- Interpolation
It is estimating the value between two known values.
- Extrapolation
It is estimating a value at an external location outside the range.
- Linear Interpolation
A method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.
- Formula
d1 : The distance from x to x1.
d2 : The distance from x to x2.
If the distance ratio is normalized,
α = d1/(d1+d2), β = d2/(d1+d2)
so that the sum is 1,
(α + β = 1)
it can be simplified as follow.
https://darkpgmr.tistory.com/117
- Bilinear Interpolation
A method that uses the distance weighted average of the four nearest pixel values to estimate a new pixel value.
1) Find the x-axis and y-axis distance ratios between the four points 6, 9, 10, 12 and (5,5).
2) The values of P and Q are obtained by applying linear interpolation to the x-axis.
3) Apply linear interpolation to the y-axis to find the value of (5,5) from P and Q.
https://blog.naver.com/aorigin/220947541918
- ZOH(Zero-order Hold Interpolation)
Real systems do not produce sample data and nor is the input to a real system a series of impulses. So what we need to do next is consider the interconnection between a computer world with sampled signals and a real world with continuous systems.
It is one thing to give a pictorial representation of how to connect the discrete and continuous worlds.
'Hold' means the most recently received value.
If a computer outputs a series of impulses as below, ZOH converts output into a staircase.
For instance, we keep the most recent value until we receive a new value, as this approximates to repeated small steps. So your reconstructed signal is a bit like a staircase.
From a physical arrangement point of view, a zero hold is implemented as in the figure below.
 U(z) : the discrete signal U(s) : a continuous time signal, it gives us the staircase or pseudo continuous G(s) : the real system Y(s) : continuous output |
- Combine all the elements together leads to an information flow as below.
It computing component handles the discrete information.
- Mathematical formulation
 * : the sampled signal A/s : constants e-nT : action being active from a given point by delays T : a rectangular wave y*(0) : being the value H(s) : it gives us the staircase for a single impulse subtract (1/s) from (e-sT/s) as below.  Then, the result is this, naught and T.  |
reference : https://www.youtube.com/watch?v=vnhAG5NiYqM&t=304s