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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.
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TL;DR: A simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.
Abstract: A simple, yet complete and detailed description of the fast Fourier transform for general N is given with the aim of making the underlying idea quite apparent. To help with this didactic goal, a simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.
12 citations
TL;DR: In this article, the authors proposed a design method of fast Fourier transform (FFT) large-scaled integration (LSI) for an orthogonal frequency division multiplexing (OFDM) system.
Abstract: We propose a design method of fast Fourier transform (FFT) large-scaled integration (LSI) for an orthogonal frequency division multiplexing (OFDM) system. The proposed FFT LSI is designed with simple current mode circuits, wired-OR connection and gate-width-ratioed current mirror. For a low power consumption, two design methods are proposed, current-cut (CC) and rounding process. The CC operation is performed with on-off operation of a current source. The rounding process is adopted for the component of the FFT matrix. Bit error rate (BER) in the OFDM system is simulated from "0.1" rounding step to "1.0". The BER performance of the FFT matrix with the "0.2" rounding step has little degradation from that of the original FFT matrix. The 8-point FFT LSI with the "0.2" rounding step is designed and implemented using a 0.8 µm complementary metal-oxide semiconductor (CMOS) technology. On the basis of measurement of the 8-point FFT LSI, the power consumption of the 64-point FFT LSI using CC can be estimated as being less than 10 mW.
12 citations
TL;DR: The problem of computing N Chebyshev coefficients is considered when , and two methods are discussed.
Abstract: The problem of computing N Chebyshev coefficients is considered when . Two methods are discussed. The first method is related to the Fast Fourier Transform (FFT) and required a total number of operations proportional to N log2 N. The second method, although not as efficient as efficient as the FFT exemplified interesting properties of the discrete Chebyshev polynomials.
12 citations
TL;DR: This method avoids the drawbacks of the undersampling of the low frequency and high frequency components which occurs in the standard FFT-based method and is only suitable for square screens.
Abstract: This work describes an accurate method for simulating turbulent phase screens. The phase screen is divided into a fast Fourier transform (FFT)-based screen and a tilt screen. The simulation of the FFT-based screen is different from that of the standard method. In the simulation, the discrete power spectrum of the turbulence is obtained from the discrete Fourier transform of the phase autocorrelation matrix, not from the theoretical power spectrum. This method avoids the drawbacks of the undersampling of the low frequency and high frequency components which occurs in the standard FFT-based method. The maximum error in the phase structure function can be reduced to <0.13% , and the additional execution time increases by only several percents. This method is only suitable for square screens.
12 citations
TL;DR: This paper proposes an algorithm for the fast Fourier transform on hyperbolic cross points for nonequispaced spatial knots in two and three dimensions that is based on the NFFT and an appropriate partitioning of the hyperBolic cross.
Abstract: The discrete Fourier transform in d dimensions with equispaced knots in space and frequency domain can be computed by the fast Fourier transform (FFT) in $${\cal O}(N^d \log N)$$
arithmetic operations. In order to circumvent the ‘curse of dimensionality’ in multivariate approximation, interpolations on sparse grids were introduced. In particular, for frequencies chosen from an hyperbolic cross and spatial knots on a sparse grid fast Fourier transforms that need only $${\cal O}(N \log^d N)$$
arithmetic operations were developed. Recently, the FFT was generalised to nonequispaced spatial knots by the so-called NFFT. In this paper, we propose an algorithm for the fast Fourier transform on hyperbolic cross points for nonequispaced spatial knots in two and three dimensions. We call this algorithm sparse NFFT (SNFFT). Our new algorithm is based on the NFFT and an appropriate partitioning of the hyperbolic cross. Numerical examples confirm our theoretical results.
12 citations