Transform-based block implementation of digital filters is useful for high throughput filtering due to inherent parallelism and complexity reduction provided by using the fast transforms. In basic form, for example the overlap-save implementation, the block digital filter (BDF) is represented by a vector. In this paper, the basic form of block filtering and the optimal design of BDF are described. Therefore, we propose a generalization of the block digital filtering where the BDF is represented by a matrix. This generalized form and its corresponding optimal BDF design are developed. The generalized BDF allows reducing the global distortion of the block filtering.