Linear Interpolation listed data points on to anothe list

I have range of measurments as shown

x_data = (0.7127, 0.6954, 0.6789, 0.6744, 0.6697, 0.6649, 0.6600, 0.6551, 0.6501, 0.6450,

0.7127, 0.7091, 0.6988, 0.6827, 0.6626, 0.6574, 0.6520, 0.6466, 0.6411, 0.6356,

0.6300, 0.6245, 0.6190)

I want to interpolate (linear) the above x data on to new unformly spaced z value given by:

z_new = 0:10/6371:0.244

Given that the x list has differnet length than the new data (z) how do we do this interpolation?

I tried this from mathworks online but not working:

"vq = interp1(x,v,xq) returns interpolated values of a 1-D function at specific query points using linear interpolation. Vector x contains the sample points, and v contains the corresponding values, v(x). Vector xq contains the coordinates of the query points"

Thank you

Answer 1

[Image Analyst]

You're mixing up x_data, x, z_new, and v. I think the nomenclature is confusing you. Try this:

x_data = [0.7127, 0.6954, 0.6789, 0.6744, 0.6697, 0.6649, 0.6600, 0.6551, 0.6501, 0.6450,...
0.7127, 0.7091, 0.6988, 0.6827, 0.6626, 0.6574, 0.6520, 0.6466, 0.6411, 0.6356,...
0.6300, 0.6245, 0.6190];
x = 1 : numel(x_data);
v = x_data;
subplot(2, 1, 1);
plot(x, v, 'b.--', 'LineWidth', 2, 'MarkerSize', 20)
grid on;
xlabel('Index', 'Interpreter','none');
ylabel('x_data', 'Interpreter','none')
% This z_new is no good since the interpolation x values are
% not in the range of x_data indexes.
z_new = 0:10/6371:0.244; % BAD!
size(z_new)

ans = 1×2

1 156

% Let's use a z_new that goes from the first index
% to the first index + 0.244, in other words in the range [1, 1.244]
% And since the original z_new had 156 points, let's use 156 points
% with the new z_new.
z_new = linspace(1, 1.244, 156);
vq = interp1(x,v,z_new);
subplot(2, 1, 2);
x = 1 : numel(vq);
plot(x, vq, 'r-', 'LineWidth', 2)
grid on;
title('vq', 'Interpreter','none');
xlabel('Index', 'Interpreter','none');
ylabel('Interpolated x_data', 'Interpreter','none')

If that is not the interpolation region you want, feel free to set the z_new range anywhere from 1 to 23 (which is the number of elements in x_data).

[root]

Thanks The znew values should range from 0 to max(x) with steps of 10/6371. (sorry I entred 0.244 above which is not correct).

can we still get interpolated x values on this new z range using the above x_data?

[Image Analyst]

I'm not sure what is x and what is y with your data. I'm assuming the x value is the index and the y value is the badly-named x_data. So you can then get new x_data values between any indexes if you know what indexes you want to go between. There is no value of 0 for either the index or a value of x_data. Zero is not in the range that x_data covers. So exactly what indexes do you want to find/interpolate between?

[root]

Thanks for your clarification .

The data to be interpolated is the given x_data. I want to interpolate this on znew where znew has a value if 0:max(x_data) with stepsize of 10/6371.

[Image Analyst]

That does not make any sense. Please show on a numberline or a graph the actual x_data points, and the values for which you want interpolated as your output. Keep in mind that any points specified outside the range of your input data will be NaN.