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.

Primitive Image Transformations Used to Perform a Fast Fourier Transform

Abstract: The Fourier transform is one of the most important transformations in image processing. A major component of this influence comes from the ability to implement it efficiently on a digital computer. This paper describes a new methodology to perform a fast Fourier transform (FFT). This methodology emerges from considerations of the natural physical constraints imposed by image capture devices (camera/eye). The novel aspects of the specific FFT method described include: 1) a bit-wise reversal re-grouping operation of the conventional FFT is replaced by the use of lossless image rotation and scaling and 2) the usual arithmetic operations of complex multiplication are replaced with integer addition. The significance of the FFT presented in this paper is introduced by extending a discrete and finite image algebra, named Spiral Honeycomb Image Algebra (SHIA), to a continuous version, named SHIAC.

A new 1D FFT-based algorithm for computing the MD FFT on arbitrary lattices

Abstract: This work presents an original two-stages MD FFT algorithm where in the first stage the signal is processed by multiplier-free butterflies in such a way that at the second stage the computation only needs 1D FFT's. The proposed method is more efficient than any other MD FFT algorithm known to the authors. >

Improved frequency domain Super-Resolution algorithm with conjugate gradient - NUFFT method as its reconstruction core

Abstract: In the paper frequency domain Super-Resolution algorithm with enhanced reconstruction stage is presented. The Fourier transform properties of relocated images are used to easy estimation of rotation and translation, as well as artifacts caused by subsampling. Previously, the bicubic interpolation has been employed in the reconstruction phase, in this paper it is replaced by iterative conjugate-gradient method with inverse nonuniform fast Fourier transform at its core. The new algorithm indeed gives improved results, if compared to those of the previous ones.

A Scale Adaptive Tracking Algorithm Based on Kernel Ridge Regression and Fast Fourier Transform

Abstract: The change of object’s scale is an important reason leading to tracking failure in visual tracking. A scale adaptive tracking algorithm based on kernel ridge regression and Fast Fourier Transform is proposed in this paper. Firstly, the algorithm build regression model using appearance information of object, and then get the position of object in the search region using the regression model. Finally, it estimates the best scale by considering the weight image of all pixels in the candidate region. The experimental results show that the proposed algorithm not only can track the object real time, but also adapt to the changing of object’s scale and the interference of background. Compared with the traditional ones, it owns good robustness and efficiency.

A New Overlap Save Algorithm for Fast Convolution

Abstract: The most widely used block convolution method is the overlap save algorithm (OSA), where a block of M data to be convolved with a filter is concatenated with the previous block and 2M-point FFT and multiplications are performed for this overlapped block. By discarding half of the results, we obtain linear convolution results from the circular convolution. This paper proposes a new transform which reduces the block size to only M for the block convolution. The proposed transform can be implemented as the M multiplications followed by M-point FFT Hence, existing efficient FFT libraries and hardware can be exploited for the implementation of proposed method. Since the required transform size is half that of the conventional method, the overall computational complexity is reduced. Also the reduced transform size results in the reduction of data access time and cash miss-hit ratio, and thus the overall CPU time is reduced. Experiments show that the proposed method requires less computation time than the conventional OSA.