This research presents a pulse-by-pulse analysis of Oscillometric blood pressure waveform at systolic, diastolic and mean arterial pressure points. Using a mathematical optimization technique, pulses are characterized into component harmonic by minimizing the least square error. The results at the important pressure points are analyzed and compared for different subject using different waveform extraction techniques. Blood pressure is estimated using the harmonic parameters. The approach studies changes in the parameters as oscillometric blood pressure recording is done. 8 harmonic parameters are obtained from the pulse characterization and are used to estimate Systolic arterial Blood Pressure, Mean arterial Blood Pressure, and Diastolic arterial Blood Pressure. The estimates are compared with our reference value to determine which has the best agreement. The proposed method is further compared with Maximum Amplitude Algorithm and Pulse Morphology Algorithm. The effect of oscillometric waveform extraction methods on the proposed method is observed. The experiment established the fact that the extraction technique can alter the shape of oscillometric pulses. The methods were compared and it was observed that the used extraction methods did not make any significant difference on the accuracy, using this technique.