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It's the instantaneous time domain changes that determine the pattern on screen. You can have more than 3 different video frequencies in effect on a segment of a line of video and the phase relationship of those video frequencies determine where on the line they add to and or subtract from each other and the nature and position of the pattern they make.
The side bands don't exactly describe the just the signal. If you modulate one sine wave with another regardless of the modulation scheme you get the main sidebands and an infinite series of harmonics at multiples of the carrier. You also get additional harmonics from non-linearities in all non-ideal (read that real world) modulators. (Ever been close to a radio tower and gotten the station on multiple places on the dial? Those are harmonics.) So there can be things in a spectrum analyzer view of a sideband that are more incidental energy than desired ideal signal.
The passband of a signal chain tells you what frequencies will be let through, but not whether in actual video they're intended or unintended to be in the picture. Without the precise phase timing duration and the rate of rise and fall of the different video frequency elements you could get a variety of patterns and images from the same sideband pattern you see from a line or frame duration sideband spectrum sample.
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