# Can we get the same result from between partial FFT?

I'm trying to implement fft and gaussian low pass filter multiplication to 16x16 image.

As I know fft can be separable. What if there are 16x16 one image, then is this the same ? between 4x4 part of the whole 16x16 fft result and just only 4x4 fft result?

If they are same then I think that the latter method is more resource efficienciable.

## 1 Answer

I don't think "separable" means what you think it means – it means that you can implement the 2 DFT as the concatenation of a $N_{rows}$ amount of $N_{columns}$ long DFTs followed by $N_{columns}$ DFTs of length $N_{rows}$.

So, no, your approach is not correct.

• I agree. so I modify to 'partial'. As i know H.264 and MPEG sort of things are using these methods to manipulate the image with 4x4 and 8x8 and 16x16 macro block with fft. so I thought that I can implement that kinds of way. – start01 Mar 11 '18 at 12:32
• No, you can't. Really, maybe sit down and look at the formula for the DFT. It's really apparent. – Marcus Müller Mar 11 '18 at 12:34