View source for YIQ

{{Short description|Color space}}

[[File:YIQ IQ plane.svg|thumb|300px|The YIQ color space at Y=0.5. Note that the I and Q chroma coordinates are scaled up to 1.0. See the formulae below in the article to get the right bounds.]]
[[File:YIQ components.jpg|right|thumb|An image along with its Y, I, and Q components]]

'''YIQ''' is the [[color space]] used by the analog [[NTSC]] color TV system. ''I'' stands for ''in-phase'', while ''Q'' stands for ''quadrature'', referring to the components used in [[quadrature amplitude modulation]]. Other TV systems used different color spaces, such as [[Y′UV|YUV]] for [[PAL]] or [[YDbDr]] for SECAM. Later [[Digital television|digital standards]] use the [[YCbCr]] color space. These color spaces are all broadly related, and work based on the principle of adding a color component named ''[[chrominance]]'', to a black and white image named ''[[Luma (video)|luma]]''.

In YIQ the '''Y''' component represents the luma information, and is the only component used by black-and-white television receivers. '''I''' and '''Q''' represent the chrominance information, with I indicating (roughly) [[Orange (colour)|orange]]-[[blue]] contrast, and Q indicating [[purple]]-[[green]] contrast. I and Q can be thought of as a second pair of axes on the same graph as the YUV color space, rotated 33°; therefore IQ and UV represent different coordinate systems on the same plane.

The YIQ system is intended to take advantage of [[Color vision|human color-response]] characteristics. The eye is more sensitive to changes in the orange-blue (I) range than in the purple-green range (Q)&mdash;therefore less [[Bandwidth (signal processing)|bandwidth]] is required for Q than for I. [[CCIR System M|Broadcast NTSC]] limits I to 1.3&nbsp;MHz and Q to 0.4&nbsp;MHz. I and Q are frequency interleaved into the 4&nbsp;MHz Y signal, which keeps the bandwidth of the overall signal down to 4.2&nbsp;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.

Very few television sets perform true I and Q decoding, due to the high costs of such an implementation. Compared to the cheaper R-Y and B-Y decoding which requires only one filter, I and Q each requires a different filter to satisfy the bandwidth differences between I and Q.  These bandwidth differences also require that the 'I' filter include a time delay to match the longer delay of the 'Q' filter. The [[Rockwell Collins|Rockwell]] Modular Digital Radio (MDR) was one I and Q decoding set, which in 1997 could operate in frame-at-a-time mode with a PC or in realtime with the Fast IQ Processor (FIQP).  Some [[RCA]] "[[Colortrak]]" home TV receivers made circa 1985 not only used I/Q decoding, but also advertised its benefits along with its [[comb filter]]ing benefits as full "100 percent processing" to deliver more of the original color picture content.  Earlier, more than one brand of color TV (RCA, Arvin) used I/Q decoding in the 1954 or 1955 model year on models utilizing screens about 13&nbsp;inches (measured diagonally). The original [[Henry Kloss#Advent Corporation|Advent]] projection television used I/Q decoding. Around 1990, at least one manufacturer ([[Ikegami Tsushinki|Ikegami]]) of professional studio picture monitors advertised I/Q decoding.

== Image processing ==
The YIQ representation is sometimes employed in color [[Digital image processing|image processing]] transformations. For example, applying a [[histogram equalization]] directly to the channels in an RGB image would alter the [[color balance]] of the image. Instead, the histogram equalization is applied to the Y channel of the YIQ or YUV representation of the image, which only normalizes the brightness levels of the image.

== Formulas ==
These formulas allow conversion between YIQ and RGB color spaces, where R, G, and B are gamma-corrected values. Values for the original 1953 NTSC colorimetry and later SMPTE C FCC standard.

The following formulas assume:

:<math>R, G, B, Y \in \left[ 0, 1 \right], \quad I \in \left[-0.5957, 0.5957\right], \quad Q \in \left[-0.5226, 0.5226\right]</math>

The ranges for I and Q<ref>{{cite web |title=Color Spaces |url=https://culorijs.org/color-spaces/ |access-date=27 February 2022 |website=culori}}</ref><ref>{{cite web |last=Sedgewick |last2=Wayne |date=2020 |title=Built-in Types of Data |url=https://introcs.cs.princeton.edu/java/12types/ |access-date=27 February 2022 |website=introcs.cs.princeton.edu}}</ref> are a result of the coefficients in the 2nd and 3rd rows of the RGB-to-YIQ equation matrix below, respectively.

