To quantify and differentiate control and insomnia sleep onset patterns through biomedical signal processing of overnight polysomnograms.The approach consisted of three tandem modules: 1) biosignal processing module, which used state-space time-varying autoregressive moving average (TVARMA) processes with recursive particle filter, 2) hypnogram generation module that implemented a fuzzy inference system (FIS), and 3) insomnia characterization module that discriminated between control and subjects with insomnia using a logistic regression model trained with a set of similarity measures ( d1, d2 , d3, d4). The study employed sleep onset periods from 16 control and 16 subjects with insomnia.State-spaced TVARMA processes with recursive particle filtering provided resilience to nonlinear, nonstationary, and non-Gaussian conditions of biosignals. FIS managed automated sleep scoring robust to intersubjects' and interraters' variability. The similarity distances quantified in a scalar measure the transitions amongst sleep onset stages, computed from expert and automated hypnograms. A statistical set of unpaired two-tailed t -tests suggested that distances d1 , d2, and d3 had larger statistical significance ( ) to characterize sleeping patterns. The logistic regression model classified control and subjects with insomnia with sensitivity 87 % , specificity 75 %, and accuracy 81 %.Our approach can perform a supportive role in either biosignal processing, sleep staging, insomnia characterization, or all the previous, coping with time-consuming procedures and massive data volumes of standard protocols.The introduction of graph spectral theory and logistic regression for the diagnosis of insomnia represents a novel concept, attempting to describe complex sleep dynamics throughout transitions networks and scalar measures.