Manual calculation of fourier and inverse fourier transform

You can use this code to manually find fourier transform and inverse fourier transform (without using fft and ifft by matlab) for both 1D/2D

For the Fourier Transformation:

x is the arbitrary vector that you can set.

x_fourier is the fourier transform by matlab function fft.

A is the fourier transform by manual calculation/DFT algorithm. A will match with x_fourier.

Similarly, y is the arbitrary matrix that you can set.

y_fourier is the fourier transform by matlab function fft2.

B is the fourier transform by manual calculation/DFT algorithm. B will match with y_fourier.

For the Inverse Fourier Transformation:

Inverse_A and inverse_B are the inverse fourier transformation, calculated manually for 1D and 2D, respectively. They should match with x and y, respectively.