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.

Convolution-Based Trigonometric Interpolation of Band-Limited Signals

Abstract: This paper presents a method to obtain a trigonometric polynomial that accurately interpolates a given band-limited signal from a finite sequence of samples. The polynomial delivers accurate approximations in the range covered by the sequence, except for a short frame close to the range limits. Besides, its accuracy increases exponentially with the frame width. The method is based on using a band-limited window in order to reduce the truncation error of a convolution series. It is shown that the polynomial can be efficiently constructed and evaluated using algorithms designed for the discrete Fourier transform (DFT). Specifically, two basic procedures are presented, one based on the fast Fourier transform (FFT), and another based on a recursive update algorithm for the short-time FFT. The paper contains three applications. The first is a variable fractional delay (VFD) filter, which consists of a short-time FFT combined with the evaluation of a trigonometric polynomial. This filter has low complexity and can be implemented using CORDIC rotations. The second is the interpolation of nonuniform Fourier summations, where the proposed method eliminates the need to interpolate any kernel sample. Finally, the third can be viewed as a generalization of the FFT convolution algorithm and makes it possible to interpolate the output of an finite-impulse-response (FIR) filter efficiently.

Variable length fft system and method

Abstract: A variable length fast Fourier transform (FFT) system and a method for performing the FFT system in a global navigation satellite system (GNSS) signal acquisition and tracking, which includes a memory and a number of processing elements are disclosed. Based on the GNSS signal tracking, the variable length FFT system performs a first FFT operation together with a first data length. Based on the GNSS signal acquisition, the variable length FFT system is divided into several FFT subsystems to simultaneously perform different operations with various data lengths different from the first data length. Thus, the variable length FFT system can enhance the hardware utility and increase throughputs.

The split-radix fast Fourier transforms with radix-4 butterfly units

Abstract: We present a split radix fast Fourier transform (FFT) algorithm consisting of radix-4 butterflies. The major advantages of the proposed algorithm include: i). The proposed algorithm consists of mixed radix butterflies, whose structure is more regular than the conventional split radix algorithm. ii). The proposed algorithm is asymptomatically equal computation amount to the split radix algorithm, and is fewer operations than the radix-4 algorithms. iii). The proposed algorithm is in the conjugate-pair version, which requires less memory access than the conventional FFT algorithms.

Real FFT based on graphic processing unit for image processing

Abstract: By analysis of general real Fast Fourier Transform(FFT)algorithm,an improved real FFT algorithm is presented based on Graphic Processing Unit(GPU).A general real FFT can reduce the computation consumption of the conventional complex FFT algorithm by about 40%,and the presented real FFT algorithm improves the reduction to 50%.On the basis of the specific configuration of data storage,the presented real FFT algorithm can be applied in two directions continuously to generate the 2D Fourier spectrum,also the parallel real FFT transform can be implemented by using the 1D complex FFT function from the CUFFT library.The precision and the efficiency of the presented real FFT are inspected by Wiener filter's application,image processing results demonstrate that the presented real FFT algorithm shows operating properly and working well.With the help of the presented real FFT,Wiener filter can restore a 2 048×2 048 8-bit image by motion speed of 19.26 ms,which is 2.34 times as compared with that of the Wiener filter based on complex FFT on GPU,and is 37.46 times that of the Wiener filter based on real FFT on CPU.The experiment results show that the presented algorithm is practical for image processing.