I stand corrected. First, I did find a reference to Pixel Aspect Ratio (PAR) and down sampling uncompressed NTSC video in the joint Forensic Imaging and Multi-media Glossary (PDF) published by the IAI and LEVA, the final version of which was released in July, 2006. Second, in an effort to simplify this discussion, I’ve over simplified the Interpolation Methodology I described in Part 2. I will be expanding on that in this post, in far more detail than I had originally intended.

Those of you who have been doing Forensic Video & DME Analysis since analog was the dominant video format, may recall being taught Aspect Ratio correction a couple of different ways. Unquestionably, Aspect Ratio correction is one of the most convoluted concepts and processes, frequently misunderstood by not only equipment manufacturers and hardware/software engineers, but also by the very people who wrote many of the related standards! In other words, many people far smarter than I have gotten it wrong, and still do. Fortunately, there are other folks far smarter than I that have gotten it right, such as Chris Pirazzi of LurkerTech.com, who wrote the uncompressed Y’CbCr Video format for Apple QuickTime.

Interpolation Methodology (Updated from Part 2)

In Part 2 I described an interpolation methodology stating that down sampling was the proper way to correct Aspect Ratio. This is a very simplified approach to a very complex topic, which technically is incorrect for PAL/576i sources; my apologies for overlooking our friends from across the pond(s). Let me start over and accommodate PAL as well, which is going to require going a little deeper.

First, as previously stated, it’s important to understand that the ITU Rec. 601 standard specifies 720 luminance samples for both uncompressed NTSC and PAL. Of those 720 samples, only approximately 704 contain visual information. ITU Rec. 601 also specifies a luminance sampling frequency of 13.5 MHz. It does NOT specify the Pixel Aspect Ratio.

Later, Analog-to-Digital (A/D) converters came along, to convert analog video lines into a series of square pixels. For these devices, the industry adopted 12 3/11 MHz (a.k.a. ~12.273) and 14.75 MHz as the luminance sampling rates for square pixel 480i (NTSC) and 576i (PAL) video signals, respectively.

So, if we sample non-square at 13.5 MHz, and square at either 12.273 (NTSC) or 14.75 (PAL), we can now calculate the PAR of ITU Rec. 601 non-square pixels. We do so using the following equation: Square Pixel Sampling Frequency ÷ Non-square pixel Sampling frequency = Pixel Aspect Ratio (non-square).

PAR for 480i NTSC: 12.273 ÷ 13.5 = 0.909 (10/11)
PAR for 576i PAL: 14.75 ÷ 13.5 = 1.092 (59/54)

Great, so we now have our PAR info. Using the SAR x PAR = DAR equation, we can now do some more math.

NTSC 480i Uncompressed: 720/486 = 1.48 SAR. 1.48 (SAR) x .909 (PAR) = 1.345 (DAR)
PAL 576i Uncompressed: 720/576 = 1.25 SAR. 1.25 (SAR) x 1.092 (PAR) = 1.365 (DAR)

Did you notice that neither equate to a DAR of 4:3 (~1.33)?  Right, that’s because we need to crop to accommodate the non-visual information from each video line. I’ll expand on that later. Let’s look at a few other examples though.

NTSC DVD-Video 480i: 704/480 = 1.467 SAR. 1.467 (SAR) x .909 (PAR) = 1.333 (DAR)
PAL DVD-Video 576i: 704/576 = 1.222 SAR. 1.222 (SAR) x 1.092 (PAR) = 1.334 (DAR)

Now we're getting somewhere. How about a few more.

SIF NTSC: 352/240 = 1.467 SAR. 1.467 (SAR) x .909 (PAR) = 1.333 (DAR)
SIF PAL: 352/288 = 1.222 SAR. 1.222 (SAR) x 1.092 (PAR) = 1.334 (DAR)

"Um, why not just use the stored pixel matrices to solve for PAR? You know, PAR = DAR/SAR. Wouldn't that be much easier?"   Yes, yes it would, but it's also one of the many, many reasons we have so much confusion about PAR.

Remember, analog video doesn't have pixels. ITU Rec. 601 is the foundation of the non-square pixel, but it doesn't tell us the full story. A/D converters standardized on square pixel sampling rates of 12.273 MHz for 480i (NTSC) and 14.75 MHz for 576i (PAL). To accurately define the actual shape of the non-square pixels, we need to use the luminance sampling rates for square and non-square 480i/576i in the PAR = DAR/SAR equation to properly convert, as shown above. A few references that you may find helpful:

Wikipedia - Pixel Aspect Ratio, Inconsistency in defined pixel aspect ratio values
LurkerTech.com - Square and non-square pixels

The most important part of this convoluted discussion, IMHO, is to understand the two PAR values of .909 (NTSC) and 1.092 (PAL). These carry through to all of the other non-square pixel based standards I mentioned previously, such as DVD-Video, DV, and SIF. It’s also very important that when we correct Aspect Ratio we always maintain the sampled number of lines, which I’ve mentioned in prior posts as well.

In the next post I’ll discuss the cropping issue mentioned earlier with the uncompressed examples, show some more math (woo hoo!), discuss field & sample doubling, and maybe even try to come up with a way to wrap this series up. Wish me luck! Be safe out there my friends.