This paper presents the design and implementation of the QPSK demodulator using digital signal processing techniques. The QPSK demodulator is designed and implemented using two different approaches. In the first approach, digital filters are used for implementing the demodulator.  In the second approach, the DFT is used for implementing the demodulator. The first approach is performed using digital low-pass filters, Costas loop, and NCO.  In the second approach, the DFT is used in development of the QPSK demodulator by computing the spectrum of the coming modulated signal and finding the maximum peak of the spectrum as it is used to determine the carrier frequency and its phase. The data bits are then determined from the phase of the carrier. Both approaches are implemented using python software and raspberry pi processor for to be used as embedded system and also as experimentation. Both design methods are tested and verified through simulation experiments.