Obtain square arrays NxN with increasing N and represent on a
graph on a semilogarithmic scale (only the ordinates) as N varies the time taken ad
run DCT2 with your homemade algorithm and library algorithm.

The times should have been proportional to N^3 for the homemade DCT2 and to N^2 for the version
fast (more precisely to N^2 * log (N)). The times obtained with the fast version could have
an irregular trend due to the type of algorithm used.

Second part

Write software that performs the following tasks:

• Create a simple interface so that the user can choose from the lesystem
  a .bmp image in shades of gray;

Allow the user to choose:

• an integer F which will be the width of the window in which DCT2 is executed;
• an integer d between 0 and (2F-2) which will be the cutoff threshold of the frequencies.
• divide the image into square blocks f of pixels of size FxF starting
  top left, discarding leftovers;

For each block f carry out the following operations:

• apply DCT2 (from the library): c = DCT2 (f);
• delete frequencies c_kl with k + l >= d (I am assuming that frequencies start from 0: if d = 0 I delete them all, if d = (2F-2) I delete only the most high, i.e. the one with k = F-1, l = F-1).
• apply the inverse DCT2 to array c as modified: ff = IDCT2 (c);
• round ff to the nearest integer, set negative values to zero and 255 those greater than 255 in order to have admissible values (1 byte);
• recompose the image by putting the ff blocks together in the right order.
• display on the screen side by side: the original image and the image obtained
  after modifying the frequencies in the blocks.

Missing to recompose the matrices.
For practical and delivery reasons I divided the MxN matrix into many blocks of FxF size, now the problem is to create a function that recomposes the matrix to be MxN (starting from the list of blocks).
The list of blocks is just a list of matrix. The block were created from left high.

Create a simple interface so that the user can choose from the file system a .bmp image in shades of gray.

Allow the user to choose:

• an integer F which will be the width of the window in which DCT2 is executed;
• an integer d between 0 and (2F - 2) which will be the cutoff threshold of the frequencies.