Synthetic aperture radar (SAR) imaging technologies are increasingly finding applications in the geosciences and are becoming instrumental in enhancing the fundamental understanding of the physical processes pertaining to the earth and the environment. Of particular importance are studies conducted about the earth surface property characteristics using SAR remote sensing techniques. These studies are relevant for the better understanding of concepts such as soil moisture content, backscattering from crops, nearshore ocean surface currents, and subsurface imaging in hyperarid regions. In this work, impulse response or point spread functions are used as ambiguity functions in the efficient computation of raw data generation operations and efficient filtering techniques are presented for imaging kernel operations. The efficiency in these operations is obtained through the use of Kronecker products algebra as a basis for the mathematical formulation of multidimensional fast Fourier transform algorithms.