The primary risk factor of hypertension, is the lack of awareness caused by the unavailability of ubiquitous blood pressure (BP) measurement. In this study, we have investigated the BP estimation using the photoplethysmogram (PPG) signal and a suitable subject-specific mathematical model. The linear transfer function (LTF) technique was used to identify the subject-specific model. Firstly, we tried to identify the model considering arterial blood pressure (ABP) as input and PPG as output, and we achieved an average estimation accuracy (normalized root mean square, NRMSE) of 84.4%. Next, we fitted an inverse model, where ABP is the output, and PPG is the input, and we achieved an average estimation accuracy (NRMSE) of 84.7%. Finallly, We verified that the two identified models mentioned above are inverse of each other. In this study, we have used ABP and PPG signals of 10 (male = 7, female = 3) subjets from the MIMIC II database. The results are quite promising for the use of the PPG in the detection and diagnosis of cardiovascular diseases.