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Signal is something that carries information. Usually, something is a pattern of variations of physical quantity that can be manipulated, stored, or transmitted by a physical processes. I am wondering that how image can be a signal. Ok, it is stored, manipulated, transmitted digitally, but how it can carry variations? Also how video can be kind of a signal?

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A signal doesn't have to be a single quantity; the variation doesn't have to happen along a single axis, either.

An image is information (e.g. brightness) varying in two dimension (e.g. along a X- and a Y-axis).

Simple as that; counts both for digital and analog images.

That information that changes might be one-dimensional (e.g. only brightness for a black and white / grayscale image), or multidimensional (e.g. red, green, blue for a color picture).

Video is information varying in three dimensions: two dimensions like an image, and time as third dimension.

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To build on Marcus's answer, when we have multidimensional data (e.g., stereo audio, video images), we often want to transform it into a one-dimensional signal so that we can transmit it over a single wire or as a radio signal.

There are many ways to do this. For example, with stereo audio, we translate one of the channels1 to a different range of frequencies and then add it to the other channel. This creates a single signal that can be transmitted and then decoded to produce the original two channels of audio. The general term for this is "frequency-division multiplexing".

For video, we take a different approach. We sample the pixel data in time, and then serialize all of that data (i.e., send pixels one at a time) into a high-bandwidth channel, combining the data with synchronization signals that allow us to keep track of where each data item belongs in the image. Again, this one-dimensional signal can be transmitted over a wire or over the air. The general term for this is "time-division multiplexing".


1 I'm ignoring the details of sum and difference processing for simplicity.

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