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.

Fast fourier transform twiddle multiplication

Abstract: An FFT engine implementing a cycle count method of applying twiddle multiplications in multi-stages. When implementing a multistage FFT, the intermediate values need to be multiplied by various twiddle factors. The FFT engine utilizes a minimal number of multipliers to perform the twiddle multiplications in an efficient pipeline. Optimizing a number of complex multipliers based on an FFT radix and a number of values in each row of memory allows the FFT function to be performed using a reasonable amount of area and in a minimal number of cycles. Strategic ordering and grouping of the values allows the FFT operation to be performed in a fewer number of cycles.

Deterministic Sparse Fourier Approximation Via Approximating Arithmetic Progressions

Abstract: We present a deterministic algorithm for finding the significant Fourier frequencies of a given signal f ∈ CN and their approximate Fourier coefficients in running time and sample complexity polynomial in log N, L1(f)/||f||2, and 1/τ, where the significant frequencies are those occupying at least a τ-fraction of the energy of the signal, and L1(f) denotes the L1-norm of the Fourier transform of f. Furthermore, the algorithm is robust to additive random noise. This strictly extends the class of compressible/Fourier sparse signals efficiently handled by previous deterministic algorithms for signals in CN. As a central tool, we prove there is a deterministic algorithm that takes as input N, e and an arithmetic progression P in ZN, runs in time polynomial in ln N and 1/e, and returns a set AP that e-approximates P in ZN in the sense that |Ex∈APe2πiω/N - Ex∈Pe2πiωx/N| <; e for all ω = 0,..., N-1. In other words, we show there is an explicit construction of sets AP of size polynomial in lnN and 1/e that e-approximate given arithmetic progressions P in ZN. This extends results on small-bias sets, which are sets approximating the entire domain, to sets approximating a given arithmetic progression; this result may be of independent interest.

High-Speed Image Registration Algorithm with Subpixel Accuracy

Abstract: A new, fast and computationally efficient lateral subpixel shift registration algorithm is presented. It is limited to register images that differ by small subpixel shifts otherwise its performance degrades. This algorithm significantly improves the performance of the single-step discrete Fourier transform approach proposed by Guizar-Sicairos and can be applied efficiently on large dimension images. It reduces the dimension of Fourier transform of the cross correlation matrix and reduces the discrete Fourier transform (DFT) matrix multiplications to speed up the registration process. Simulations show that our algorithm reduces computation time and memory requirements without sacricing the accuracy associated with the usual FFT approach accuracy.

A better FFT bit-reversal algorithm without tables

Abstract: The bit-reversal counteralgorithm of B. Gold and C.M. Radar (1969) bit reverses a continuous sequence of N numbers by running a loop N -1 times. The heuristic approach presented repeats a similar loop only N/4 times. >

A Fast Algorithm for Computation of Electromagnetic Wave Propagation in Half-Space

Abstract: A new frequency-domain algorithm, the planar Taylor expansion through the fast Fourier transform (FFT) method, has been developed to speed the computation of the Green's function related formulas in the half-space scenario for both the near-field (NF) and the far-field (FF). Two types of Taylor-FFT algorithms are presented in this paper: the spatial Taylor-FFT and the spectral Taylor-FFT. The former is for the computation of the NF and the latter is for the computation of the FF or the Fourier spectrum. The planar Taylor-FFT algorithm has a computational complexity of O(N2 log2 N2) for an N times N computational grid, comparable to the multilevel fast multipole method (MLFMM). What's more important is that, the narrowband property of many electromagnetic fields allows the Taylor-FFT algorithm to use larger sampling spacing, which is limited by the transverse wave number. In addition, the algorithm is free of singularities. An accuracy of -50 for the planar Taylor-FFT algorithm is easily obtained and an accuracy of -80 dB is possible when the algorithm is optimized. The algorithm works particularly well for narrowband fields and quasi-planar geometries.