[#1] YCbCr与RGB的转换公式

1 YCbCr简介
YCbCr颜色空间是将RGB颜色空间进行坐标转换后得到的，常用于数字电视系统。
Y取值范围：16~235
Cb、Cr的取值范围：16~240
YCbCr经常和YUV混淆。两者的主要差别在于YUV是模拟信号，YCbCr是数字信号。
2 YCbCr与RGB的转换公式
因为SDTV（标清视频）和HDTV（高清视频）应用具有不同的色度特征，所以对于RGB和YCbCr之间的转换的公式，分两种情况进行说明：
对于SDTV（包括480i 576i），对应的标准是ITU-R BT.601：

对于HDTV（包括720P 1080i 1080P），对应的标准是ITU BT.709：

3 YCbCr转RGB的verilog源码
/*
计算公式： R = 1.164(Y - 16) + 1.793(CR - 128) = 1.164Y + 1.793CR - 248.128;
G = 1.164(Y - 16) - 0.534(CR - 128) - 0.213(CB - 128) = 1.164Y - 0.213CB - 0.534CR + 76.992;
B = 1.164(Y - 16) + 2.115(CB - 128) = 1.164Y + 2.115CB - 289.344;
其中，时序在计算过程中完全没有用到
输入到输出有三个clock的时延。
第一级流水线计算所有乘法；
第二级流水线计算所有加法，把正的和负的分开进行加法；
第三级流水线计算最终的和，若为负数取0；
仿真通过
*/
`timescale 1ns/1ps
module ycbcr_to_rgb(
input clk,
input wire[7 : 0] i_y_8b,
input wire[7 : 0] i_cb_8b,
input wire[7 : 0] i_cr_8b,

input i_h_sync,
input i_v_sync,
input i_data_en,

output wire[7 : 0] o_r_8b,
output wire[7 : 0] o_g_8b,
output wire[7 : 0] o_b_8b,

output reg o_h_sync,
output reg o_v_sync,
output reg o_data_en
);

/***************************************parameters*******************************************/
//multiply 256
parameter para_1164_10b = 10'd297; //1.160
parameter para_1793_10b = 10'd459; //1.793
parameter para_0534_10b = 10'd137; //0.535
parameter para_0213_10b = 10'd54; //0.211
parameter para_2115_10b = 10'd541; //2.113
parameter para_248128_18b = 18'd63521;//248.128
parameter para_76992_18b = 18'd19710; //76.992
parameter para_289344_18b = 18'd74072;//289.344
/********************************************************************************************/

/***************************************signals**********************************************/
wire sign_r;
wire sign_g;
wire sign_b;
reg[17 : 0] mult_y_for_r_18b;
reg[17 : 0] mult_y_for_g_18b;
reg[17 : 0] mult_y_for_b_18b;

reg[17 : 0] mult_cb_for_g_18b;
reg[17 : 0] mult_cb_for_b_18b;

reg[17 : 0] mult_cr_for_r_18b;
reg[17 : 0] mult_cr_for_g_18b;

reg[17 : 0] add_r_0_18b;
reg[17 : 0] add_g_0_18b;
reg[17 : 0] add_b_0_18b;

reg[17 : 0] add_r_1_18b;
reg[17 : 0] add_g_1_18b;
reg[17 : 0] add_b_1_18b;

reg[17 : 0] result_r_18b;
reg[17 : 0] result_g_18b;
reg[17 : 0] result_b_18b;

reg i_h_sync_delay_1;
reg i_v_sync_delay_1;
reg i_data_en_delay_1;

reg i_h_sync_delay_2;
reg i_v_sync_delay_2;
reg i_data_en_delay_2;

/********************************************************************************************/

/***************************************initial**********************************************/
initial
begin
mult_y_for_r_18b <= 18'd0;
mult_y_for_g_18b <= 18'd0;
mult_y_for_b_18b <= 18'd0;

mult_cb_for_g_18b <= 18'd0;
mult_cb_for_b_18b <= 18'd0;

mult_cr_for_r_18b <= 18'd0;
mult_cr_for_g_18b <= 18'd0;

add_r_0_18b <= 18'd0;
add_g_0_18b <= 18'd0;
add_b_0_18b <= 18'd0;

add_r_1_18b <= 18'd0;
add_g_1_18b <= 18'd0;
add_b_1_18b <= 18'd0;

result_r_18b <= 18'd0;
result_g_18b <= 18'd0;
result_b_18b <= 18'd0;

i_h_sync_delay_1 <= 1'd0;
i_v_sync_delay_1 <= 1'd0;
i_data_en_delay_1 <= 1'd0;

i_h_sync_delay_2 <= 1'd0;
i_v_sync_delay_2 <= 1'd0;
i_data_en_delay_2 <= 1'd0;

o_h_sync <= 1'd0;
o_v_sync <= 1'd0;
o_data_en <= 1'd0;
end
/********************************************************************************************/

