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.

Pruning the decimation-in-time FFT algorithm with frequency shift

Abstract: Fourier transformed components within desired narrow-band can be efficiently calculated by the pruned version of the decimation-in-time FFT algorithm. A new pruning method is proposed here which invloves frequency shift. The shifting simplifies the pruning algorithm because its flowgraph has a repetitive pattern of butterflies between adjacent stages.

Real-time pipeline fast fourier transform processors

Abstract: A real-time pipeline processor, which is particularly suited for VLSI implementation, is based on a hardware oriented radix-22 algorithm derived by integrating a twiddle factor decomposition technique in a divide and conquer approach. The radix-22 algorithm has the same multiplicative complexity as a radix-4 algorithm, but retains the butterfly structure of a radix-2 algorithm. A single-path delay-feedback architecture is used in order to exploit the spatial regularity in the signal flow graph of the algorithm. For a length-N DFT transform, the hardware requirements of the processor proposed by the present invention is minimal on both dominant components: Log4N-1 complex multipliers, and N-1 complex data memory.

A recursive fast Fourier transformation algorithm

Abstract: A new composite filter-bank structure is presented for the efficient implementation of the recursive discrete transformation. This structure is based on a proper combination of the concepts of polyphase filtering and the fast Fourier transformation (FFT) algorithm. Its computational complexity is in direct correspondence with the FFT, and can be operated both in sliding and block-oriented modes. The inherent parallelism of this structure enables very high speed in practical implementations. >

A Fast Algorithm for Fourier Continuation

Abstract: A new algorithm is presented which provides a fast method for the computation of recently developed Fourier continuations (a particular type of Fourier extension method) that yield superalgebraically convergent Fourier series approximations of nonperiodic functions. Previously, the coefficients of an approximating Fourier series have been obtained by means of a regularized singular value decomposition (SVD)-based least-squares solution to an overdetermined linear system of equations. These SVD methods are effective when the size of the system does not become too large, but they quickly become unwieldy as the number of unknowns in the system grows. We demonstrate a novel decoupling of the least-squares problem which results in two systems of equations, one of which may be solved quickly by means of fast Fourier transforms (FFTs) and another that is demonstrated to be well approximated by a low-rank system. Utilizing randomized algorithms, the low-rank system is reduced to a significantly smaller system of equations. This new system is then efficiently solved with drastically reduced computational cost and memory requirements while still benefiting from the advantages of using a regularized SVD. The computational cost of the new algorithm in on the order of the cost of a single FFT multiplied by a slowly increasing factor that grows only logarithmically with the size of the system.

A three-dimensional DFT algorithm using the fast Hartley transform

Abstract: A three-dimensional (3-D) Discrete Fourier Transform (DFT) algorithm for real data using the one-dimensional Fast Hartley Transform (FHT) is introduced. It requires the same number of one-dimensional transforms as a direct FFT approach but is simpler and retains the speed advantage that is characteristic of the Hartley approach. The method utilizes a decomposition of the cas function kernel of the Hartley transform to obtain a temporary transform, which is then corrected by some additions to yield the 3-D DFT. A Fortran subroutine is available on request.