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A joint source-channel coding system based on linear multirate filter banks is optimized with respect to minimum block mean squared error, while constraining the channel power. A more general discrete-time block based multiple-input multiple-output system is first optimized. From this system analysis and synthesis filter banks solving the joint source-channel coding problem are derived. A joint optimal transmitter and receiver filter bank system is found. Illustrative examples showing the system performance as well as filter transfer functions are given. The performance results are compared to the optimal performance theoretical attainable curves.