/***************************************arithmetic*******************************************/
//LV1 pipeline : mult
always @ (posedge clk)
begin
mult_y_for_r_18b <= i_y_8b * para_1164_10b;
mult_y_for_g_18b <= i_y_8b * para_1164_10b;
mult_y_for_b_18b <= i_y_8b * para_1164_10b;
end

always @ (posedge clk)
begin
mult_cb_for_g_18b <= i_cb_8b * para_0213_10b;
mult_cb_for_b_18b <= i_cb_8b * para_2115_10b;
end

always @ (posedge clk)
begin
mult_cr_for_r_18b <= i_cr_8b * para_1793_10b;
mult_cr_for_g_18b <= i_cr_8b * para_0534_10b;
end
//LV2 pipeline : add
always @ (posedge clk)
begin
add_r_0_18b <= mult_y_for_r_18b + mult_cr_for_r_18b;
add_r_1_18b <= para_248128_18b;
add_g_0_18b <= mult_y_for_g_18b + para_76992_18b;
add_g_1_18b <= mult_cb_for_g_18b + mult_cr_for_g_18b;
add_b_0_18b <= mult_y_for_b_18b + mult_cb_for_b_18b;
add_b_1_18b <= para_289344_18b;
end
//LV3 pipeline : y + cb + cr
assign sign_r = (add_r_0_18b >= add_r_1_18b);
assign sign_g = (add_g_0_18b >= add_g_1_18b);
assign sign_b = (add_b_0_18b >= add_b_1_18b);
always @ (posedge clk)
begin
result_r_18b = sign_r ? (add_r_0_18b - add_r_1_18b) : 18'd0;
result_g_18b = sign_g ? (add_g_0_18b - add_g_1_18b) : 18'd0;
result_b_18b = sign_b ? (add_b_0_18b - add_b_1_18b) : 18'd0;
end

//output
assign o_r_8b = (result_r_18b[17:16] == 2'b00) ? result_r_18b[15 : 8] : 8'hff;
assign o_g_8b = (result_g_18b[17:16] == 2'b00) ? result_g_18b[15 : 8] : 8'hff;
assign o_b_8b = (result_b_18b[17:16] == 2'b00) ? result_b_18b[15 : 8] : 8'hff;
/********************************************************************************************/

/***************************************timing***********************************************/
always @ (posedge clk)
begin
i_h_sync_delay_1 <= i_h_sync;
i_v_sync_delay_1 <= i_v_sync;
i_data_en_delay_1 <= i_data_en;

i_h_sync_delay_2 <= i_h_sync_delay_1;
i_v_sync_delay_2 <= i_v_sync_delay_1;
i_data_en_delay_2 <= i_data_en_delay_1;

o_h_sync <= i_h_sync_delay_2;
o_v_sync <= i_v_sync_delay_2;
o_data_en <= i_data_en_delay_2;
end
/********************************************************************************************/
endmodule
4 RGB转YCbCr的verilog源码
/*
计算公式： Y = 0.183R + 0.614G + 0.062B + 16;
CB = -0.101R - 0.338G + 0.439B + 128;
CR = 0.439R - 0.399G - 0.040B + 128;
其中，时序在计算过程中完全没有用到
输入到输出有三个clock的时延。
第一级流水线计算所有乘法；
第二级流水线计算所有加法，把正的和负的分开进行加法；
第三级流水线计算最终的和，若为负数取0；
仿真通过
*/
`timescale 1ns/1ps
module rgb_to_ycbcr(
input clk,
input wire[7 : 0] i_r_8b,
input wire[7 : 0] i_g_8b,
input wire[7 : 0] i_b_8b,

input wire i_h_sync,
input wire i_v_sync,
input wire i_data_en,
input i_de_vld,

output wire[7 : 0] o_y_8b,
output wire[7 : 0] o_cb_8b,
output wire[7 : 0] o_cr_8b,

output reg o_h_sync,
output reg o_v_sync,
output reg o_data_en,
output reg o_de_vld
);

/***************************************parameters*******************************************/
//multiply 256
parameter para_0183_10b = 10'd47;
parameter para_0614_10b = 10'd157;
parameter para_0062_10b = 10'd16;
parameter para_0101_10b = 10'd26;
parameter para_0338_10b = 10'd86;
parameter para_0439_10b = 10'd112;
parameter para_0399_10b = 10'd102;
parameter para_0040_10b = 10'd10;
parameter para_16_18b = 18'd4096;
parameter para_128_18b = 18'd32768;
/********************************************************************************************/

/***************************************signals**********************************************/
wire sign_cb;
wire sign_cr;
reg[17: 0] mult_r_for_y_18b;
reg[17: 0] mult_r_for_cb_18b;
reg[17: 0] mult_r_for_cr_18b;

reg[17: 0] mult_g_for_y_18b;
reg[17: 0] mult_g_for_cb_18b;
reg[17: 0] mult_g_for_cr_18b;

reg[17: 0] mult_b_for_y_18b;
reg[17: 0] mult_b_for_cb_18b;
reg[17: 0] mult_b_for_cr_18b;

reg[17: 0] add_y_0_18b;
reg[17: 0] add_cb_0_18b;
reg[17: 0] add_cr_0_18b;

reg[17: 0] add_y_1_18b;
reg[17: 0] add_cb_1_18b;
reg[17: 0] add_cr_1_18b;

reg[17: 0] result_y_18b;
reg[17: 0] result_cb_18b;
reg[17: 0] result_cr_18b;

reg i_h_sync_delay_1;
reg i_v_sync_delay_1;
reg i_data_en_delay_1;
reg i_de_vld_delay_1;

reg i_h_sync_delay_2;
reg i_v_sync_delay_2;
reg i_data_en_delay_2;
reg i_de_vld_delay_2;

