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.

Modification of a two-dimensional fast Fourier transform algorithm by the analog of the Cooley-Tukey algorithm for a rectangular signal

Abstract: One-dimensional fast Fourier transform (FFT) is the most popular tool for computing the two-dimensional Fourier transform. As a rule, a standard method of combination of one-dimensional FFTs--the so-called algorithm "by rows and columns" [1]--is used in the literature. In [2, 3], the authors showed how to compute the FFT for a signal with the number of samples 2 s × 2 s with the use of an analog of the Cooley-Tukey algorithm. In the present paper, a two-dimensional analog of the Cooley-Tukey algorithm is constructed for a rectangular signal with the number of samples 2 s × 2 s + l. The number of operations in this algorithm is much less than that in the successive application of a one dimensional FFT by rows and columns. The testing of the algorithm on image-type signals shows that the speed of computation of the FFT by the algorithm proposed is about 1.7 times higher than that of the algorithm by rows and columns.

Improvement of phase difference correcting spectrum method based on all-phase FFT

Abstract: The phase difference correcting spectrum method based on all-phase fast Fourier transform(FFT)calculates the conventional FFT without effects of negative frequency.As a result,there is a decline in accuracy of low-frequency signal parameters estimation.Aiming at this problem,an improved phase difference correcting spectrum method based on all-phase FFT is proposed.The effects of negative frequency to FFT are considered in classic FFT.The all-phase FFT spectrum analysis theory and the phase difference correcting method are introduced.The cause that the negative frequency has a negative impact on low-frequency signal spectrum analysis is analyzed.The equations of frequency,amplitude and phase estimating for single-frequency signals sampled in non-integer-period are derived with the effects of negative frequency to spectrum analysis being considered.The simulation results show that the improvement of considering negative frequency contribution is able to improve the accuracy in low-frequency cosine signal parameter estimation in the conventional way,and the anti-noise ability of the original algorithm is also improved.

FFT-based methods for nonlinear image restoration in confocal microscopy

Abstract: Recently we developed a new method for attenuation correction in 3D imaging by a confocal scanning laser microscope (CSLM) in the (epi)fluorescence mode. The fundamental element in our approach consisted of multiplying the measured fluorescent intensity by a correction factor involving a convolution integral of this intensity, which can be computed efficiently by the fast Fourier transform (FFT). The resulting algorithm is one or two orders of magnitude faster than an existing iterative method, but it was found to have a somewhat smaller accuracy. In this paper we improve on this latter point by reformulating the problem as a statistical estimation problem. In particular, we derive first-order-moment and cumulant estimators leading to a nonlinear integral equation for the unknown fluorescent density, which is solved by an iterative method in which in each step a discrete convolution is performed by using the FFT. We find that only a few iterations are needed. It is shown that the estimators proposed here are more accurate than the existing iterative method, while they retain the advantage in computational efficiency of the FFT-based approach.

Inverse fast fourier transform (IFFT) with overlap and add

Abstract: A system for efficiently filtering interfering signals in a front end of a GPS receiver is disclosed. Such interfering signals can emanate from friendly, as well as unfriendly, sources. One embodiment includes a GPS receiver with a space-time adaptive processing (STAP) filter. At least a portion of the interfering signals are removed by applying weights to the inputs. One embodiment adaptively calculates and applies the weights by Fourier Transform convolution and Fourier Transform correlation. The Fourier Transform can be computed via a Fast Fourier Transform (FFT). This approach advantageously reduces computational complexity to practical levels. Another embodiment utilizes redundancy in the covariance matrix to further reduce computational complexity. In another embodiment, an improved FFT and an improved Inverse FFT further reduce computational complexity and improve speed. Advantageously, embodiments can efficiently null a relatively large number of jammers at a relatively low cost and with relatively low operating power.

Modified algorithm for real time sar signal processing

Abstract: The generation of the picture out of the SAR raw data is a computational intensive task. Both range compression and azimuth compression utilized Fast Fourier Transform (FFT) algorithms and Inverse Fast Fourier Transform (IFFT) in order to perform convolution with respective reference signal. Thus FFT and IFFT occupied about 70% of the total computation operation in SAR image formation. In this paper a modified algorithm based on conventional FFT is proposed to optimize the computation performance. It is shown that the proposed algorithm can essentially achieve better performance with minimum computational burden compare to conventional FFT.