[1] Signal sampling representation.
The continuous signal S(t) is represented by a green colored line while the discrete samples are indicated by the blue vertical lines.
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Sampling (signal processing)
Sampling (signal processing)
[1] In signal processing, sampling is a continuous-time signal's reduction into a discrete-time signal.
discrete: individually separate and distinct
An example is a soundwave's conversion to a sequence of "samples".
A sample is the signal's value at a point in time/space; a definition that differs from the term's usage in the field of statistics, that refers to a set of such values.
A sampler is a device/operation extracting samples from a continuous signal. A theoretical ideal sampler makes samples equivalent to a continuous signal's instantaneous value at the desired points.
An original signal can be rebuild via a sequence of samples, up to the Nyquist limit, by passing the sequence of samples into a reconstruction filter.
The Nyquist limit is the max frequency/velocity that's accurately measured in a digital system, defined as half the sampling rate (Pulse Repetition Frequency or PRF in Doppler)
Theory
Theory
[1] Functions (as in math) of space, time, or any other dimension can be sampled, and akinly in 2+ dimensions. I.e., In Nyquist context:
E.g., In 1D: f(t) = temperature at time t; sample per second
At position (0,0): brightness = 200
At (0,1): brightness = 210
At (1,0): brightness = 190
E.g., In 2D: f(x, y) = brightness at position x, y; image
At time 0 s: volume = 0.5
At time 0.1 s: volume = 0.7
At time 0.2 s: volume = 0.3
E.g., In 3D: f(x, y, z) = density at all point in a volume for a brain's MRI/CT scan tissue x, y, z;
Sample per 1 mm in x-direction
Sample per 1 mm in y-direction
Sample per 2 mm in z-direction (slices)
References
References
[1] Wikipedia
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