We review Fourier-domain methods for demosaicking Bayer-filter color cameras and monochrome polarization cameras, and then generalize the approach for the quad-Bayer-filter mosaic and for color-polarization cameras. For each of these four mosaic filter types, we provide theoretical expressions for the sampling functions, the Fourier-domain channels, and the linear combination of reconstructed channels (the demosaicking algorithm) needed to estimate the input (presampled) image. A useful advantage of the Fourier-domain approach is that it provides a direct means of visualizing and quantifying when aliasing is likely or unlikely to be present. For the Bayer and quad-Bayer-filter types, we provide simulated images, while for the polarization camera types we provide experimental images and videos to illustrate the algorithm and analyze crosstalk error.