Discrete Version of Richard’s Theorem and Applications to Cascaded Lattice Realization of Digital Filter Transfer Matrices and Functions
نویسنده
چکیده
The well-known Richards’ Theorem of the continuous-time filter theory is reformulated in the digital domain in a convenient manner, leading to a simple derivation of cascaded lattice digital filter structures, realizing lossless bounded transfer functions. The theorem is also extended to the matrix case, leading to a derivation of m-input p-output cascaded lattice filter structures with lossless building blocks, that realize an arbitrary p x M digital Lossless Bounded Real (LBR) transfer matrix. Extensions to the synthesis of arbitrary, stable p X m transfer matrices in the form of such cascaded lattices is also outlined. The derivation also places in evidence a means of testing the stability of an arbitrary p X m transfer matrix of a discrete-time linear system.
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