Broadcast Video Color Space Equations

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I need a video engineer who is expert in the math of broadcast video color space, to provide a series of current color space equations (accepted standards) for use in video measurement equipment (vectorscope, waveform monitor etc). Equations will be used in a software application.

Equations to cover SD and HD broadcast standards. RGB, YCrCb, YUV, IRE, YPbPr cross conversions where applicable. Mention gamma considerations if applicable,

RGB to YUV, YUV to RGB, YCrCb to RGB, RGB to YCrCb, you get the idea. Must take into account values for white and black. In IRE case difference between 7.5 IR and 0 for example.

Waveform monitor equations to cover difference in luma and chroma when plotted in 7.5 and 0 IRE cases. We need to discuss to ensure clarity of the work..

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