Sliding Discrete Fourier Transform with Kernel Windowing

The sliding discrete Fourier transform (SDFT) is an efficient method for computing the N-point DFT of a given signal starting at a given sample from the N-point DFT of the same signal starting at the previous sample [1]. However, the SDFT does not allow the use of a window function, generally incorporated in the computation of the DFT to reduce spectral leakage, as it would break its sliding property. This article will show how windowing can be included in the SDFT by using a kernel derived from the window function, while keeping the process computationally efficient. In addition, this approach allows for turning other transforms, such as the modified discrete cosine transform (MDCT), into efficient sliding versions of themselves.