Algorithms and systolic architectures for multidimensional adaptive filtering via McClellan transformations

Algorithms are developed simultaneously with systolic architectures for multidimensional adaptive filtering Because of the extremely high data rate required for real-time video processing, there is a strong motivation to limit the size of any adaptation problem. Combining the McClellan transformations with systolic arrays to adapt and implement the least-squares filter yields a novel solution to the problem of adapting a large zero-phase finite impulse response (FIR) multidimensional filter, having arbitrary directional biases, with only a few parameters. These filters can be adapted abruptly on a block-by-block basis without causing blocking effects. After developing a basic processing element for a systolic array realization of the Chebyshev structure for the McClellan transformation, it is shown that for a given 2-D transformation function, the adaptation of the 1-D prototype filter becomes a small multichannel adaptation problem similar to adaptive array problems. A similar approach is also taken in developing algorithms to adapt the 2-D transformation function