# Horizontal resolution: Pixels or lines

Historically, resolution is understood to mean “limiting resolution,” or the point at which adjacent elements of an image cease to be distinguished. Various disciplines measure and specify resolution differently. Resolution can be specified as:

• The number of units (i.e., lines or line-pairs) per unit-distance along the vertical and horizontal axis such as lines/mm.

• The number of units (i.e., lines) for a full display such as lines per picture height (LPH).

In television, the resolution is specified in terms of LPH. The various conventional broadcast TV systems in use today were originally designed to achieve equal horizontal and vertical resolution, known as “square pixels.”

### The analog heritage

The vertical resolution is independent of the system bandwidth and defines the capability of the system to resolve horizontal lines. It is expressed as the number of distinct horizontal lines, alternately black and white, which can be satisfactorily resolved on a television screen. Vertical resolution depends primarily on the number of scanning lines per picture and the combined effects of the camera and display capabilities.

Ideally, the vertical resolution would be equal to the number of active lines per frame. This would happen if the scanning lines were centered on the picture details.

However, the scanning lines cannot be assumed to occupy a fixed position relative to vertical detail at all times. Complete loss of vertical resolution will occur when the scanning spot straddles picture details. From subjective data, obtained with progressive (non-interlaced) scanning, it has been found that the vertical resolution is equal to 70 percent (the Kell factor) of the number of active lines. In the NTSC standard, there is a total of 525 lines per frame, of which about 40 are blanked, leaving, typically, about 485 active lines per frame. Given a Kell factor of 0.7, the effective vertical resolution is:

NV = 0.7 × 485 ≈ 339 LPH

The horizontal resolution defines the capability of the system to resolve vertical lines. It depends on the camera and display capabilities, as well as the bandwidth and the high-frequency amplitude and phase response of the transmission medium. In a 4:3 aspect ratio television system, it is expressed as the number of distinct vertical lines, alternately black and white, which can be satisfactorily resolved in three quarters of the width of a television screen. A system with a horizontal to vertical aspect ratio of 4:3, as in conventional television, needs to allow for (4:3) NV horizontal details to be resolved over the width of the display.

In the NTSC system, this results in 339 × 4/3 ≈ 452 horizontal details to be resolved. Due to the limited system bandwidth, exploring a pair of contiguous white and black fine details (line-pair) results in a sinewave with a positive half-wave corresponding to the white detail and a negative half-wave corresponding to the black detail. Scanning 452 horizontal details results in an electrical signal with 226 complete cycles during the active horizontal scanning line.

In the NTSC standard, the total horizontal scanning line duration is 63.5 µsec, and the horizontal blanking duration is 10.7 µsec. This results in an active line duration of 52.85 µsec. The duration of a single cycle is:

T = 52.85 µsec/226 ≈ 0.2338 µsec The fundamental frequency resulting from scanning 452 horizontal details is:

F = 1/T = 1/0.2338 µsec ≈ 4.28MHz.

This is the bandwidth required for equal horizontal and vertical resolution. The horizontal resolution factor for a 4.28MHz bandwidth is: 339/4.28MHz = 79.2 lines/MHz rounded to 80 lines/MHz. In countries using the NTSC standard (CCIR M), the maximum transmitted baseband video frequency is 4.2MHz, resulting in a transmitted horizontal resolution of:

NH = 4.2MHz × 80 lines/MHz ≈ 336 lines.

The resulting horizontal versus vertical resolution ratio is, therefore, 336/339 ≈ 0.99. From an analog point of view, this represents a quasi square pixel. It is important to note that the analog television concept is based on the vertical resolution and the Kell factor, and assumes a single format from the camera through the production-transmission-reception process to the CRT display.

 Table 1. ITU-R BT 601 4:3 format Y channel characteristics. Click here to see an enlarged diagram.
Color television introduced the color CRT wherein there are separate Red, Green and Blue phosphor dots whose number and characteristics have an effect on the reproduced resolution. The transmission of color information as a subcarrier modulated in amplitude and phase resulted in a frequency-division multiplexing of luminance-chrominance information which needed to be decoded to display the original Red, Green and Blue information. The final luminance resolution depended finally on the ability of the decoder to separate the two informations without mutual crosstalk and bandwidth reduction.

The computer world introduced the concept of picture element shortened to “pixel” and sometimes “pel.” Computers use progressive scanning to display digitally generated pixels and thus have no display related limitations other than the display resolution and the analog drive (Red, Green, Blue) circuits characteristics.

### Digital concepts

Rec 601, the first successful international digital video standard, specifies data acquisition in terms of samples per total line and per active line. No mention of pixels here! Resolution-related Y channel characteristics are shown in Table 1.

The luminance (Y) sampling frequency is 13.5MHz, resulting in 720 samples per active line. One would be tempted to assume that at every sampling instant, there would be a pixel ready to be sampled. This would be true in an ideal world where, given the Nyquist frequency of 6.75MHz, there would be 6.75 × 80 × 4/3 = 720 active pixels on each line, yielding a horizontal resolution of 6.75 × 80 = 540 LPH.

 Figure 1. Relationship between the idealized luminance bandwidth, the resulting number of pixels per active line and the horizontal resolution. Click here to see an enlarged diagram.

In reality, the A/D converter is preceded by a low-pass (anti-aliasing) filter with a specified cut-off frequency of 5.75MHz. This results in 5.75 × 80 × 4/3 = 613 sampled pixels per active line and a horizontal resolution of 5.75 × 80 = 460 LPH. (See Figure 1).

Note that in all these calculations, I used a rounded figure of 80 lines/MHz. Expressing the horizontal resolution in a specific number of horizontal pixels is in conflict with the concept of the television resolution, which uses LPH.

Resolution-related Y channel characteristics of three ATSC 16:9 formats, shown in Table 2, allow you to compare conflicting resolution figures. Unfortunately, technical literature and equipment specifications often quote unrealistic figures, and it is up to the reader to draw the proper conclusions.

Another contentious subject is the vertical resolution. Essentially, does the Kell factor apply to interlaced scanning, progressive scanning or both? As explained in my article “Revisiting Kell,” published in the Broadcast Engineering March 2003 edition, the Kell factor was developed with progressive scanning in mind and applies to both interlaced and progressive scanning. Similar considerations apply to HDTV scanning systems.

The problem is further complicated by the use of various compression algorithms and format conversions in a production/transmission chain. The last element in the chain to leave its imprint is the ever more popular flat-panel display (LCD or plasma).

 Table 2. 16:9 formats Y channel characteristics. Click here to see an enlarged diagram.
With digital television concepts and implementations, there is a trend towards expressing the picture resolution as the number of pixels per active line multiplied with the number of active lines per frame. This trend tends to ignore the original definitions of horizontal and vertical resolution and is gradually replacing them in equipment and system specifications.

It is important to remember that television resolution is expressed in LPH. Ignoring this may result in quoting figures that are difficult, if not impossible, to compare. A return to basic concepts is essential in order to understand contemporary technologies.

### Conclusion

Michael Robin, a fellow of the SMPTE and former engineer with the Canadian Broadcasting Corp.'s engineering headquarters, is an independent broadcast consultant located in Montreal, Canada. He is co-author of “Digital Television Fundamentals,” published by McGraw-Hill and translated into Chinese and Japanese.

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