SLIDING IS SMOOTHER THAN JUMPING
Russell Bradford, Richard W. Dobson, John ffitch · 2005
The existence of the sliding DFT has been known for some time, but it does not seem to be in wide use, possibly because of its perceived computational cost. In this paper we review the mathematical background, and implementation issues, and then consider the advantages and disadvantages of the Sliding Discrete Fourier Transform (SDFT) as compared with a more traditional FFT algorithm. We also propose a much more efficient Simple Sliding Inverse DFT that makes sliding a serious alternative to jumping between overlapping frames. Finally we assess the quality of transformations based on the SDFT in a Csound implementation. uses a divide-and-conquer method and costs +*-,. operations to calculate for a window of size. In the traditional implementation the window is moved on / by samples, usually /10+ with, and the DFT is recalculated. The idea behind the Sliding Discrete Fourier Transform (SDFT) is to make use of the known values of 2 to calculate the value for the next window. In particular we assume than we are moving by 1 sample only: