Electronic – How did the Telstar 525/405-line conversion system from 1962 work

For PAL, used in Europe, part of Africa, part of South America, Asia and Australia, the number of scan lines is 625. For NTSC, used in most of the Americas and Japan, the number of scan lines is also an odd number, 525. This answer discusses the latter, as I cannot find a definitive answer why PAL uses an odd number of lines.

The National Television System Committee (NTSC, established in 1940) recommended a frame rate of 30 frames (images) per second, consisting of two interlaced fields per frame at 262.5 lines per field and 60 fields (30 frames) per second. Other standards in the final recommendation were an aspect ratio of 4:3, and frequency modulation (FM) for the sound signal (which was quite new at the time).

When the standard for color television was approved, there was a slight reduction of the frame rate from 30 frames per second to 30/1.001 (approximately 29.97) frames per second.

Each frame is composed of two fields, each consisting of 262.5 scan lines, for a total of 525 scan lines, but only 483 scan lines make up the visible raster. The remainder (the vertical blanking interval) allow for vertical synchronization and retrace. This blanking interval was originally designed to simply blank the receiver's CRT to allow for the simple analog circuits and slow vertical retrace of early TV receivers. However, some of these lines may now contain other data such as closed captioning.

The actual figure of 525 lines was chosen as a consequence of the limitations of the vacuum-tube-based technologies of the day. In early TV systems, a master voltage-controlled oscillator was run at twice the horizontal line frequency, and this frequency was divided down by the number of lines used (in this case 525) to give the field frequency (60 Hz in this case).

For interlaced scanning, an odd number of lines per frame was required in order to make the vertical retrace distance identical for the odd and even fields, which meant the master oscillator frequency had to be divided down by an odd number. At the time, the only practical method of frequency division was the use of a chain of vacuum tube multivibrators, the overall division ratio being the mathematical product of the division ratios of the chain. Since all the factors of an odd number also have to be odd numbers, it follows that all the dividers in the chain also had to divide by odd numbers, and these had to be relatively small due to the problems of thermal drift with vacuum tube devices. The closest practical sequence to 500 that meets these criteria was 3 × 5 × 5 × 7 = 525.

This diagram show both the visible lines and the horizontal and vertical retrace lines. I was not aware the latter zigzagged back and forth, but have seen that on a couple of independent diagrams.

Note the half-lines, starting at the top for the odd field and ending at the bottom for the event field.

Here is a good website that describes interlaced scanning in much more detail.

I'm assuming you are trying to get a bode plot which shows the magnitude and phase response you would get if you were to test the the system by slowly sweeping the frequency a constant amplitude sine wave input and measuring the output amplitude and phase at various points.

If this is the case then there is only one frequency \$ \omega \$. Now we know that \$ e^{j \theta} = \cos(\theta) + i \cdot sin(\theta)\$.

You can therefore treat each exponential term as a vector with amplitude and phase and add them as vectors.

Note however, that if you compare the results with a real digital filter you will not get exactly the same result because the digital filter is only taking measurements at certain instants in time (the sampling frequency) and the data is quantised. However providing the sampling frequency is much larger than the frequency of interest it is a reasonable approximation.