Interpolate 1-D data using the FFT method and visualize the result.

Generate some sample points in the interval $$[0,3\pi ]$$ for the function $$f(x)={\sin }^2(x)\cos (x)$$. Use a spacing interval dx to ensure the data is evenly spaced. Plot the sample points.

dx = 3*pi/30;
x = 0:dx:3*pi;
f = sin(x).^2 .* cos(x);
plot(x,f,'o')

Use FFT interpolation to find the function value at 200 query points.

N = 200;
y = interpft(f,N);

Calculate the spacing of the interpolated data from the spacing of the sample points with dy = dx*length(x)/N, where N is the number of interpolation points. Truncate the data in y to match the sampling density of x2.

dy = dx*length(x)/N;
x2 = 0:dy:3*pi;
y = y(1:length(x2));

Plot the results.

hold on
plot(x2,y,'.')
title('FFT Interpolation of Periodic Function')

Generate three separate data sets of normally distributed random numbers. Assume the data is sampled at the positive integers, 1:N. Store the data sets as rows in a matrix.

A = randn(3,20);
x = 1:20;

Interpolate the rows of the matrix at 500 query points each. Specify dim = 2 so that interpft works on the rows of A.

N = 500;
y = interpft(A,N,2);

Calculate the spacing interval of the interpolated data dy. Truncate the data in y to match the sampling density of x2.

dy = length(x)/N;
x2 = 1:dy:20;
y = y(:,1:length(x2));

Plot the results.

subplot(3,1,1)
plot(x,A(1,:)','o');
hold on
plot(x2,y(1,:)','--')
title('Row 1')

subplot(3,1,2)
plot(x,A(2,:)','o');
hold on
plot(x2,y(2,:)','--')
title('Row 2')

subplot(3,1,3)
plot(x,A(3,:)','o');
hold on
plot(x2,y(3,:)','--')
title('Row 3')