# 2D Fourier transform for surface fitting

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Sangani Prithvi on 3 Sep 2021
Commented: Image Analyst on 4 Sep 2021
I'm having a scattered x,y,z data and I'm looking for the Fourier series which can fit the scattered data forming a surface. Can anyone suggest any good method that can be adopted for this. I've tried using fft2 but the data is very random, the amplitude and phase spectra are very difficult to be interpreted.

Image Analyst on 3 Sep 2021
Did you try making your data into an image with scatteredInterpolant and then calling fft2, and then zeroing out the high frequency components, then inverse transforming. I've attached some demos that might help.
Sangani Prithvi on 4 Sep 2021
Thanks for the response. I'm trying to actually denote the 'z' values as the function of 'x' & 'y' values in trigonometric functions (like Fourier series). I tried to interpret the data, but I'm not able to find the amplitudes and phase angle to convert the data into Fourier series.
Image Analyst on 4 Sep 2021
What's the function? Like sin(x) + cos(y) or something? Should be just a few lines of code if you use meshgrid to get a list of all (x,y) locations.
x1 = linspace(0, 5*pi, 400);
y1 = linspace(0, 3*pi, 300);
xPeriod = 2;
yPeriod = 2.4;
amplitude = 5;
[x, y] = meshgrid(x1, y1);
z = amplitude * (sin(2 * pi * x / xPeriod) + cos(2 * pi * y / yPeriod));
surf(x, y, z, 'Lines', 'none');
grid on;