This paper examines the application of two pipeline methods, conventional and wave pipeline, to improve a Kalman-filter-based architecture specialized for signal reconstruction. A few algorithmic and architectural specifications induced by such a specific application are considered and a new architecture, based on a previously developed systolic architecture and using the wave pipeline method, is proposed. Changes on the architecture result from the analysis of path lengths, latency and throughput with regard to pipeline design. The performance of the wave pipelined systolic architecture is validated by comparison with conventional pipelined technique and Motorola's general-purpose DSP56001 digital signal. Applications of these systolic architectures are possible in a wide variety of fields such as channel equalization, telecommunications, metrology, biomedical engineering, seismology and spectrometry.