# Maths behind why removing values from DFT is not a brick wall filter

I sort of understand that when removing values from a signals DFT is not the same as a brick wall filter since it will only zero the frequencies that are perfectly periodic. Other spectrum frequencies who are not exactly periodic will have their energies spread over the whole DFT result. Is this right?

I'd like to know how you can mathematically prove that zeroing frequencies is not a brick wall filter using the DFT and inverse DFT.

• when you are "using the DFT and inverse DFT", are you filtering a signal much longer than the DFT length using something like Overlap-Add or Overlap-Save? May 6, 2017 at 4:48
• yeah the signal would be much larger than the length of the DFT. May 6, 2017 at 5:00
• so you're using Overlap-Add or Overlap-Save? May 6, 2017 at 6:47
• neither I think. I'm not looking to make a filter really I am more curious as to why zeroing certain frequencies of a frequency spectrum does not work as a brick wall filter. If I had a signal and took the DFT of a section of the signal, zeroed the result at certain frequencies and then took the IDFT why is the final result not a brick wall filter and how does the maths explain it. May 6, 2017 at 7:43
• i disagree with your premise. remember the DFT (and iDFT) inherently periodically extend the data passed to it. what comes out of the DFT are literally the Fourier coefficients of the periodically extended function. when you zero those frequency components, those frequencies have zero amplitude. if you do that to all frequency components above some index, it's a brick wall filter applied to your periodic function. May 6, 2017 at 7:48