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Describes a noise-resistant pulse oximetry algorithm suited to both signal reconstruction and oxygen saturation estimation. The algorithm first detects relatively clean signal sections from which the heart rate is estimated. The heart rate is used to construct a synthetic reference signal that matches an idealized pulse signal. An adaptive filter continuously processes the sensor signals, reconstructing signals in a linear subspace defined by the reference signal. A projective subspace algorithm is then applied to find the oxygenation level of the blood. The authors show that under specific circumstances this algorithm solves the sufficiency condition for signal reconstruction in linear saturation estimators. The core principle of using a frequency modulated synthetic reference signal can be applied to adaptive filtering of other physiological signals controlled by the heartbeat, such as blood pressure and electrocardiogram.