Changes in the vocal folds due to aging may change the pitch of the voice. An elderly signal can be automatically distinguished from a normal signal through various analyses. With most smart biomedical devices, elderly voices have been neglected due to optimization that does not take the elderly into account. The objective of this study was to use a symmetric higher-order differential energy function to analyze the elderly signal and extract the fundamental frequency. This study suggests a symmetric higher-order differential energy function based on gender analysis. The elderly voices of 40 Korean subjects (20 females and 20 males) ranging in age from 70-80 years were used. Symmetrical instantaneous frequency estimators with orders 5 and 4 were selected for female and male voices, respectively in this study through gender analysis. The experiments were compared to the F0 extracted by various methods such as manual extraction, WaveSurfer, TF32, Praat and an instantaneous frequency estimator based on before-and-after gender analysis. The F0 value obtained through the instantaneous frequency estimator after gender analysis is the most similar to the results from manual extraction, exhibiting an accuracy of 80%. The results will help to provide ease of access for the elderly by means of speech. Future investigations will incorporate multiple analytical methods to implement more reliable detectors for automated medical diagnostic systems.