Starting from basic signals expressions, the rigorous formulation of frequency domain convolution is demonstrated, in general and impulse terms, including antenna patterns and squint angle. The major differences with conventional algorithms are discussed and theoretical concepts clarified. In a second part, the philosophy of advanced SAR algorithms is compared with that of a SCANSAR observation (several subswaths). It is proved that a general impulse response can always be written as the product of three factors, i.e., a phasor, an antenna coefficient, and a migration expression, and that the details of antenna effects can be ignored in the usual SAR system, but not the range migration (the situation is reversed in a SCANSAR reconstruction scheme). In a next step, some possible inverse filter kernels (the matched filter, the true inverse filter, ...) for general SAR or SCANSAR mode reconstructions, are compared. By adopting a noise corrupted model of data, we get the corresponding Wiener filter, the major interest of which is to avoid all divergence risk. Afterwards, the vocable `a class of filter' is introduced and summarized by a parametric formulation. Lastly, the homogeneity of the reconstruction, with a noncyclic fast Fourier transform deconvolution is studied by comparing peak responses according to the burst location. The more homogeneous sensitivity of the Wiener filter, with a stepper fall when the target begins to go outside the antenna pattern, is confirmed. A linear optimal merging of adjacent looks (in azimuth) minimizing the rms noise is also presented, as well as consideration about squint ambiguity.