Xilinx pg013 LogiCORE IP RGB to YCrCb Color-Space Converter v5 ...

Color-Space Conversion BackgroundCb = [ CCOE ⋅ ( B – Y RAW )] OWIDTH+ CbOFFSETCr = [ DCOEF ⋅ ( R – Y RAW )] OWIDTH+ CrOFFSETEquation 4-14Equation 4-15where [ ] k denotes rounding to k bits. The architecture contains three possible operatorsthat might introduce noise. Quantization noise is inserted when data is rounded.1. Data is rounded to MWIDTH-2 bits after calculating Y raw ,2. Data is rounded to OWIDTH bits at the output.3. If CCOEF and DCOEF are chosen such that Cb and Cr may over- or underflow, clippingnoise gets inserted to the signal flow.Before analyzing the effects of these noise sources, first look at the input Signal toQuantization Noise Ratio (SQNR). Assuming uniformly distributed quantization error,RGBMAXP x X 2 dxRGBMINSQNR 10log RGB= ------- = 10P log------------------------------------------N1Δ-- Δ ⁄ 2e 2 d– Δ ⁄ 2xEquation 4-16Substituting LSB =2 -INBITS , where INBITS is the input (RGB) precision, SQNR RGB becomes afunction of the input dynamic range. In the next three calculations, when calculatingSQNR RGB for the typical dynamic ranges, INBITS = 8 for all three cases.When RGB values are in the (0, 255) range:1255-------- 255x 2 x1 d ---------------- [ 255 3 ]03 ⋅ 255SQNR 10 RGB= log------------------------------------1 ⁄ 2x 2 = 10log-----------------------------------=1dx-----– 1 ⁄ 21254.15dBEquation 4-17when RGB values are in the (16, 240) range:1224-------- 240x 2 d16xSQNR RGB= 10log------------------------------------x 2 =1 ⁄ 2 dx– 1 ⁄ 253.92dBEquation 4-18and when RGB values are in the (16, 235) range:1219-------- 235x 2 d16xSQNR RGB= 10log------------------------------------x 2 = 53.74dB1 ⁄ 2 dx(–1) ⁄ 2Equation 4-19RGB to YCrCb Color-Space Converter www.xilinx.com 38PG013 April 24, 2012