The growing importance of data analytics in biomedicine is increasingly becoming recognized in biomedical engineering curricula through the introduction of machine learning classes that generally run in parallel to, but separately from, more traditional engineering courses, such as signal and systems analysis. We propose a new approach that systematically integrates signal processing and systems analysis with key techniques in machine learning. In the proposed course, the student obtains hands-on experience in applying algorithms that can be applied to practical problems of physiological signal conditioning, analysis and interpretation. This is achieved by exposing the student to a sequence of 4 applications-based modules that represent different biomedical engineering problems: human activity recognition from wearable devices, epileptic seizure detection, quantification of dynamic respiratory-cardiac coupling in humans under different conditions, and detection of sleep apnea episodes from heart rate variability data. Within each module, the student gains the experience of working with the data in question "from the ground up". We also introduce a general plan for assessment of student learning, and discuss the expected outcomes and limitations of this integrative approach to teaching.Clinical Relevance- The proposed course is targeted at biomedical engineering students at the senior undergraduate or first-year graduate level who are interested in learning how to analyze physiological signals. The course would also be suitable for clinician-scientists who have prior training in statistics with some exposure to engineering mathematics.