Prime-factor FFT algorithm

About: Prime-factor FFT algorithm is a research topic. Over the lifetime, 2346 publications have been published within this topic receiving 65147 citations. The topic is also known as: Prime Factor Algorithm.

A CORDIC-friendly FFT architecture

Abstract: Fast Fourier Transform (FFT) is one of the basic building blocks in signal processing and communications systems. The butterflies-based structure of the FFT is the main reason for the reduced number of arithmetic operations required to implement the transform. From implementation point of view, the complex rotations used in butterflies can be implemented by using COordinate Rotation DIgital Computer (CORDIC). This implementation strategy reduces the hardware complexity compared to the direct implementation of the butterflies using complex multipliers. In this paper, we introduce a restructure of the butterflies of the radix-2 FFT to be more CORDIC friendly. This algorithm-level modification of the FFT is friendly towards all CORDIC types, including those introducing non-fixed gain. Compared with the conventional radix-2 FFT algorithm, the proposed algorithm introduces a substantial increase in performance. For example, it achieves superior signal to quantization noise ratio (SQNR), with around 14 dB gain for 8 to 1024 points FFT. In addition, in pipeline architectures the modification leads to an improvement in latency or a reduction in the total area, with an improvement in either of 38% for 1024 points FFT.

An efficient split-radix FFT algorithm

Abstract: In this paper, an efficient split-radix FFT algorithm is proposed for computing the length-2/sup r/ DFT that reduces significantly the number of data transfers, index generations, and twiddle factor evaluations or accesses to the lookup table. It is shown that the arithmetic complexity of the proposed algorithm is no more than that of the existing split-radix algorithm. The basic idea behind the proposed algorithm is that a radix-2 and a radix-8 index maps are used instead of a radix-2 and a radix-4 index maps as in the classical split-radix FFT. In addition, since the algorithm is expressed in a simple matrix form using the Kronecker product, it facilitates an easy implementation of the algorithm, and allows for an extension to the multidimensional case.

An algorithm with high accuracy for analysis of power system harmonics

Abstract: In the paper, some problems of the current algorithms that are used to analyze the power system harmonics are pointed out FFT-Adaline algorithm for analysis of power system harmonics is presented FFT-Adaline algorithm combines the advantages of Adaline ANN algorithm with interpolated FFT algorithm with Hanning-window The new algorithm eliminates the main error factor of interpolated FFT algorithm with Hanning-window and Adaline ANN algorithm, and therefore obviously improves the accuracy of harmonic analysis The simulating result shows that the new algorithm can be applied to the precise analysis for power system harmonics By aid of the high- speeded DSP and high-powered CPU, the FFT-Adaline algorithm is quite useful in industry applications

On Errors and Bias of Fourier Transform Methods in Quadratic Term Structure Models

Abstract: We analyze and compare the performance of the Fourier transform method in affine and quadratic term structure models. We explain why the method of the reduction to FFT in dimension one is efficient for ATSMs of type $A_0(n)$ but may lead to sizable errors for QTSMs unless computational errors are taken into account properly. We suggest a certain improvement and generalization which make FFT more accurate and, for the same precision, faster than Leippold and Wu (2002) method. We deduce simple general recommendations for the choice of parameters of computational schemes for QTSMs, which ensure a given precision, and an approximate formula for the bias which FFT produces.

Order of N complexity transform domain adaptive filters

Abstract: Implementation of the transform domain adaptive filters is addressed. Recent results have shown that if the input data to a radix-2 fast Fourier transform (FFT) structure is sliding one sample at a time, only N-1 butterflies need to be calculated for updating the FFT structure, after the arrival of every new data sample. This is opposed to most of the previous reports that, assume order of N log N complexity, for such implementation. In this paper the sliding implementation of the other useful transforms, that can also be implemented with the order of N complexity, are worked out in detail. >