Two-dimensional block implementation of symmetric half-plane recursive digital filters

Two-dimensional (2-D) block implementation of 2-D symmetric half-plane (SHP) recursive filters is considered. A 2-D block-recursive equation is first derived. It is found that all the coefficient matrices associated with the input and previous output blocks are Toeplitz in their submatrices. Therefore, high-speed convolution algorithms can be utilized to perform the associated submatrix-vector multiplications. The block implementation using the fast Fourier transform is compared to the direct implementation as regards computational requirements.<
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