In this manuscript we present an overview of novel signal processing techniques developed by our group to reduce scoring time in the assessment of the severity of sleep-related breathing disorders in heart failure patients and to detect sleep/wake fluctuations during periodic breathing. Besides describing these methods, we present the results of validation experiments. Our work shows that novel signal processing techniques can reduce costs and resources needed to screen the patients and can provide relevant information for better understanding the role of wake/sleep transitions in the development and maintenance of breathing disorders.