To improve applicability of automatic sleep staging an efficient subjectindependent method is proposed with application in sleep-wake detection and in multiclass sleep staging (awake, non-rapid eye movement (NREM) sleep and rapid eye movement (REM) sleep). In turn, NREM is further divided into three stages denoted here by N1, N2, and N3. To assess the method, polysomnographic (PSG) records of 40 patients from our ISRUC-Sleep dataset, which was scored by an expert clinician in the central hospital of Coimbra, are used. To find the best combination of PSG signals for automatic sleep staging, six electroencephalographic (EEG), two electrooculographic (EOG), and one electromyographic (EMG) channels are analyzed. An extensive set of feature extraction techniques are applied, covering temporal, frequency and timefrequency domains. The maximum overlap wavelet transform (MODWT), a shift invariant transform, was used to extract the features in time-frequency domain. The extracted feature set is transformed and normalized to reduce the effect of extreme values of features. The most discriminative features are selected through a two-step method composed by a manual selection step based on features' histogram analysis followed by an automatic feature selector. The selected feature set is classified using support vector machines (SVMs). The system achieved the best performance by combining 6 channels (C3, C4, O1, left EOG (LOC), right EOG (ROC) and chin EMG (X1)) for sleep-wake detection, and 9 channels (C3, C4, O1, O2, F3, F4, LOC, ROC, X1) for multiclass sleep staging.