Split-radix FFT algorithm

About: Split-radix FFT algorithm is a research topic. Over the lifetime, 1845 publications have been published within this topic receiving 41398 citations.

Measurement of power system harmonic based on adaptive Kaiser self-convolution window

Abstract: As the rapid development in power electronic devices, the harmonic pollution becomes one of principle power quality problems in power system. The fast Fourier transform (FFT) is widely used for analysing and measuring power system harmonics. However, the limitation of the FFT such as an aliasing effect, spectrum leakage picket-fence effect, would contribute to inaccuracy results. Furthermore, the real power system harmonic is actually a non-stationary signal while FFT is a tool for stable signal. This study focuses on a novel FFT based method for time-varying power system harmonic measurement. The harmonic signal is preprocessed by infinite impulse response filter bank and Teager–Kaiser energy operator for fast detection of instability onset time. Then an adaptive Kaiser self-convolution window-based interpolated FFT algorithm is used to estimate each harmonic component. The results of both simulation and practical implementation show that the proposed method is suitable to deal with time-varying harmonic and achieves a higher accuracy compared with the traditional FFT-based techniques.

On hardware implementation of radix 3 and radix 5 FFT kernels for LTE systems

Abstract: This paper treats the hardware architecture and implementation of mixed radix FFTs with cores of radix 3 and radix 5 in addition to the standard radix 2 core. The implementation flow graphs of the higher radix cores are presented together with a description of how these cores affect a pipelined FFT implementation. It is shown that the mixed radix FFT is more expensive than the radix 2 implementation - a mixed radix FFT of 1200 points require 36 real multipliers in a pipelined implementation whereas a 2048 radix 2 FFT needs 30 real multipliers. However, half of the multipliers in the mixed radix case can be constant. Therefore it is still feasible to use the mixed radix FFT if an algorithm calls for it.

Cooley-Tukey FFT like algorithms for the DCT

Abstract: The Cooley-Tukey FFT algorithm decomposes a discrete Fourier transform (DFT) of size n = km into smaller DFT of size k and m. In this paper we present a theorem that decomposes a polynomial transform into smaller polynomial transforms, and show that the FFT is obtained as a special case. Then we use this theorem to derive a new class of recursive algorithms for the discrete cosine transforms (DCT) of type II and type III. In contrast to other approaches, we manipulate polynomial algebras instead of transform matrix entries, which makes the derivation transparent, concise, and gives insight into the algorithms' structure. The derived algorithms have a regular structure and, for 2-power size, minimal arithmetic cost (among known DCT algorithms).

Phase-unwrapping algorithm by a rounding-least-squares approach

Abstract: A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm’s performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.

Feedforward FFT Hardware Architectures Based on Rotator Allocation

Abstract: In this paper, we present new feedforward FFT hardware architectures based on rotator allocation. The rotator allocation approach consists in distributing the rotations of the FFT in such a way that the number of edges in the FFT that need rotators and the complexity of the rotators are reduced. Radix-2 and radix-2 k feedforward architectures based on rotator allocation are presented in this paper. Experimental results show that the proposed architectures reduce the hardware cost significantly with respect to previous FFT architectures.