Phase measurement techniques are required in many applications like direction finding and crack detection in metals. This thesis concentrates on the use of Digital Signal Processing (DSP) algorithms and tools to achieve the phase extraction and measurement. Both frequency and time domain techniques are tested. The thesis covers both of them starting from theory, passing through the algorithms development and ending with testing them using simulation tools. Specifically, the MATLAB tools have been used to test the techniques using different sampling frequencies, carrier frequencies, signal-to-noise ratios (SNR), decimation factors, and under the quantization effect of 16 – bit quantizer. The signals under tests were Phase Sift Keying (PSK) modulated. The idea is to orient the developed techniques to be implemented toward the Direction Finding (DF) applications. The percentage error criterion which was used to evaluate the obtained results in this work reflects a fact that the obtained results are in close agreement with the true one.