Examine the r.m.s. errors when increasing/decreasing each integer coefficient by Step 3: one. 27 ( 33) combinations must be evaluated in because each coefficient can take three values, i.e. increased, decreased and unchanged from the initial value. Select the combination of the coefficients that gives the minimum r.m.s. error. This Step 4: combination is the resultant optimized one. The same procedure is applied for the colour-difference equations, using equations (11) and (12). (11) (12) 3 Simple calculation method for squared difference sum By expressing the difference between integer and real coefficients as and the ij k'ij r'ij, – digital RGB signals as the sum of the squared differences of equations (10) to (12) can be Xj, written as the following: (13) where and denote the lower and upper boundaries of the input signal range, respectively, for L H which the integer coefficients are to be optimized. As and are constant in the digital system consideration, the summations for are also L H Xj constant. Then equation (13) can be expressed as a function only of ij. (14) where: Thus the calculation of r.m.s. errors or equations (10) to (12) can be simply performed by equation (14). ______________
Step 3: Examine the r.m.s. errors when increasing/decreasing each integer coefficient by one. 27 ( 33) combinations must be evaluated in because each coefficient can take three values, i.e. increased, decreased and unchanged from the initial value. Step 4: Select the combination of the coefficients that gives the minimum r.m.s. error. This combination is the resultant optimized one. The same procedure is applied for the colour-difference equations, using equations (11) and (12). (11) (12) 3 Simple calculation method for squared difference sum By expressing the difference between integer and real coefficients as ij k'ij – r'ij, and the digital RGB signals as Xj, the sum of the squared differences of equations (10) to (12) can be written as the following: (13) where L and H denote the lower and upper boundaries of the input signal range, respectively, for which the integer coefficients are to be optimized. As L and H are constant in the digital system consideration, the summations for Xj are also constant. Then equation (13) can be expressed as a function only of ij. (14) where: Thus the calculation of r.m.s. errors or equations (10) to (12) can be simply performed by equation (14). ______________
R-REC-BT.601-7-201103-I!!MSW-E.docx