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.

Generalized FFTS - A Survey of Some Recent Results

Abstract: In this paper we survey some recent work directed towards generalizing the fast Fourier transform (FFT). We work primarily from the point of view of group representation theory. In this setting the classical FFT can be viewed as a family of efficient algorithms for computing the Fourier transform of either a function defined on a finite abelian group, or a bandlimited function on a compact abelian group. We discuss generalizations of the FFT to arbitrary finite groups and compact Lie groups.

A fast method for the numerical evaluation of continuous Fourier and Laplace transforms

Abstract: The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the “fractional Fourier transform,” previously developed by the authors, is applied to this problem with a substantial savings in computation.

Pruning the decimation in-time FFT algorithm

Abstract: Significant time-saving can be achieved by a simple modification to the radix-2 decimation in-time fast Fourier transform (FFT) algorithm when the data sequence to be transformed contains a large number of zero-valued samples. The time-saving is accomplished by replacing M - L stages of the FFT computation with a simple recopying procedure where 2Mis the total number of points to be transformed of which only 2Lare nonzero.

New continuous-flow mixed-radix (CFMR) FFT Processor using novel in-place strategy

Abstract: The paper proposes a new continuous-flow mixed-radix (CFMR) fast Fourier transform (FFT) processor that uses the MR (radix-4/2) algorithm and a novel in-place strategy. The existing in-place strategy supports only a fixed-radix FFT algorithm. In contrast, the proposed in-place strategy can support the MR algorithm, which allows CF FFT computations regardless of the length of FFT. The novel in-place strategy is made by interchanging storage locations of butterfly outputs. The CFMR FFT processor provides the MR algorithm, the in-place strategy, and the CF FFT computations at the same time. The CFMR FFT processor requires only two N-word memories due to the proposed in-place strategy. In addition, it uses one butterfly unit that can perform either one radix-4 butterfly or two radix-2 butterflies. The CFMR FFT processor using the 0.18 /spl mu/m SEC cell library consists of 37,000 gates excluding memories, requires only 640 clock cycles for a 512-point FFT and runs at 100 MHz. Therefore, the CFMR FFT processor can reduce hardware complexity and computation cycles compared with existing FFT processors.

Measuring power system harmonics and interharmonics by an improved fast Fourier transform-based algorithm

Abstract: The fast Fourier transform (FFT) has been widely used for the signal processing because of its computational efficiency. Because of the spectral leakage and picket-fence effects associated with the system fundamental frequency variation and improperly selected sampling time window, a direct application of the FFT algorithm with a constant sampling rate may lead to inaccurate results for continuously measuring power system harmonics and interharmonics. An improved FFT-based algorithm to measure harmonics and interharmonics accurately is proposed. In the proposed algorithm, a frequency-domain interpolation approach is adopted to determine the system fundamental frequency, and the interpolatory polynomial method is applied to reconstruct the sampled time-domain signal; it is followed by using the FFT to calculate the actual harmonic components. Then, the frequency-domain interpolation is again applied to find the interharmonic components. The performance of the proposed algorithm is validated by testing the actual measured waveforms. Results are compared with those obtained by directly applying a typical FFT algorithm and by the IEC grouping method. It shows that the solutions determined by the proposed algorithm are more accurate, and a reasonable computational efficiency is maintained.