The Temporal Sampling Framework (TSF) theorizes that the characteristic phonological difficulties of dyslexia are caused by an atypical oscillatory sampling at one or more temporal rates. The LEEDUCA study conducted a series of Electroencephalography (EEG) experiments on children listening to amplitude modulated (AM) noise with slow-rythmic prosodic (0.5-1 Hz), syllabic (4-8 Hz) or the phoneme (12-40 Hz) rates, aimed at detecting differences in perception of oscillatory sampling that could be associated with dyslexia. The purpose of this work is to check whether these differences exist and how they are related to children's performance in different language and cognitive tasks commonly used to detect dyslexia. To this purpose, temporal and spectral inter-channel EEG connectivity was estimated, and a denoising autoencoder (DAE) was trained to learn a low-dimensional representation of the connectivity matrices. This representation was studied via correlation and classification analysis, which revealed ability in detecting dyslexic subjects with an accuracy higher than 0.8, and balanced accuracy around 0.7. Some features of the DAE representation were significantly correlated ($p<0.005$) with children's performance in language and cognitive tasks of the phonological hypothesis category such as phonological awareness and rapid symbolic naming, as well as reading efficiency and reading comprehension. Finally, a deeper analysis of the adjacency matrix revealed a reduced bilateral connection between electrodes of the temporal lobe (roughly the primary auditory cortex) in DD subjects, as well as an increased connectivity of the F7 electrode, placed roughly on Broca's area. These results pave the way for a complementary assessment of dyslexia using more objective methodologies such as EEG.