Improvements to the Sliding Discrete Fourier Transform Algorithm [Tips & Tricks]

Abstract

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SlidingConv: Domain-Specific Description of Sliding Discrete Cosine Transform Convolution for Halide

“…The sliding transform efficiently computes frequencies using an incremental formula based on the relationship between adjacent frequency components in a short-time DFT/DCT/DST. SDFT is summarized in detail in the following papers [53]- [55].…”

Adaptive Smith Predictor for Enhanced Stability of Power Hardware-in-the-Loop Setups

“…In real-time application, the frequency-domain data must be processed frequently and promptly. Sliding DFT (SDFT) is deduced from the DFT circular shift property [26] with the time-domain sequence circularly shifted by one sample through multiplying e j 2πk N and the signal spectral being updated on a sample-by-sample basis [26], [27]. This attribute enables the SDFT to present higher computation efficiency and low computation cost than Fast Fourier Transform (FFT) in processing signals with selective frequencies [26].…”

“…The linearization method as elaborated in [29] is applied to the non-linear matrices in (27) and the numerical values of the coefficient matrices A and B are further calculated by solving the corresponding linear algebraic equations.…”

Rapid Extraction of the Fundamental Components for Non-Ideal Three-Phase Grid Based on an Improved Sliding Discrete Fourier Transform

“…In [16], the SDFT was used for harmonic detection in the three-phase grid-tie inverter system; besides, SDFT has been often used in cooperation with the phase-locked loop for the stable operation and control of the grid-connected converters [17,18]. Although the SDFT algorithm is computationally efficient, this method still might have drawbacks, e.g., a slow dynamic performance and sensitivity to the frequency, and types of measures have been researched to make improvements [19], and types of improvements have been carried out in [20]. In [21], an adaptive sampling frequency based on the phase error was designed for the SDFT algorithm to improve the estimation accuracy.…”