The pulse oximeter's photoplethysmographic (PPG) signals, measure the local variations of blood volume in tissues, reflecting the peripheral pulse modulated by cardiac activity, respiration and other physiological effects. Therefore, PPG can be used to extract the vital cardiorespiratory signals like heart rate (HR), respiratory rate (RR) and respiratory activity (RA) and this will reduce the number of sensors connected to the patient's body for recording vital signs. In this paper, we propose an algorithm based on ensemble empirical mode decomposition with principal component analysis (EEMD-PCA) as a novel approach to estimate HR, RR and RA simultaneously from PPG signal. To examine the performance of the proposed algorithm, we used 45 epochs of PPG, electrocardiogram (ECG) and respiratory signal extracted from the MIMIC database (Physionet ATM data bank). The ECG and capnograph based respiratory signal were used as the ground truth and several metrics such as magnitude squared coherence (MSC), correlation coefficients (CC) and root mean square (RMS) error were used to compare the performance of EEMD-PCA algorithm with most of the existing methods in the literature. Results of EEMD-PCA based extraction of HR, RR and RA from PPG signal showed that the median RMS error (quartiles) obtained for RR was 0 (0, 0.89) breaths/min, for HR was 0.62 (0.56, 0.66) beats/min and for RA the average value of MSC and CC was 0.95 and 0.89 respectively. These results illustrated that the proposed EEMD-PCA approach is more accurate in estimating HR, RR and RA than other existing methods.