TV Bandwidth and Baseband Spectrum
The analysis here addresses the 625 line (CCIR) monochrome system. Other systems with different line numbers and picture repetition frequency can be treated in a similar way. Colour tv systems have different spectral characteristics which are not dealt with here.
The bandwidth of a tv signal is determined by the number of picture elements (pixels) necessary to send per unit time. We start by assuming that the horizontal and vertical resolutions in the picture should be identical. The number of active lines per picture is 625 minus 2 x 25 (there are 25 lines lost per field due to field blanking - this period allows the insertion of field synchronisation pulses and allows the receiver's vertical timebase time to reset the scan to the top of the screen). So there are 575 active lines per picture.
The maximum spatial frequency in the vertical direction corresponds to lines being alternately black and white. There are 575/2 cycles per picture height = 287.5 cycles per picture height maximum.
The aspect ratio of conventional analogue tv is 4:3; therefore the maximum horizontal number of cycles is: 287.5 x 4/3 = 383.33
The active line duration is 52 µs (See diagram). This time period therefore has to accommodate 383.33 cycles. In one second there are then 383.33 / (52 x 10 -6) cycles = 7,371,371 cycles. Or to put it another way, the maximum possible temporal frequency is 7.371 MHz.
This figure does not agree with the value, used in practice, of 5.5 MHz. The reason has been determined from subjective tests, where viewers, seeing real pictures, were asked to compare horizontal and vertical resolution as the horizontal resolution was varied. Subjectively equal resolutions (for 625 lines) were obtained for video bandwidths in the region of 5.5 MHz. There is no need to use the higher figure if it is not appreciated by the viewer as signal bandwidth is a quantity that needs to be minimised.
The ratio of theoretical to actual horizontal resolution is called the Kell factor after the engineer who defined it, and it is found, for a range of different line standards, to take values around 0.75; the figures for the 625 line system calculated above correspond to a Kell factor of 0.746.
The reason that the Kell factor is less than unity arises from the effective sampling of the picture in the vertical direction and the continuous nature of the process horizontally. The maximum vertical spatial picture frequency is limited because 1 spatial cycle requires 2 picture lines (corresponding to the Nyquist cut-off) whereas in the horizontal direction the system can transmit frequencies above the nominal cut-off (5.5MHz) albeit with reducing amplitude with increasing frequency.
The basic calculation in the last section gives an upper limit to the bandwidth of a television signal, but does not reveal the subtleties of its distribution of energy in the frequency domain.
There is considerable redundancy in tv signals - adjacent lines are very similar as are adjacent pictures. This produces a signal which is very highly structured, with well-defined repetition rates at line, field and frame frequencies. The tv signal spectrum therefore has strong frequency components at 25, 50 and 15,625 Hz and their harmonics. Without going into great detail, it is easy to see that with a waveform (almost) repeating itself at a fixed rate (line frequency) the spectrum will reflect this periodicity and consist of clumps of energy centred round harmonics of the line frequency. This can be proved without much difficulty, and observed with a spectrum analyser where it is found that the concentration of energy around line harmonics (multiples of 15.625 kHz) is very marked indeed.
The low frequency field rate components of the signal impose a microstructure on the spectrum, so that what appear to be homogeneous energy concentrations around line scan harmonics actually consist of spectral lines spaced at multiples of 50 and 25 Hz each side of the 15.625 kHz harmonic.
Many factors combine to define the exact shape of the spectrum of a video signal, but it is possible to make a reasonable qualitative and even quantitative estimates from observation of the picture. Thus, a picture with strong vertical detail (a white fence for example) will produce energy around high order harmonics of line frequency. If the picture is in sharp focus, the waveform will be have fast rise and fall times and will therefore have greater power in its higher harmonics than a blurred picture.
Repetitive detail with a strong horizontal bias gives rise to energy at very low frequencies, between DC and 15.625 kHz at multiples of 50 Hz. If the picture contains moving detail, this is reflected in the spectrum by a shift of some of the 50 and 25 Hz spectral lines.
Video signals differ markedly from that produced by an audio source. These differences persist when the tolerance of the signal to distortions is considered. Thus, tv signals can be subjected to peak-clipping as a matter of course without seriously degrading picture quality and they can suffer quite severe non-linear distortion again without loss of intelligibility. Distortions to which video signals are not tolerant are the various frequency-dependent effects. A small amount of high frequency loss is not too serious (it produces loss of detail horizontally), but phase distortion such as produced by a dispersive transmission medium is: whereas phase (or delay) distortion on a sound source is not detected by the human ear, differences in the arrival time of the various frequency components of the waveform corresponding to picture detail cause severe degradation of picture quality. An example might be 'ringing' following sharp transitions, which produces a series of vertical stripes of decreasing intensity to the right of the transition.
- It is interesting to repeat the bandwidth calculation for the old 405 line system.
- active line period = 80.7 µs
- number of active lines = 405 - 28 = 377
This gives a bandwidth of 3.11 MHz. This is almost the same as system bandwidth (3 MHz) and the Kell factor is 3/(3.1144) = 0.96.
This all means that the horizontal resolution of the 405 line system was better than it needed to be and, indeed, that it was better than that of the later (US) 525 line system.
- According to Arthur Dungate on his Alexandra Palace site, the 405 line service had an aspect ratio of 5:4 until 1950 when it was changed to 4:3. This would mean that the original Kell factor (when the system was designed in the mid-1930s) was 1.03, which was wasteful of bandwidth. 1930s electronic technology must also have been stretched unnecessarily by this. Can anyone shed light on why this was done? Was this just a result of imperfect knowledge of tv system design? Was it intended to allow a change the aspect ratio to something less square when CRT technology improvements allowed it? (which is presumably what happened). Let me know. The change in aspect ratio must have meant that people who already had a tv in 1950 needed to permanently reduce the picture height - which probably produced black bars top and bottom.
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