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# YIQ

YIQ is the color space used in the NTSC television standard. I stands for intermodulation, while Q stands for quadrature. Its counterpart in PAL and other systems is YUV.

The Y component represents the luminance information, and is the only component used by black-and-white television receivers. I and Q represent the chrominance information. In YUV the U and V components can be thought of as x and y coordinates within the colorspace. I and Q can be thought of as a second pair of axes on the same graph, rotated 33° from V and U, respectively. Thus, I and Q are simply another way of locating a point in the U and V plane.

The reason for doing this is to take advantage of a trait of the human eye. It is more sensitive to changes in the orange-blue (I) range than in the purple-green range (Q). Thus less bandwidth is required for Q than for I. Broadcast NTSC limits I to 1.3 MHz and Q to 0.5 MHz, which keeps the bandwidth of the overall signal down to 4.2 MHz. In YUV systems, since U and V both contain information in the orange-blue range, both components must be given the same amount of bandwidth as I to achieve similar color fidelity.

True I and Q decoding in television receivers is rare, because of the costs of implementation.

## Formula

This formula approximates the conversion from the RGB color space to YIQ. R, G and B are defined on a scale from zero to one:

 Y = 0.299R + 0.587G + 0.114B I = 0.735514(R - Y) - 0.267962(B - Y) = 0.595716R - 0.274453G - 0.321263B Q = 0.477648(R - Y) + 0.412626(B - Y) = 0.211456R - 0.522591G + 0.311135B

or using matrices

$\begin{bmatrix} Y \\ I \\ Q \end{bmatrix} = \begin{bmatrix} 0.299 & 0.587 & 0.114 \\ 0.595716 & -0.274453 & -0.321263 \\ 0.211456 & -0.522591 & 0.311135 \end{bmatrix} \begin{bmatrix} R \\ G \\ B \end{bmatrix}$

Two things to note:

• The top row is identical to that of the YUV color space
• If $\begin{bmatrix} R & G & B \end{bmatrix}^{T} = \begin{bmatrix} 1 & 1 & 1 \end{bmatrix}$ then $\begin{bmatrix} Y & I & Q \end{bmatrix}^{T} = \begin{bmatrix} 1 & 0 & 0 \end{bmatrix}$. In other words, the top row coefficients sum to unity and the last two rows sum to zero.