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I have been reading a couple of definitions on signal such as:

Any quantity measurable through time over space or any higher dimension can be taken as a signal.

And this,

In the physical world, any quantity exhibiting variation in time or variation in space (such as an image) is potentially a signal that might provide information on the status of a physical system

Taking human voice as example,

A sound signal is converted to an electrical signal by a microphone, generating a voltage signal as an analog of the sound signal, making the sound signal available for further signal processing. Sound signals can be sampled at a discrete set of time points.

enter image description here

I can understand where times comes in but where's the "space" come here according to the definition of signal?

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  • $\begingroup$ sampling in space instead of time is what they do with image processing. from the POV of an algorithm, the samples are just samples. the algorithm doesn't know or care if they were sampled from a function of time or a function of space or a function of some other independent variable. $\endgroup$ – robert bristow-johnson Apr 4 at 19:41
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My impression of your question is that you have a small misunderstanding here. In the definition it is not said time and space, a signal can vary in time or space. Some signals vary with time, as your example human voice that varies over time in air pressure (or equivalently voltage), some vary with space, like image and some vary with both time and space such as video. I feel, your misunderstanding in human voice example is that you believe there should be an space dimension too in the game.

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A beam former processes in time and space. As an example, a tv station broadcasts at some location that has a direction from the receiver. An antenna ( a beam former) pointed in that direction will enhance the broadcast and simultaneously attenuate broadcasts from other directions.

There are a lot of things that Signal Processing is applied to like graphs ( node edge graphs not graphs like plots) , DNA, ocean currents, brain signals, blood pressure and flow, stock prices, .....

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The "space" after the microphone is the space or dimension of the electric field, measured in Volts. Or, before the microphone, the space of atoms moving (in average aggregate) to form the pressure waves of sound, measured in Pascals. Or the vertical space of a graph where either can be plotted, as both change over time (usually the horizontal axis.) Or all of the above, and more, in some higher dimensional space.

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There's a hint in the text:

variation in space (such as an image)

An image does not vary over time, but it does vary over space. As such, it's a signal, which can be processed similarly to other signals such as a digital recording from a microphone. The difference is the microphone recording is a one dimensional signal over time, whereas the image is a two-dimensional signal over space.

For example, scaling an image to a smaller size is equivalent to reducing the sample rate (decimation) of an audio signal. Likewise, scaling the image to a larger size is equivalent to increasing the sample rate (interpolating). Likewise, high-pass and low-pass filters can be applied to images.

GIMP has a generic convolution matrix filter:

enter image description here

This is just a simple FIR filter where you can type in any coefficients you like.

Anything that involves waves propagating (sound, light, mechanical stress, radio waves, etc) also has a natural relationship between time and space. You could make an audio recording with a microphone in one position for one second. Or, you could put a large number of microphones in a line, about 340 meters long (because that's how far time travels in one second) and sample them all in the same instant. Either way, most signal processing techniques are applicable to either signal.

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