Apnea of prematurity is an important and common clinical problem, and is often the rate-limiting process in NICU discharge. Accurate detection of episodes of clinically important neonatal apnea using existing chest impedance (CI) monitoring is a clinical imperative. The technique relies on changes in impedance as the lungs fill with air, a high impedance substance. A potential confounder, however, is blood coursing through the heart. Thus, the cardiac signal during apnea might be mistaken for breathing. We report here a new filter to remove the cardiac signal from the CI that employs a novel resampling technique optimally suited to remove the heart rate signal, allowing improved apnea detection. We also develop an apnea detection method that employs the CI after cardiac filtering. The method has been applied to a large database of physiological signals, and we prove that, compared to the presently used monitors, the new method gives substantial improvement in apnea detection.