An equivalence relationship between convolution block filters and state block filters is established. The single-output basis filter for each convolution block filter is found. It is shown that the average round-off noise variance at the output of all block filters is inversely proportional to the block length. A sufficient condition on the block length is found that guarantees complete suppression of the limit cycles in the block filter. A minimum output noise variance block structure is found that, when compared to its single variate counterpart, has a lower output noise variance and is not as computationally complex to implement.