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DC restoration of an AC coupled video signal can be performed by clamping to some reference voltage, during the horizontal sync periods of the video. This all seems fine in a running system, when the hsync is detected, clamp to the reference for a short time and everything runs smoothly.

My question is: How is the first sync detected?

Without having DC restored the signal when the circuit starts operating, isn't the ADC's output unreliable, hence the sync pulses can't be detected?

In fact, the input to the ADC may well be out of specification: Consider the case of driving an AD9200, with a 1v peak to peak AC coupled video signal. The absolute minimum voltage of the analog sense pin (relative to analog ground) in this chip is -0.3v, with an unrestored video signal isn't it quite possible that a -0.5v is present on the analog sense pin? This could be prevented by adding a diode to ground to maintain a positive difference between ground and the analog sense pin; is this commonly done?

For reference there exist ICs to perform sync detection, for example the LM1881. Is it necessary to use one of these ICs or equivalent circuitry to detect sync pulses prior to any ADC, or can a more simple solution help with the clamp-bootstrapping?

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You're over-thinking this.

The Wikipedia article on Analog television has a lot more detail, but basically the sync pulses are the most negative (or most positive if the signal is inverted) voltage that appears at any time. Therefore, a simple peak-detector circuit is all that is needed to find them, and a "slicer" (comparator) separates them from anything else in the video stream by establishing a threshold that is slightly below the peak.

This dates from the early days of analog broadcast TV, where the AGC circuits depended on the sync pulses of the inverted video signal being at a constant (maximum) level, regardless of the actual video content.

Once you have sync, it is straightforward to sample within the front/back porch intervals to get the reference black level.

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