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.

Self-sorting in-place FFT algorithm with minimum working space

Abstract: Presents a modification of Temperton's (1991) self-sorting, in-place radix-p FFT algorithm. This modification reduces the required temporary working space from order of p/sup 2/ to p+1, providing a better match to the limited number of registers in a CPU. >

Pipelined Architectures for Real-Valued FFT and Hermitian-Symmetric IFFT With Real Datapaths

Abstract: This brief presents novel parallel pipelined architectures for the computation of the fast Fourier transform (FFT) of real signals and inverse FFT of Hermitian-symmetric signals using only real datapaths. The real FFT structure is transformed by transferring twiddle factors to subsequent stages, such that each stage in the proposed flow graph contains one column of butterfly units and one column of twiddle factor blocks, and each column of the flow graph contains only N samples. This is a key requirement for the design of architectures that are based on only real datapaths. This structure is then mapped to pipelined architectures. The proposed architectures can be used with any FFT size or level of parallelism, which is a power of two. A systematic method to design architectures for FFTs with different levels of parallelism and radix values is presented. By modifying the FFT flow graph for real-valued samples, this methodology leads to architectures with fewer adders, delays, and interconnections.

A new radix-2/8 FFT algorithm for length-q/spl times/2/sup m/ DFTs

Abstract: In this paper, a new radix-2/8 fast Fourier transform (FFT) algorithm is proposed for computing the discrete Fourier transform of an arbitrary length N=q/spl times/2/sup m/, where q is an odd integer. It reduces substantially the operations such as data transfer, address generation, and twiddle factor evaluation or access to the lookup table, which contribute significantly to the execution time of FFT algorithms. It is shown that the arithmetic complexity (multiplications+additions) of the proposed algorithm is, in most cases, the same as that of the existing split-radix FFT algorithm. The basic idea behind the proposed algorithm is the use of a mixture of radix-2 and radix-8 index maps. The algorithm is expressed in a simple matrix form, thereby facilitating an easy implementation of the algorithm, and allowing for an extension to the multidimensional case. For the structural complexity, the important properties of the Cooley-Tukey approach such as the use of the butterfly scheme and in-place computation are preserved by the proposed algorithm.

Algorithms meeting the lower bounds on the multiplicative complexity of length-2/sup n/ DFTs and their connection with practical algorithms

Abstract: In a previous work (see Electron. Lett., vol.20, no.17, p.690, 1984), the author described an algorithm that computes a length-2/sup n/ discrete Fourier transform using 2/sup 2+1/-2n/sup 2/+4n-8 nontrivial (i.e. not=+or-j=+or- square root -1) complex multiplications. In the present work, it is first shown that this algorithm actually provides the attainable lower bound on the number of complex multiplications. A slight modification of the last step of this algorithm is also shown to provide the attainable lower bound on the number of real multiplications. A connection with the split-radix FFT algorithm (SRFFT) is then explained, showing that SRFFT is another variation of these optimal algorithms, where the last step is computed recursively from shorter FFTs in a suboptimal manner. Finally, once the connection between the minimal complexity and SRFFT (which is the best known practical algorithm) is understood, it provides useful information on the possibility of further improvements of the SRFFT. >

The zoom FFT using complex modulation

Abstract: A recent paper by Yip discussed the zoom transform as derived from the defining equation of the FFT. This paper simplifies the concepts and removes some of the restrictions assumed by Yip; ie., the total number of points need not be a power of 2. The technique is based on first specifying the desired center frequency, bandwidth, and frequency resolution. The signal is then sampled, modulated, and lowpass filtered. This result is purposely aliased, then transformed using an FFT algorithm. The result is an M-point frequency spectra of the desired bandwidth centered about the center frequency with a higher degree of resolution than could be directly obtained using an M-point transform.