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Sampling -in general- is the process of reading values from a continuous "stream", at discrete time steps, most often with purpose to recreate the original stream as accurately as possible.
Continuous "stream" means that the values are arranged in a smooth way within time (assume that the independent variable is time for now), in such a way, that no matter how small time interval you consider, there is always a piece of the stream emitted within that interval, even if it degenerates to a signal value (for a single infitesimal instant)

By "graph sampling", I understand the process of sampling the graph of a function with respect to its "x", its independent variable.

By "time sampling", I understand the above process for any function, where "x" represents time.

Sampling is used wherever you want to digitally re-create an accurate version of an original analog stream. E.g., a vinyl disc playing, produces a continuous stream of voltages that are sent to the speakers and are turned into air pressure, the sound. To recreate that stream in digital, one should sample the function of voltage over time, and play them back, in the right timing.

Useful terms:
Sampling resolution: the data size occupied by a single sample. The bigger the better, since you can represent a wider range of values, or at better resolution.

Sampling frequency: the number of samples "extracted" from the stream per second. Obviously: the more, the better! This is counted in Hertz (Hz)

Nyquist frequency: the maximum frequency that can be reproduced by the digital version of the stream, and it is exactly the half of sampling frequency.

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