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while I was sitting in city center with so many LED (especially red ones mounted) signboards and I was bitting an apple, the signboards suddenly begin to shake for only a second while my head is shaking.

I couldn't understand why this had happened to my eyes? Maybe the XTALs in the LED-driver-circuits are out of the frequency because of high voltage or so many times these are used, and/or grid's frequency has been added on to the device.

What should be done to prevent this frequency shake?

Is this topic belongs to harmonic distortion - THD ? That maybe a reason by XTAL's frequency?

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The signboard LEDs are multiplexed, meaning that each is on for only a very brief time in sequence. Your eye-brain system fuses the flashes together if they are closely enough spaced but if your head is moving relative to the board the flashes can break up into individual dashes or dots.

The multiplex rate is a design decision of the signboard manufacturers. They could make it so fast that this would not (practically) happen.

A variation on this is to take an old-school analog oscilloscope with a trace time of maybe tens of milliseconds. The scope has a dot of light that moves from left to right faster than you can perceive so it looks like a horizontal line. Whack yourself on the top of your head and you'll see the impulse response of your eyes.

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    \$\begingroup\$ +1. Bonus points for "Whack yourself on the top of your head and you'll see the impulse response of your eyes. ". That's a wonderful technical reason to whack a drowsy student during lab classes! :-) \$\endgroup\$ Commented Aug 16, 2015 at 16:59
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The LEDs on the sign are multiplexed to save power and I/O pins, as well as keep circuit wiring complexity down. As a result the LEDs flash quickly, usually row by row or block by block. They flash so quickly that you can't see them blink... Until you start eating an apple or use an electric brush. In that case your head / eyes move ever so slightly an different parts of the sign image are displayed at a slightly different position on your eye.

It is pretty much how a film projector or TV works, by quickly changing the image, you perceive it as motion.

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  • \$\begingroup\$ How does it save power? \$\endgroup\$ Commented Aug 16, 2015 at 16:57
  • \$\begingroup\$ @SpehroPefhany lower pin count in controllers, fewer I/O ports, fewer active components controlling the LEDs. \$\endgroup\$
    – jippie
    Commented Aug 16, 2015 at 17:16
  • \$\begingroup\$ Also isn't every LED on for a shorter time than if each were powered on for the full duration? That should save some energy... \$\endgroup\$
    – BenG
    Commented Aug 17, 2015 at 3:13

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