This paper presents a new approach to identify the respiratory phases of heart cycles from acceleration signals (i.e., seismocardiogram) recorded from the sternum, in back to front direction. The acceleration signals were recorded simultaneously with a single lead electrocardiogram (ECG), and the respiratory signal (using a chest band strain gauge) from 20 healthy subjects. Two accelerometer-derived respiration (ADR) signals were computed by computing the lower and upper envelope of the accelerometer signal. In the proposed methodology, for each subject a metric so-called, the piecewise total harmonic distortion (THD) was used to identify which one of lower and upper envelopes is the best ADR for detecting respiratory phases. The accuracy of piecewise THD in the selection of the correct envelope of SCG signal as an estimation of ADR is 84.6%. Consequently, respiratory phases of heart cycles were identified using the estimated ADR signals. Results confirm that the proposed envelope detection based ADR technique can detect respiratory phases of heartbeats with the accuracy of above 75%. In other words, using aforementioned methods, THD thresholding and piecewise THD, the capability of ADR signal to detect respiratory phases is increased approximately 14% compared to the lower envelope of the accelerometer (ADRLower) and 4% compared to the upper envelope of accelerometer signal (ADRUpper).