The development of Internet of Healthcare Things (IoHT) technology leads to high upgrades in monitor signal systems concerning healthcare. Battery life-saving is one of the biggest issues facing healthcare monitoring signal systems. The most important approach to achieve this goal is to decrease the signal size (i.e., data or signal compression); thus, we need to make data compression. In this study, we introduced a novel approach to decrease the size of the transmitted Phonocardiography (FPCG) bio-medical signal by a set of Fractional Order Chebychev Discrete Orthogonal Moments with the Modified Gram-Schmidt Method (FrCMs- MGSM). The efficiency of the proposed approach has been estimated over a benchmark dataset called Fetal PCG, using many sound metrics: QS, CR, SNR, PRD, and PSNR. The efficiency of the proposed approach was evident when compared to recently published approaches. The empirical findings show that the suggested strategy is highly effective regarding compression time (0.99) and computing efficiency (37.64). The outcomes also demonstrate a (4388 ms) reduction in wearable device wake-up time. Thanks to the suggested compression algorithm, which significantly reduces energy consumption.