A+Brief+Frequency+Analysis

In this experiment I produced frequency spectra, hoping to prove that the 1080-line vertical sampling frequency is the cause of the inter-line anomaly found by Andrew Browne.

As 1080 is not an exact multiple of the number of TV lines in the film recording, this must mean that some of the HD lines will be composed of a partial mixture of two of the original SD scan-lines. Also the mixture will vary as you move down the frame.

If the thin black boundary between two of the original TV lines is being merged into some of the HD lines, then this could cause every other line to appear dimmer, as has been observed. (However this should affect every other HD line, not every other TV line.) It could also cause the hue errors manifested as apparent excess V-gain, by partial mixing of U and V amplitudes between adjacent lines.

I've produced this frequency spectrum of Andrew Browne's image: The lowest frequency spike corresponds to Fsc, with a smaller spike at roughly 2*Fsc. This could be an additive beat frequency produced by adjacent scan lines partially merging.

The next set of spikes are beat frequency pairings formed between the horizontal sampling frequency and Fsc (as well as 2*Fsc).

These then repeat harmonically at double, triple, quadruple the sampling frequency, etc...

Now lets rotate the image through 90 degrees, and look at the frequency spectrum in the columns: The lowest spike here is the frequency formed between (for the sake of example) line 1 and line 9 (i.e. scan-lines not HD lines!), and represents Andrew Browne's 8-line sequence.

The next spike up is the frequency formed between lines 1 and 3, and is at four times the frequency of the lower spike.

Above that you have a set of beat frequency pairs between the above two spikes and the vertical sampling frequency. Then the harmonic repetition as before.

The line-structure frequency itself seems to be indiscernible.

I draw several conclusions from this:

1) The beat frequencies may partly obscure the line structure.

2) The sampling frequency appears to be higher than it should be relative to the inter-line frequencies. I suggest this is caused by the true inter-line frequencies being obscured and smeared out by the relatively low sample rate.

3) The sample rate is clearly not an exact multiple of the scan-line rate, as expected.

4) The frequency formed between lines 1 and 3 seems to prove that one field is dimmed relative to the other.

I also analysed one of Andrew Steer's images: Here we see a spike at Fsc, above which is a barely discernible spike at 2*Fsc (probably an additive beat frequency caused by inter-line merging as before). Then a beat frequency pair centred around 9*Fsc (approximately). This must be the Fsc beating with the horizontal sampling frequency.

In this case I have also filtered out the chroma, to reveal the high frequency patterning caused by the beat frequencies. (I.e. the filtered image is shown in the upper left quadrant only).

I suspect you would get a stronger peak at 2*Fsc if the whole image were analysed. Certainly I found a more obvious peak when I analysed part of the SD sample image, as below: This would seem to prove that inter-line merging is occurring.

On a final note, I wonder if it would be possible to detect the CRT spot wobble frequency, if you sampled horizontally at a higher resolution? If so, you could use this as a reference to reconstruct horizontal geometry across the whole image, and not just the coloured areas.

Alex Weidmann 17/4/08

I've done some further tests today, following the points raised in the discussion of this page, and I think I've solved Andrew Browne's anomaly.

Below you can see a frequency plot for the columns in the Andrew Steer image I looked at last time (i.e. have rotated it through 90 degrees for ease of analysis). I have applied a band-pass filter, isolating the wavelength formed at 15-HD-lines, corresponding to the 8-SD-line repetition of the chroma signal.

As you can see this frequency forms a diagonal criss-cross pattern. Let's call it frequency F.

Now when the HDCAM does it's horizontal down-sampling, it mixes adjacent columns. Therefore it forms an additive beat frequency at 2F, which doesn't show up in my frequency plot for reasons we will see later.

So now we have F and 2F in each column where there is chroma.

Then the HDCAM mixes the columns again when it up-samples on output. Therefore you get new additive beat frequencies formed at 3F and 4F, and these both show up in my graph.

Below you see a band-pass filter isolating the frequency at 3F:

As you can see this is in a diagonal criss-cross formation. When this criss-cross pattern is in sympathy with the chroma dot patterning, it amplifies the chroma dots; but where it is in opposition, it depresses them. The net result of this is to produce a 7.5-HD-line modulation down each column, resulting in horizontal banding across the frame.

In other words the diagonal nature of the chroma dot pattern essentially cancels out the diagonal nature of 3F, forming horizontal banding.

Finally I've isolated the frequency at 4F.

This produces horizontal banding with a period of 3.75-HD-lines, such that every other SD-line from the original footage is depressed. Thus it appears as if one of the interlaced fields is darker; but in fact this just results from the beat frequencies.

I think the horizontal nature of the banding results from the diagonal formations cancelling each other out at some point in the beat frequency-forming process. It implies that 2F is mixing with 2F' to form 4F (where 2F' is in anti-phase with 2F). This makes sense, since adjacent columns would have 2F roughly in anti-phase on the HDCAM upscaling. Thus 2F would almost cancel with 2F' on the upscaling, and 2F would virtually disappear from the fequency spectrum.

Aranged symmetrically around 15F you see a set of sum and difference beat frequencies, formed between the vertical sampling frequency and the base-band frequency spikes at F, 3F and 4F. It's position at 15F confirms the scaling I have used above.

It should be noted that, while this aliasing may be helpful in separating out the two fields; it's not at all helpful in extracting the embedded chroma information. You're only getting a good chroma signal every 7.5 HD-lines, and the colour information on the intervening lines is being lost, including virtually all of the chroma information from field 2. Hence you have a loss in both vertical and temporal chroma resolution.

Also the U and V carriers' maxima are only 2 HD pixels apart horizontally: so by compressing the horizontal axis and expanding it again, there's likely to be some mixing of the U and V signals.

Alex Weidmann 21/4/08