I want to make a linear interpolation a cubic spline of the second order interpolation. How?

Here is my current code. What do I need to do in order to use the cubic spline interpolation?

% Close all open figures, clear the workspace of all existing variables,
% and blank the command window
close all; clear all; clc;

% Read the data
a=dlmread('Ethanol_05273.txt');
alpha_x=a(873:2048,1)/1000;
alpha_y=a(873:2048,2);

% Visualise the data
plot(alpha_x,alpha_y); grid on;

% FFT the data without windowing
alpha_x_f=10000./alpha_x;
F=linspace(min(alpha_x_f),max(alpha_x_f),1024);
alpha_y_f=interp1(10000./alpha_x,alpha_y,F,'pchip');
FT=fft(alpha_y_f);
figure;
plot(abs(FT));

% Apply a Hanning window before FFTing the data

% Create a Hanning weights vector of the size of the alpha_y_f vector. Note
% that the apostrophe (') just transposes the w vector
w = hann(length(alpha_y_f))';
% Visualise the Hanning weights (just for info)
figure; plot(w); title('Hanning window');
% Apply the Hanning weights, pointwise, to alpha_y_f
alpha_y_f_windowed = w.*alpha_y_f;
% Just for info, visualise the 'windowed' and 'non-windowed' data
figure; hold all;
plot(F,alpha_y_f,'red'); plot(F,alpha_y_f_windowed,'blue');
legend('non-windowed','windowed');
% FFT the 'windowed data'
FT_windowed=fft(alpha_y_f_windowed);
% Plot the FFT of the windowed data
figure; plot(abs(FT_windowed)); title('Hanning windowed FFT');

Answer 1

[KSSV]

Read about spline. https://in.mathworks.com/help/matlab/ref/spline.html

[Paul Clarkson]

I'm new to matlab and don't know where this would be applied. I know it would be in place of interp1 but which arguments I need to put in what places for the function.

Answer 2

[Star Strider]

My guess is that you refer to this assignment:

alpha_y_f=interp1(10000./alpha_x,alpha_y,F,'pchip');

so to use a spline interpolation instead, use 'spline' as the ‘method’ argument.

However for signal processing purposes (that you appear to be doing), I prefer the Signal Processing Toolbox resample (link) function, since it incorporates an anti-aliasing filter. Then do the fft.