The discrete Fourier transform (DFT) is the most widely used technique for determining the frequency spectra of digital signals. However, in the sliding transform scenario where the transform window is shifted one sample at a time and the transform process is repeated, the use of DFT becomes difficult due to its heavy computational burden. This paper proposes an optimal sliding DFT (oSDFT) algorithm that achieves both the lowest computational requirement and the highest computational accuracy among existing sliding DFT algorithms. The proposed oSDFT algorithm directly computes the DFT bins of the shifted window by simply adding (or subtracting) the bins of a previous window and an updating vector. We show that the updating vector can be efficiently computed with a low complexity in the sliding transform scenario. Our simulations demonstrate that the proposed algorithm outperforms the existing sliding DFT algorithms in terms of computational accuracy and processing time.

Guaranteed-Stable Sliding DFT Algorithm With Minimal Computational Requirements

Improved discrete Fourier transform algorithm for harmonic analysis of rotor system

Voltage dips are significant threat for distributed generation (DG) connected via grid-tie inverter to the power system. Fast detection of voltage dips is essential for proper operation of the DGs. The paper presents an overview of different methods for their detection. The dips can be traced by appearance of voltage harmonics. Therefore, categorization of harmonics estimation techniques is given at the beginning. Then, methods of signal analysis, both parametric and nonparametric, are explained. At the end, hybrid methods, recursive methods and methods based on artificial intelligence are presented.

Overview of voltage dips detection analysis methods

Constraining error-A sliding discrete Fourier transform investigation

Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style treatment, existing recursive techniques are reviewed, explained and compared within a coherent framework; some fresh insights are provided and new enhancements/modifications are proposed. It is shown that the replacement of resonators by (non-recursive) modulators in sliding DFT (SDFT) analyzers with either a finite impulse response (FIR), or an infinite impulse response (IIR), does improve performance somewhat; however stability is not guaranteed, as the cancellation of marginally stable poles by zeros is still involved. The FIR deadbeat observer is shown to be more reliable than the SDFT methods, an IIR variant is presented, and ways of fine-tuning its response are discussed. A novel technique for stabilizing IIR SDFT analyzers with a fading memory, so that all poles are inside the unit circle, is also derived. Slepian and sum-of-cosine windows are adapted to improve the frequency responses for the various FIR and IIR DFT methods.

Digital Filter Designs for Recursive Frequency Analysis

Recursive sliding discrete Fourier transform with oversampled data

Wireless sensor networks WSN are gaining popularity in the industrial and academic communities as an unobtrusive and low power alternative solution to gather data from an everincreasing variety of environments and phenomena. This paper focuses on the development of a configurable, low power and cost-effective gateway based on an ARM9 microprocessor to link a WSN to the internet through the GSM network or an ethernet connection. A bespoke application written in Visual C# executed by Windows Embedded CE and a configurable hardware platform permit the functionality of the gateway to be adapted to the requirements of a WSN deployment. The gateway may be configured remotely and provides the WSN with persistent data storage and frequent data uploads to a file server via the internet. This study has been successful in the development of a generic gateway which was found to be more configurable and cost effective than previous gateway implementations.

Developing a WSN internet gateway for an African context

The Discrete Fourier Transform has played a fundamental role in signal analysis for radar systems, usually in its Fast Fourier Transform form. Traditionally, samples from a region of interest have been acquired, and processed in a block-processing fashion. The result is a delayed output equal to the time taken to acquire the data and then perform the Fourier Transform. To overcome this limitation, this work focuses on the development of a parallel framework for the execution of the Discrete Fourier Transform using a recursive algorithm, using many simple processing elements. The Fourier coefficients are updated every time a new sample is presented to the system, with a small latency. The system described in this work shows a 64 point Discrete Fourier Transform computation in parallel, which achieves a throughput of 817MSPS(29.42Gbit/s). The framework proposed promotes adjustable parallelism using the many simple processing elements. We show the engine is capable of dynamically correcting accumulated errors due to finite arithmetic, and allows simple adoption on existing systems.

A. van der Byl

Papers

Recursive sliding discrete Fourier transform with oversampled data

Constraining error-A sliding discrete Fourier transform investigation

Developing a WSN internet gateway for an African context

Recursive fourier transform hardware