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 Transformation Based on Number Theoretic Transforms

Abstract: Many fast algorithms have been proposed for computing the discrete Fourier transformation. Most of them are based on factorization with the goal of reducing the number of multiplications. They use floating point arithmetic to avoid repetitious scaling and a sizeable wordlength to minimize quantization errors. This paper shows that the DFT of a sequence with prime length, P, can be computed efficiently, for selected P's, using number theoretic transforms. The proposed technique, denoted as FFT/NTT, is illustrated for p = 2M + 1. Advantages include availability of fast algorithms for a set of prime lengths, residue arithmetic with benefit in speed and hardware costs, parallel implementation with short wordlengths through the use of the Chinese remainder theorem, and exact computation except for scaling and round off for the input array and the trigonometric sequences.

A new parallel 2-D FFT architecture

Abstract: An efficient parallel architecture has been developed that can perform a 2-D Fourier transform in O(( square root N)N log square root N) time. The speedup is achieved through a decomposition of the of the 2-D Fourier transform into two smaller M*M 2-D transforms and a parallel implementation of the smaller transform. Memory bandwidth is not a problem in this architecture with a new memory partitioning strategy that successfully divides the large memory into N smaller, independent memories. The flexibility and modularity of the new 2-D FFT algorithm allows for a variety of sizes for the parallel 2-D FFT units. The decomposition of the 2-D FFT can be applied as many times as necessary until the right tradeoff between size and speed is obtained. The architecture offers an attractive tradeoff between size and speedup with an improvement of processor performance/size by over a factor of five. >

Computing discrete Fourier transform on a rectangular data array

Abstract: The authors generalize the weighted redundancy transform (WRT) algorithm for computing the multidimensional discrete Fourier transform (DFT) in the case in which the sample size (blocklength) is not the same on every axis. The proposed algorithm, like the WRT algorithm, is based on the one-dimensional fast Fourier transform (FFT) and, compared to the traditional ways of computing the multidimensional DFT, offers substantial savings in the number of one-dimensional FFT procedure calls. While the algorithm is applicable to transforms of any dimensions, only the two-dimensional case is explored in detail. >

A fast fourier transform algorithm to estimate carrier frequency deviation

Abstract: Based on the maximum-likelihood parameter estimation approach, a Fast Fourier Transform (FFT) algorithm is proposed in this paper. The proposed algorithm can directly calculate the absolute value of carrier frequency-deviation, and the precision of the proposed algorithm is independent of the input Signal-to-Noise. The proposed algorithm can be used to demodulate high data rate and bandwidth efficient QPSK signal, which is used in Tracking and Data Relay Satellite System(TDRSS).