The data to create an HD signal runs about 1.5 Gbps (gigabits per second), too much for affordable VCRs to handle. Some method of compression is necessary to reduce the amount of data in a picture. As more compression is used, the VCR expense and tape expense both go down, but also image quality goes down. Since the whole point of high definition is sharp pictures, it behooves us to compress the data the least amount possible. The method of data compression commonly used by VCRs is DCT (Discrete Cosine Transform), a system that attempts to throw away picture detail that your eye wouldn't see anyway. Compression ratios below 5:1 show very little loss. Compression systems break down a bit when there is a high degree of motion or detail in the image; there is so much data that the system must throw away even more picture detail to stay within its design limitations. So already you can see that one can't describe picture sharpness as a static thing; it changes, depending upon the content of the picture.
DCT can be used for intraframe compression (reducing the data for each video frame independent of the others) or can be applied to interframe compression, where a group of video frames are compared to each other and redundant data tossed out. MPEG-2 is an example of this. MPEG can work at different levels. At its highest compression level, it could record one "real" frame (called an I frame) and manufacture seven other frames from it (called P and B frames) which contain only data about what changes occurred from frame to frame, not the data that creates the whole image itself. This high compression MPEG-2 would be used on home and office VCRs designed to record DTV broadcasts. For true production work, one must use the low compression MPEG-2 compression scheme that uses only I-frames (only "real" frames). Most VCRs use only DCT compression while others use MPEG-2, a subset of DCT. (Sony uses MPEG-2 on its Betacam-SX for HD).
It is hard to discuss picture resolution when compression is involved. One could sample an image many times, creating a lot of data to describe the image accurately, then compress the heck out of it to end up with a fuzzy, artifact-laden image. One the other hand, one could sample the image less, making an image with less data (which is theoretically fuzzier) then compress the image less, preserving the data, leaving it technically sharper than the case mentioned above. Thus, picture sharpness (and indeed cost) is a tradeoff between the number of pixels in an image (i.e. a camers's CCD chip) that determines the initial image sharpness, and the amount of compression necessary to squeeze the data onto the video tape.
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