## [Audacity-nyquist] fft and filter clarification

 [Audacity-nyquist] fft and filter clarification From: Roger Dannenberg - 2008-02-13 18:16:20 ``` From Audacity-Nyquist Digest, Vol 15, Issue 6: > Don't blame the math. All of the common linear filters > can be represented in a mathematically equivalent form > using FFTs. That means if you do it right you should get > the same results. The artifacts usually come from using > intuition to invent filters in FFT (spectra) space rather > than going back to filter theory and doing the math. Well, I think this needs some clarification too: I believe that the statement (above) is true if you can take a DFT of the entire input signal, but that might be computationally impractical and numerically inaccurate. Assuming you need to use an overlap/add STFT approach, there is no mathematical equivalent to IIR filters (which are common linear filters) because the infinite response would not be contained within a finite window. FIR filters can always be implemented in a mathematically equivalent way (ignoring any numerical issues) through fast convolution based on overlap add/overlap save algorithms. -Roger ```

 [Audacity-nyquist] fft and filter clarification From: Roger Dannenberg - 2008-02-13 18:16:20 ``` From Audacity-Nyquist Digest, Vol 15, Issue 6: > Don't blame the math. All of the common linear filters > can be represented in a mathematically equivalent form > using FFTs. That means if you do it right you should get > the same results. The artifacts usually come from using > intuition to invent filters in FFT (spectra) space rather > than going back to filter theory and doing the math. Well, I think this needs some clarification too: I believe that the statement (above) is true if you can take a DFT of the entire input signal, but that might be computationally impractical and numerically inaccurate. Assuming you need to use an overlap/add STFT approach, there is no mathematical equivalent to IIR filters (which are common linear filters) because the infinite response would not be contained within a finite window. FIR filters can always be implemented in a mathematically equivalent way (ignoring any numerical issues) through fast convolution based on overlap add/overlap save algorithms. -Roger ```