CPP100
SECTION 9
CPP1OPS
25/10/06
www.snellwilcox.com
Version 1 Issue 6
9.2
Recursive Filtering cont.
If current input is denoted as input (n) , subsequent input frames are described as input (n+1), input (n+2) etc..
OP1 (scene change) = input (n)
OP2 (scene 1 frame) = 1/2 * input (n+1) + 1/2 * OP1
Which can be rewritten as:
OP2 (scene 1 frame) = 1/2 * input (n+1) + 1/2 * input (n)
OP3 (scene 2 frames) = 1/3 * input (n+2) + 2/3 * OP2
Which can be rewritten as:
OP3 (scene 2 frames) = 1/3 * input (n+2) + 2/3 * (1/2 * input (n+1) + 1/2 * input (n))
Which can be rewritten as:
OP3 (scene 2 frames) = 1/3 * input (n+2) + 1/3 * input (n+1) + 1/3 * input (n)
and so on for further inputs..
Each output is built up from contributions of previous inputs in a controlled manner to provide optimum noise
reduction as quickly as possible. The advantages of such an arrangement are that much higher levels of noise
reduction can be obtained than the transversal arrangement with virtually no delay. In the limiting case an
infinite amount of noise reduction can be applied to a stationary picture with picture contributions backwards
into infinity. In reality the level of noise reduction will be continuously modulated by picture differences such as
shot changes or motion. Sophisticated control of K is vital to the correct operation of a recursive noise reducer.
Without some form of motion detection, the impulse response of the recursive filter would be that of a
decaying exponential sampled at the picture frequency, and the effect on moving pictures is very like that of a
long persistence display tube with a time constant of 1/K picture periods. Its effect on motion would be to
cause unacceptable smearing of the current picture with contributions of previous pictures. Therefore a
sophisticated movement detector is used to disable contributions from previous pictures when there is a
difference between the previous output and the current input. The structure of the recursive filter can be re-
arranged as shown below:
This arrangement removes one of the multipliers at the expense of a second adder and has the added benefit
of providing a picture difference signal which is used in the picture difference processor to generate the cross-
fade value K.
