I apologize in advance: since I am not a mathematician, maybe my question is not well defined, but I hope that some of you will still understand my meaning.
Given a 2D matrix, or an image of dimensions w1,h1.
I preform a DCT 2D transform on the image (DCT = DCT type 2).
I get a 2D result matrix. (This matrix has two frequency axes - x,y. I guess that you can define a "combined" frequency by multiplying x and y).
Now I do a slight cropping of the image. The new dimensions are w2,h2. Slight cropping means that I delete rows and/or columns, but not more than 10% of the original number of rows/columns. w1,w2 are are slightly different, and also h1,h2.
Now I preform a DCT 2D transform on the cropped image.
I got a new result matrix.
I notices that even when I do a very small cropping (even when deleting only one row from the original matrix), the DCT results are MUCH different, compared with the DCT results without the cropping.
My question is: is there any simple mathematical way to describe how slight cropping influence the DCT transform?
My guess (I am not sure) is that since the dimensions of the cropped matrix are different, there are less frequencies, so maybe there is a frequency shift, but I don't know how to describe this shift Mathematically. I also don't understand why a small shift in frequency makes such a big difference in amplitude.
Many thanks for your time & patience.