fit Values and Uncertainties
4. Application to Real Survey Light Curves
4.1. The Telescope Fabra-ROA at Montsec
4.2. TFAW Real Light Curve Quantitative Performance
5. Conclusions