Assume a one-dimensional image (or signal) f = [1 4 6 8 75 3], (at points...

Transcribed Image Text:

Assume a one-dimensional image (or signal) f = [1 4 6 8 75 3], (at points i = 1, ..., 7). a) Explain what linear interpolation means. Sketch the linear interpolation Fin(x) of f for 1 ≤ x ≤7. Is Flin (2) continuous? Is Flin (2) differentiable? b) The interpolation can be expressed using the following equation 7 g(x) = Fg(x) = g(x-i)f(i). = where the function g(x) is different for different types of interpolation. Which function g(x) correspond to linear interpolation? c) Let g(x) be defined as i=1 |-|2|² if || ≤ 1, -2x³10x2 16x+8 if 1 < x≤ 2, if x > 2. (1) - Plot g(x), -3 ≤ x ≤ 3. Plot the interpolation F(x) of the function f using this g(x) for 1 ≤ x ≤ 7 (e.g. using Matlab for the calculations). Is F(x) continuous? Is F,(z) differentiable? (Here you need to have an argument that is better than you can see it in the graph"). Assume a one-dimensional image (or signal) f = [1 4 6 8 75 3], (at points i = 1, ..., 7). a) Explain what linear interpolation means. Sketch the linear interpolation Fin(x) of f for 1 ≤ x ≤7. Is Flin (2) continuous? Is Flin (2) differentiable? b) The interpolation can be expressed using the following equation 7 g(x) = Fg(x) = g(x-i)f(i). = where the function g(x) is different for different types of interpolation. Which function g(x) correspond to linear interpolation? c) Let g(x) be defined as i=1 |-|2|² if || ≤ 1, -2x³10x2 16x+8 if 1 < x≤ 2, if x > 2. (1) - Plot g(x), -3 ≤ x ≤ 3. Plot the interpolation F(x) of the function f using this g(x) for 1 ≤ x ≤ 7 (e.g. using Matlab for the calculations). Is F(x) continuous? Is F,(z) differentiable? (Here you need to have an argument that is better than you can see it in the graph").

Answer rating: 100% (QA)

The question youve presented relates to signal or image interpolation particularly focusing on 1dimensional linear interpolation and a different metho... View the full answer