=== NTSC 1953 colorimetry ===
[[File:NTSC 1953 RGB Colorcube.png|thumb|NTSC 1953 colorimetry color cube (color profile encoded, requires a compatible browser and monitor for accurate display).]]

These formulas approximate the conversion between the [[NTSC#Colorimetry|original 1953 color NTSC specification]] and YIQ.<ref>{{cite web |url=http://www.mathworks.com/help/images/ref/rgb2ntsc.html |title=rgb2ntsc: Convert RGB color values to NTSC color space |website=Image Processing Toolbox Documentation |publisher=MathWorks |access-date=28 June 2015}}</ref><ref>{{cite web |url=http://www.mathworks.com/help/images/ref/ntsc2rgb.html |title=ntsc2rgb: Convert NTSC values to RGB color space |website=Image Processing Toolbox Documentation |publisher=MathWorks |access-date=28 June 2015}}</ref><ref>47 CFR § 73.682 (20) (iv)</ref>

==== From RGB to YIQ ====
:<math>
\begin{bmatrix} Y \\ I \\ Q \end{bmatrix}
\approx
\begin{bmatrix}
  0.299 &  0.587 &  0.114 \\
  0.5959 & -0.2746 & -0.3213 \\
  0.2115 & -0.5227 &  0.3112
\end{bmatrix}
\begin{bmatrix} R \\ G \\ B \end{bmatrix}
</math> <ref name="ITU-R-BT1700">{{cite web |publisher=[[International Telecommunication Union]] |title=ITU-R BT.1700 Characteristics of composite video signals for conventional analogue television systems |at=S170m-2004.pdf: Composite Analog Video Signal NTSC for Studio Applications Page 6 |url=https://www.itu.int/rec/R-REC-BT.1700-0-200502-I/en |format=zip/pdf |date=2004-11-30 |access-date=2019-04-16}}</ref>

==== From YIQ to RGB ====
:<math>
\begin{bmatrix} R \\ G \\ B \end{bmatrix}
=
\begin{bmatrix}
  1 &  0.956 &  0.619 \\
  1 & -0.272 & -0.647 \\
  1 & -1.106 &  1.703
\end{bmatrix}
\begin{bmatrix} Y \\ I \\ Q \end{bmatrix}
</math>

Note that the top row is identical to that of the [[YUV]] color space

* <math>\begin{bmatrix} R \\ G \\ B \end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \implies \begin{bmatrix} Y \\ I \\ Q \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}</math>

=== FCC NTSC Standard (SMPTE C)===
[[File:SMPTE-C RGB color cube.png|thumb|SMPTE C color cube (color profile encoded, requires a compatible browser and monitor for accurate display).]]

In 1987, the [[Society of Motion Picture and Television Engineers]] (SMPTE) Committee on Television Technology, Working Group on Studio Monitor Colorimetry, adopted the [[SMPTE C]].<ref name="SMPTE_RP145">Society of Motion Picture and Television Engineers (1987–2004): Recommended Practice RP 145-2004. Color Monitor Colorimetry.</ref><ref name="SMPTE_EG27">Society of Motion Picture and Television Engineers (1994, 2004): Engineering Guideline EG 27-2004. Supplemental Information for SMPTE 170M and Background on the Development of NTSC Color Standards, pp. 9</ref><ref>Advanced Television Systems Committee (2003): ATSC Direct-to-Home Satellite Broadcast Standard Doc. A/81, pp.18</ref>
The previous conversion formulas were deprecated, and the NTSC standard contained in the FCC rules for over-the-air analog color TV broadcasting adopted a different matrix:<ref>{{cite book |url=https://www.govinfo.gov/content/pkg/CFR-2013-title47-vol4/pdf/CFR-2013-title47-vol4-sec73-682.pdf |title=§ 73.682 TV transmission standards |publisher=FCC |year=2013 |pages=210}}</ref><ref>{{cite book |url=https://www.itu.int/dms_pubrec/itu-r/rec/bt/R-REC-BT.470-6-199811-S!!PDF-E.pdf#page=9 |title=Rec. ITU-R BT.470-6 - Conventional Television Systems |publisher=ITU-R |year=1998 |pages=9}}</ref>