/********************************************************************************************/

/***************************************initial**********************************************/
initial
begin
mult_r_for_y_18b <= 18'd0;
mult_r_for_cb_18b <= 18'd0;
mult_r_for_cr_18b <= 18'd0;

mult_g_for_y_18b <= 18'd0;
mult_g_for_cb_18b <= 18'd0;
mult_g_for_cr_18b <= 18'd0;

mult_b_for_y_18b <= 18'd0;
mult_g_for_cb_18b <= 18'd0;
mult_b_for_cr_18b <= 18'd0;

add_y_0_18b <= 18'd0;
add_cb_0_18b <= 18'd0;
add_cr_0_18b <= 18'd0;

add_y_1_18b <= 18'd0;
add_cb_1_18b <= 18'd0;
add_cr_1_18b <= 18'd0;

result_y_18b <= 18'd0;
result_cb_18b <= 18'd0;
result_cr_18b <= 18'd0;

i_h_sync_delay_1 <= 1'd0;
i_v_sync_delay_1 <= 1'd0;
i_data_en_delay_1 <= 1'd0;

i_h_sync_delay_2 <= 1'd0;
i_v_sync_delay_2 <= 1'd0;
i_data_en_delay_2 <= 1'd0;

o_h_sync <= 1'd0;
o_v_sync <= 1'd0;
o_data_en <= 1'd0;
end
/********************************************************************************************/

/***************************************arithmetic*******************************************/
//LV1 pipeline : mult
always @ (posedge clk)
begin
mult_r_for_y_18b <= i_r_8b * para_0183_10b;
mult_r_for_cb_18b <= i_r_8b * para_0101_10b;
mult_r_for_cr_18b <= i_r_8b * para_0439_10b;
end

always @ (posedge clk)
begin
mult_g_for_y_18b <= i_g_8b * para_0614_10b;
mult_g_for_cb_18b <= i_g_8b * para_0338_10b;
mult_g_for_cr_18b <= i_g_8b * para_0399_10b;
end

always @ (posedge clk)
begin
mult_b_for_y_18b <= i_b_8b * para_0062_10b;
mult_b_for_cb_18b <= i_b_8b * para_0439_10b;
mult_b_for_cr_18b <= i_b_8b * para_0040_10b;
end
//LV2 pipeline : add
always @ (posedge clk)
begin
add_y_0_18b <= mult_r_for_y_18b + mult_g_for_y_18b;
add_y_1_18b <= mult_b_for_y_18b + para_16_18b;

add_cb_0_18b <= mult_b_for_cb_18b + para_128_18b;
add_cb_1_18b <= mult_r_for_cb_18b + mult_g_for_cb_18b;

add_cr_0_18b <= mult_r_for_cr_18b + para_128_18b;
add_cr_1_18b <= mult_g_for_cr_18b + mult_b_for_cr_18b;
end
//LV3 pipeline : y + cb + cr

assign sign_cb = (add_cb_0_18b >= add_cb_1_18b);
assign sign_cr = (add_cr_0_18b >= add_cr_1_18b);
always @ (posedge clk)
begin
result_y_18b = add_y_0_18b + add_y_1_18b;
result_cb_18b = sign_cb ? (add_cb_0_18b - add_cb_1_18b) : 18'd0;
result_cr_18b = sign_cr ? (add_cr_0_18b - add_cr_1_18b) : 18'd0;
end

//output
assign o_y_8b = (result_y_18b[17:16] == 2'b00) ? result_y_18b[15 : 8] : 8'hFF;
assign o_cb_8b = (result_cb_18b[17:16] == 2'b00) ? result_cb_18b[15 : 8] : 8'hFF;
assign o_cr_8b = (result_cr_18b[17:16] == 2'b00) ? result_cr_18b[15 : 8] : 8'hFF;
/********************************************************************************************/

/***************************************timing***********************************************/
always @ (posedge clk)
begin
i_h_sync_delay_1 <= i_h_sync;
i_v_sync_delay_1 <= i_v_sync;
i_data_en_delay_1 <= i_data_en;
i_de_vld_delay_1 <=i_de_vld;

i_h_sync_delay_2 <= i_h_sync_delay_1;
i_v_sync_delay_2 <= i_v_sync_delay_1;
i_data_en_delay_2 <= i_data_en_delay_1;
i_de_vld_delay_2 <=i_de_vld_delay_1;

o_h_sync <= i_h_sync_delay_2;
o_v_sync <= i_v_sync_delay_2;
o_data_en <= i_data_en_delay_2;
o_de_vld <= i_de_vld_delay_2;
end
/********************************************************************************************/
endmodule

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参考文档：
1、https://en.wikipedia.org/wiki/YCbCr
2、视频技术手册第五版