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.

General FFT pruning algorithm

Abstract: The efficiency of the fast Fourier transform may be increased by removing operations on input values which are zero, and on output values which are not required; this procedure is known as FFT pruning algorithm. Up to now some algorithms have been proposed considering decimation-in-time (DIT) or decimation-in-frequency (DIF) procedures, and considering that for a N = 2/sup M/ input points of the FFT only quantities equals to 2/sup k/ (to an integer k), of nonzero input or desired output points are required. In this paper we propose a new FFT pruning algorithm where the number of nonzero inputs or desired outputs can be arbitrary. The idea of the proposed algorithm works well with DIT as well as DIEF procedures, and the implementation is similar to the FFT algorithms that use in-place computation, with a small alteration.

The Hopping Discrete Fourier Transform [sp Tips&Tricks]

Abstract: The discrete Fourier transform (DFT) produces a Fourier representation for finite-duration data sequences. In addition to its theoretical importance, the DFT plays a key role in the implementation of a variety of digital signal-?processing algorithms. Several algorithms including the fast Fourier transform (FFT) and the Goertzel algorithm have been introduced for the fast implementation of the DFT [1], [2].

Why the DFT is faster than the FFT for FDTD time-to-frequency domain conversions

Abstract: Although it is a time-domain method, the finite-difference time-domain (FDTD) method has been used extensively for calculating frequency domain parameters such as specific absorption rate, radar cross-section, and S-parameters. When a broad frequency band is of interest, using a broad-band pulsed excitation can provide this frequency response with a single FDTD simulation. The frequency domain data can be calculated from the time domain data using either a discrete Fourier transform (DFT) or a fast Fourier transform (FFT). This letter examines both methods and analyzes why the DFT is generally more efficient and easier to use than the FFT for FDTD time-to-frequency domain conversions. >

Minimizing the memory requirement for continuous flow FFT implementation: continuous flow mixed mode FFT (CFMM-FFT)

Abstract: In this paper, an efficient implementation of the Continuous Flow 2N point Real to Complex FFT is presented. The computation is based on the Radix-2 version of Cooley-Tukey algorithm. The key feature of this implementation is the alternation between DIF (Decimation In Frequency) and DIT (Decimation In Time) in the computation of FFT and IFFT of successive symbols. It allows minimizing the total memory requirement. This method requires only 2*N complex memory locations to perform a 2*N point Real-to-Complex FFT of a continuous data flow when other current methods need 3*N or more. The Real to Complex FFT is computed in two steps: a Complex to Complex FFT then Post-Processing. The Complex to Real IFFT is also computed in two steps: Pre-Processing then a Complex to Complex IFFT. 'Cycle Stealing' allows sharing the clock cycles and the data memory banks between the Complex to Complex FFT/IFFT and the Post/Pre-Processing. Only four memory banks and two physical cells (Butterflies) are used to compute an FFT of up to 8192 real input samples with a computation speed twice as fast as the input data rate. This implementation allows a scalable FFT/IFFT: the same hardware resources are used for different FFT sizes 2*N=2" where (1/spl les/n/spl les/13).

Decimation-in-time-frequency FFT algorithm

Abstract: A new fast Fourier transform algorithm is presented. The decimation-in-time (DIT) and the decimation-in-frequency (DIF) FFT algorithms are combined to introduce a new FFT algorithm, decimation-in-time-frequency (DITF) FFT algorithm, which reduces the number of real multiplications and additions. The DITF FFT algorithm reduces the arithmetic complexity while using the same computational structure as the conventional Cooley-Tukey (CT) FFT algorithm. The algorithm is extended to radix-R FFT as well as the multidimensional FFT algorithm using the vector-radix FFT. >