The main objective of the work described in this paper is to develop an algorithm to detect the start and the end of sleep stage of 10 year old children and to compute the frequency domain heart rate variability (HRV) before and after wake up. These measures are low frequency (LF), high frequency (HF) and the ratio of LF/HF (LF/HF). These measures are used to compare between normal and intrauterine growth restricted children (IUGR) at the age of 10 (IUGR are believed to be more prone to heart diseases in adulthood). Another comparison in this work is between boys and girls. The one hour analysis before and after wake up showed that IUGR children have higher frequency domain measures before and after wake up. Girls showed significantly higher values of LF/HF ratio than the boys. These significant differences between IUGR and normal might suggest underdevelopment or deficiency in the autonomic nervous system in IUGR.