In this paper, we present an algorithm to identify umbilical and uterine arteries from a set of four different maternal and fetal arteries using their Doppler signatures. To distinguish these arteries, we use 132 Doppler signals collected from pregnant women with gestational ages between 24 to 40 weeks. Initially we filter them to remove noise; spectrograms are generated to extract good cycles, which are then analyzed to derive independent features that could uniquely represent an artery. A non-linear classification technique using k-NN (k-nearest neighbor) classifier is further applied to identify umbilical and uterine arteries. The proposed algorithm achieves sensitivity and specificity of above 95% and 97% for identification of uterine artery and above 63% and 80% for umbilical artery.