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.

Recursive algorithm for phase retrieval in the fractional fourier transform domain.

Abstract: We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.

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].

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).

Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

Abstract: Preface. Acknowledgments. Acronyms. 1 Signals and Their Mathematical Models. 1.1 Systems. 1.2 Signals. 1.3 Mathematical Models of Signals. References. 2 Fourier Analysis. 2.1 Representations of Groups. 2.1.1 Complete Reducibility. 2.2 Fourier Transform on Finite Groups. 2.3 Properties of the Fourier Transform. 2.4 Matrix Interpretation of the Fourier Transform on Finite Non-Abelian Groups. 2.5 Fast Fourier Transform on Finite Non-Abelian Groups. References. 3 Matrix Interpretation of the FFT. 3.1 Matrix Interpretation of FFT on Finite Non-Abelian Groups. 3.2 Illustrative Examples. 3.3 Complexity of the FFT. 3.3.1 Complexity of Calculations of the FFT. 3.3.2 Remarks on Programming Implememtation of FFT. 3.4 FFT Through Decision Diagrams. 3.4.1 Decision Diagrams. 3.4.2 FFT on Finite Non-Abelian Groups Through DDs. 3.4.3 MMTDs for the Fourier Spectrum. 3.4.4 Complexity of DDs Calculation Methods. References. 4 Optimization of Decision Diagrams. 4.1 Reduction Possibilities in Decision Diagrams. 4.2 Group-Theoretic Interpretation of DD. 4.3 Fourier Decision Diagrams. 4.3.1 Fourier Decision Trees. 4.3.2 Fourier Decision Diagrams. 4.4 Discussion of Different Decompositions. 4.4.1 Algorithm for Optimization of DDs. 4.5 Representation of Two-Variable Function Generator. 4.6 Representation of Adders by Fourier DD. 4.7 Representation of Multipliers by Fourier DD. 4.8 Complexity of NADD. 4.9 Fourier DDs with Preprocessing. 4.9.1 Matrix-valued Functions. 4.9.2 Fourier Transform for Matrix-Valued Functions. 4.10 Fourier Decision Trees with Preprocessing. 4.11 Fourier Decision Diagrams with Preprocessing. 4.12 Construction of FNAPDD. 4.13 Algorithm for Construction of FNAPDD. 4.13.1 Algorithm for Representation. 4.14 Optimization of FNAPDD. References. 5 Functional Expressions on Quaternion Groups. 5.1 Fourier Expressions on Finite Dyadic Groups. 5.1.1 Finite Dyadic Groups. 5.2 Fourier Expressions on Q2. 5.3 Arithmetic Expressions. 5.4 Arithmetic Expressions from Walsh Expansions. 5.5 Arithmetic Expressions on Q2. 5.5.1 Arithmetic Expressions and Arithmetic-Haar Expressions. 5.5.2 Arithmetic-Haar Expressions and Kronecker Expressions. 5.6 Different Polarity Polynomials Expressions. 5.6.1 Fixed-Polarity Fourier Expressions in C(Q2). 5.6.2 Fixed-Polarity Arithmetic-Haar Expressions. 5.7 Calculation of the Arithmetic-Haar Coefficients. 5.7.1 FFT-like Algorithm. 5.7.2 Calculation of Arithmetic-Haar Coefficients Through Decision Diagrams. References. 6 Gibbs Derivatives on Finite Groups. 6.1 Definition and Properties of Gibbs Derivatives on Finite Non-Abelian Groups. 6.2 Gibbs Anti-Derivative. 6.3 Partial Gibbs Derivatives. 6.4 Gibbs Differential Equations. 6.5 Matrix Interpretation of Gibbs Derivatives. 6.6 Fast Algorithms for Calculation of Gibbs Derivatives on Finite Groups. 6.6.1 Complexity of Calculation of Gibbs Derivatives. 6.7 Calculation of Gibbs Derivatives Through DDs. 6.7.1 Calculation of Partial Gibbs Derivatives. References. 7 Linear Systems on Finite Non-Abelian Groups. 7.1 Linear Shift-Invariant Systems on Groups. 7.2 Linear Shift-Invariant Systems on Finite Non-Abelian Groups. 7.3 Gibbs Derivatives and Linear Systems. 7.3.1 Discussion. References. 8 Hilbert Transform on Finite Groups. 8.1 Some Results of Fourier Analysis on Finite Non-Abelian Groups. 8.2 Hilbert Transform on Finite Non-Abelian Groups. 8.3 Hilbert Transform in Finite Fields. References. Index.

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. >