is it possible to a read the code from an infrared remote controller using a digital camera?

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I'm thinking about a simple ceiling fan controlle. A phone camera does "see" the bursts of IR light, is there any Android application to translate it to the hexc code that I could use to make a copy of the controller (or use the phone itself for the task, equipped with an IR emitter)?

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As far as I know, there aren't any apps that do this. You see, trying to read a beam of IR among all the visible light on a camera feed might be easy for us humans, but for a machine to understand it as "data", you'd have to tell it where to look and how does "that" look. For short, you'd need to create analysis algorithms or add some filtering to the light being processed. Other than that, I am not sure one could manually create a scanning routine that could process data as fast as an IR interface does. If you are talking ON/OFF, then cool, that might be doable.

I know, because I already tried. XD

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Even if the camera does see IR light (I belive this is not a very good camera since your photos would look weird where the objects are warmer) I believe this is not possible, since the IR transmissiotn is a matter of standards (https://en.wikipedia.org/wiki/Infrared_Data_Association), and the remote device transmits the data in respect of the standard of physical layer of protocol stack, so you will not be able to receive the accurate data from your cam.

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I think, that a normal camera will not take enough pictures per second to recognize the bits of a ir signal. What camera do you want to use?

The 36 kHz carrier frequency was chosen to render the system immune to interference from TV scan lines. Since the repetition of the 36 kHz carrier is 27.778 μs and the duty factor is 25%, the carrier pulse duration is 6.944 μs. Since the high half of each symbol (bit) of the RC-5 code word contains 32 carrier pulses, the symbol period is 64 x 27.778 μs = 1.778 ms, and the 14 symbols (bits) of a complete RC-5 code word takes 24.889 ms to transmit https://en.m.wikipedia.org/wiki/RC-5