Digital mixing requires ‘scaling’ each of two digital signals and then adding them. A and B represent the two TV signals and K the positional coefficient or value at any point of the mix between them (i.e. equivalent to the position of the transition arm on a switcher desk). In a digital system, K will also be a number, assumed here as 10-bit resolution to provide a smooth mix or dissolve.
Mathematically this can be shown as:
A x K = (Mix)1
B x (1-K) = (Mix)2
Result = (Mix)1 + (Mix)2
Note that such math also applies to soft-edge keys and any transparency created between two images. As such it is a fundamental part of video processing and good quality results are essential.
When two 10-bit numbers are multiplied together, the result is a 20-bit number (see Binary). When mixing, it is important to add the two 20-bit numbers to obtain an accurate result. This result must then be truncated or rounded to 10 bits for transmission to other parts of the digital system.
Truncation by simply dropping the lower bits of the partial result (Mix)1 or (Mix)2, to 12 bits, or even 14 bits, will introduce inaccuracies. Hence it is important that all partial results, e.g. (Mix)1 and (Mix)2, maintain 20-bit resolution. The final rounding of the result to 10 bits can reveal visible 1-bit artifacts – but these can be avoided with careful rounding techniques such as Dynamic Rounding.