==== From RGB to YIQ ====
:::<math>
\left \{
\begin{array}{ccl}
E_Y^\prime&=&0.30E_R^\prime+0.59E_G^\prime+0.11E_B^\prime\\
E_I^\prime&=&-0.27(E_B^\prime-E_Y^\prime)+0.74(E_R^\prime-E_Y^\prime)\\ 
E_Q^\prime&=&0.41(E_B^\prime-E_Y^\prime)+0.48(E_R^\prime-E_Y^\prime)
\end{array}
\right .
</math>

in matrix notation, that equation system is written as:
:<math>
\begin{bmatrix} E_Y^\prime \\ E_I^\prime \\ E_Q^\prime \end{bmatrix}
=
\begin{bmatrix}
  0.30    &  0.59    &   0.11 \\
  0.599   & -0.2773  &  -0.3217 \\
  0.213   & -0.5251 &    0.3121
\end{bmatrix}
\begin{bmatrix} E_R^\prime \\ E_G^\prime \\ E_B^\prime \end{bmatrix}
</math>

Where:

* <math>E_Y^\prime</math> is the [[Gamma correction|gamma-corrected]] voltage of luma.
* <math>E_R^\prime</math>, <math>E_G^\prime</math> and <math>E_B^\prime</math> are the gamma-corrected voltages corresponding to red, green, and blue signals.
* <math>E_I^\prime</math> and <math> E_Q^\prime</math> are the amplitudes of the orthogonal components of the chrominance signal.

==== From YIQ to RGB ====
To convert from FCC YIQ to RGB:

:<math>E_R^\prime = E_Y^\prime + 0.9469 E_I^\prime + 0.6236 E_Q^\prime</math>
:<math>E_G^\prime = E_Y^\prime - 0.2748 E_I^\prime - 0.6357 E_Q^\prime</math>
:<math>E_B^\prime = E_Y^\prime - 1.1 E_I^\prime + 1.7 E_Q^\prime</math>

==== From YUV to YIQ and vice versa ====
<math>\begin{bmatrix} Y' \\ I \\ Q \end{bmatrix}
=
\begin{bmatrix} 1 & 0 & 0 \\ 0 & -\sin(33^\circ) & \cos(33^\circ) \\ 0 & \cos(33^\circ) & \sin(33^\circ) \end{bmatrix}
\begin{bmatrix} Y' \\ U \\ V \end{bmatrix}
\approx
\begin{bmatrix} 1 & 0 & 0 \\ 0 & -0.54464 & 0.83867 \\ 0 & 0.83867 & 0.54464 \end{bmatrix}
\begin{bmatrix} Y' \\ U \\ V \end{bmatrix}</math>

Due to orthogonal symmetry (symmetry is not required or enough) of the matrix the same matrix can be used for YIQ to YUV conversion.<ref>{{cite web |title=Chapter 3: Color Spaces |url=https://www.compression.ru/download/articles/color_space/ch03.pdf |access-date=2022-03-05}}</ref>

== Phase-out ==

Most NTSC territories have [[Digital television transition|switched over to digital television]]. For broadcasting in the United States, NTSC (and with it, YIQ) remained in use only for [[Low-power broadcasting|low-power television]] stations {{As of|2011|7|lc=true}}, well after full-power analog transmissions was ended by the [[Federal Communications Commission]] (FCC) on June 12, 2009, however these were also required to be shut down by the FCC on July 13, 2021,<ref>{{cite web |url=https://www.fcc.gov/consumers/guides/low-power-television-lptv-service |title=Low Power Television Service |author=<!--Not stated--> |date=<!--Not stated--> |website=fcc.gov |publisher=FCC |access-date=June 24, 2024 |quote=}}
</ref> thereby ending the use of NTSC (and YIQ for that matter) completely in that region.

== References ==
{{reflist}}

== Further reading ==
* Buchsbaum, Walter H. ''Color TV Servicing, third edition''. Englewood Cliffs, NJ: Prentice Hall, 1975. {{ISBN|0-13-152397-X}}

{{Color space}}

[[Category:Color space]]