We present a new methodology to detect and characterize sleep spindles (SSs), based on the nonlinear algorithms, empirical-mode decomposition, and Hilbert-Huang transform, which provide adequate temporal and frequency resolutions in the electroencephalographic analysis. In addition, the application of fuzzy logic allows to emulate expert's procedures. Additionally, we built a database of 56 all-night polysomnographic recordings from children for training and testing, which is among the largest annotated databases published on the subject. The database was split into training (27 recordings), validation (10 recordings), and testing (19 recordings) datasets. The SS events were marked by sleep experts using visual inspection, and these marks were used as golden standard. The overall SS detection performance on the testing dataset of continuous all-night sleep recordings was 88.2% sensitivity, 89.7% specificity, and 11.9% false-positive (FP) rate. Considering only non-REM sleep stage 2, the results showed 92.2% sensitivity, 90.1% specificity, and 8.9% FP rate. In general, our system presents enhanced results when compared with most systems found in the literature, thus improving SS detection precision significantly without the need of hypnogram information.