Generalized Sliding Discrete Fourier Transform

Yoshihisa ISHIDA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A    No.1    pp.338-345
Publication Date: 2016/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.338
Type of Manuscript: PAPER
Category: Digital Signal Processing
sliding DFT,  window function,  zero-padding,  

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The sliding discrete Fourier transform (DFT) is a well-known algorithm for obtaining a few frequency components of the DFT spectrum with a low computational cost. However, the conventional sliding DFT cannot be applied to practical conditions, e.g., using the sine window and the zero-padding DFT, with preserving the computational efficiency. This paper discusses the extension of the sliding DFT to such cases. Expressing the window function by complex sinusoids, a recursive algorithm for computing a frequency component of the DFT spectrum using an arbitrary sinusoidal window function is derived. The algorithm can be easily extended to the zero-padding DFT. Computer simulations using very long signals show the validity of our algorithm.