An oversampling pulse oximeter includes an analog to digital converter with a sampling rate sufficient to take multiple samples per source cycle. In one embodiment, a pulse oximeter (100) includes two or more light sources (102) driven by light source drives (104) in response to drive signals from a digital signal processing unit (116). The source drives (104) may drive the sources (102) to produce a frequency division multiplex signal. The optical signals transmitted by the light sources (102) are transmitted through a patient's appendage (103) and impinge on a detector (106). The detector (106) provides an analog current signal representative of the received optical signals. An amplifier circuit (110) converts the analog current signal to an analog voltage signal in addition to performing a number of other functions. The amplifier circuit (110) outputs an analog voltage signal which is representative of the optical signals from the sources (102). This analog voltage signal is received by a fast A/D converter (112) which samples the analog voltage signal to generate a digital voltage signal which can be processed by the digital signal processing unit (116). The fast A/D converter (112) operates at a rate sufficient to take multiple samples per source cycle and may have a sampling frequency, for example, of over 41 kHz. The digital signal processing unit (116) implements software for averaging the samples over a source cycle for improved measurement consistency, improved signal to noise ratio and reduced A/D converter word length.