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.

Computational Complexity Analysis of FFT Pruning - A Markov Modeling Approach

Abstract: The Fourier transform is instrumental in many signal processing applications such as digital filtering, spectral analysis and communications. In 1965, Cooley and Tukey demonstrated that the discrete Fourier transform (DFT) can be computed using the fast Fourier transform (FFT) algorithm with reduced computational complexity. When the input vector to the FFT contains mostly zeros (i.e., is sparse), it is possible to realize computational savings over a full FFT by only performing the arithmetic operations on non-zero elements. That is, the FFT is "pruned" so that only the useful computations are performed. In this paper, we derive the (non-stationary) Markov process that describes the number of occupied (i.e. non-zero) paths at each stage of a pruned FFT. With the probability distribution of the number of non-zero paths at each FFT stage, we then determine the probability distribution of the number of multiplications and additions necessary to compute the FFT of an input vector with a given sparsity distribution

Distributed Arithmetic based Split-Radix FFT

Abstract: In this paper we have designed a Split-radix type FFT unit without using multipliers. All the complex multiplications required for this type of FFT are implemented using Distributed Arithmetic (DA) technique. A method is incorporated to overcome the result overflow problem introduced by DA method. Proposed FFT architecture is implemented in 180 nm CMOS technology at a supply voltage of 1.8 V.

Computational assessment of Gabor representations

Abstract: A comparative assessment of the computational complexity of several Gabor transform algorithms is given, with results in the range O(P)/sup 2/ to O(P log/sub 2/ P), where P is the number of data points being transformed. Among the results is a novel algorithm of lower complexity than previously known FFT (fast Fourier transform) based methods. The most efficient of the methods, which uses the Zak transform as an operational calculus, performs the Gabor analysis and synthesis transforms with a complexity comparable to that of the FFT. >

Error analysis and resulting structural improvements for fixed point FFTs

Abstract: A concept for a fixed point FFT (fast Fourier transform) error analysis is explained which allows a rather fast, simple and comprehensive numerical evaluation. This avoids time-consuming simulations or cumbersome theoretical derivations of the specific FFT length and structure for any change of the input signal or for any changes in the method of scaling and wordlength-reduction. From the results obtained, conclusions are drawn from reducing fixed-point errors with little or no additional effort. >

Architecturally efficient FFT pruning algorithm

Abstract: Several fast Fourier transform (FFT) pruning algorithms have been proposed for applications where the entire spectrum of frequencies is not of relevance and even the inputs are sparse. However, these are architecturally inefficient because of the complexity of the overhead operations involved. Developed is a new generic pruning algorithm that uses only single bit combinational operations for delineating paths in the signal flow graph, as against butterflies, which are relevant for computation of the desired frequency coefficients. The entire delineation process has been divided into stages making the proposed algorithm also amenable for pipelined hardware implementation.