In this thesis, we considered the deconvolution problem when the channel is known a priori. LSE and MSE optimum solutions are investigated with deterministic and statistical approaches. We derived closed form LSE expressions and investigated the factors that affect the FIR inverse filters. It turns out that, minimum LSE can be obtained when the system zeros are distributed homogeneously on the z-plane. We proposed partition-based FIR-IIR inverse filters. The selection of FIR and IIR parts is based on partitioning the channel zeros into two regions and using the specified channel zeros to design the best delay FIR and all pole IIR inverse filters. Three methods for partitioning are presented, namely unit circle-based, ring-based and optimum-partitioning. It turns out that ring-based and optimum-partitioning FIR-IIR inverse filter performs better than the best delay FIR inverse filter for the same complexity by about 4-5 dB. For noisy observations, it is shown that, noise should also be considered in the delay selection and partitioning. We extended our results for the design of MSE optimum statistical inverse filters. It is shown that best delay FIR-IIR inverse filters are less sensitive to the estimation errors compared to the IIR Wiener filters and they perform better than the FIR Wiener filters. Furthermore, they are always causal and stable making them suitable for real-time implementations. When the statistical and deterministic filters are compared, it is shown that for low SNR statistical filters perform better by about 1-2 dB, while deterministic filters perform better by about 0.5-1 dB for high SNR