This paper presents a transceiver model that comprises two time-interleaved analog-to-digital (A/D) converter systems to sample the inphase and quadrature signals in a digital receiver. Random data is used as the information signal and quadrature modulation is employed as the modulation scheme. A polyphase filter bank is derived as a representation of the time-interleaved A/D converter system, thereby modelling its converter mismatch. Furthermore, filter bank theory is used to design reconstruction filters that mitigate aliasing and distortion and achieve matched filtering in a single post-processing scheme, therefore reducing the digital implementation complexity of the receiver. Simulations results are presented to illustrate the performance degradation due the usage of non-ideal A/D converters and to verify the propose reconstruction scheme. Finally, an analysis of the required synthesis filter complexity is presented for different error magnitudes as a guideline for the filter bank design.