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In the post I'm quoted from (Panasonic HC-VXF1 Camcorder: HD Picture Resolution:) I said "fully optimised".
This does not mean that Full FHD from a 4K camera will look less sharper than from a FHD camera. I'd expect it to look sharper because a properly-operating AA filter blurs the image slightly, so that the high-res components of an image are reduced so as not to exceed the Nyquist frequency. Because, in ADC, sampling above the Nyquist frequency introduces false heterodynes ("aliases") that were not in the original image. The aliases take the form of moiré patterns. Anti-aliasing filter - Wikipedia
Since there's a CFA on top of the sensor, which would otherwise be colour-blind/monochromatic, these moiré patterns will have false colours. In the CFA, the element spacing of G-to-G is closer than for B-to-B and R-to-R. This, and the slightly longer wavelength of R light means that R suffers most from this colour aliasing.
There's been a craze in AA-less DSLRs. Theoretically you'd need a 130MP sensor for the spacing of the pixels to be close enough together not to require an AA filter aka OLPF (Optical Low-Pass Filter). But most 16MP & 24MP APS-C models have been AA-less for quite a while now due to marketing pressure. The lack of AA makes them subjectively appear sharper, but if you look closely at fine-detail portions of an image, like the palings in a distant picket fence, you can see the aliasing.
The design of the AA filter works best at a fixed distance between pixels/lines. Change the frame size, e.g switch between 4K & FHD, and the AA design is now sub-optimal. Whether you'll notice it will depend on what you're shooting.
Also, the quality of the lens in front of the sensor affects an AA imaging system's tendacy to moiré. The sharpness of the lens itself results in a slight optical blurring which can take the place of what the AA-filter does. That's why low MP (16/24MP) AA-less consumer DSLRs won't necessarily be plagued with moiré issues. You need "sharp glass" (a high-quality lens) to invoke it.
https://www.red.com/red-101/resolution-aliasing-motion-capture
RedShark News - How to understand video scaling and framerate conversion - part one
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