This work deals with the mathematical formulation and hardware implementation of computing methods for the action of one and two-dimensional operators on discrete, finite length signals representing real time synthetic aperture radar (SAR) image formation data. We give emphasis to modular and scalable computing methods. The complex Hilbert spaces ) ( 2 N Z l and 2 ( ) R S l Z Z × are used to represent signals of very large size. These spaces are converted into algebras using circular convolution and cyclic Hadamard signal operations. The operators themselves are also represented as being part of matrix algebras for computational studies and algorithm development. Special attention is given to unitary operators, such as the discrete Fourier transform (DFT), and to finite impulse response (FIR) operators. For FIR operators, we concentrate on the study of properties of convolutional algebras and present new mathematical formulations of filtering theories.

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