The objective of this thesis is the design of complex wave digital filters (CWDFs) using the pipelineable unitary (PU) algorithm. The advantages of this method are the following: (1) The PU structure can be used for both normalized and denormalized representations of complex adaptors used in the realization of complex wave digital filter with a constraint that denormalized form can not be used without multipliers. (2) The PU algorithm allows for the decomposition of high order digital filters into a cascaded connection of simple PU building blocks. The calculation of quantified coefficients is done using the Discrete Fourier Transform (DFT). At the end, discussion and comparison of frequency responses for each type of realized CWDF has been provided with regard to one another and also with regard to the nominal frequency response of each of these CWDFs. It has been observed that filter design using PU algorithm with the two-port cross adaptor gave better results then two-port adaptor realization used in (4). Also, this type of adaptor has only one coefficient to work with, namely $\beta$ and $\beta\sp*$ which differ only by the sign of the real part.