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.

Reducing the Hamming distance of encoded FFT twiddle factors using improved heuristic algorithms

Abstract: This paper addresses the exploration of different heuristic algorithms for a better manipulation of twiddle factors of Fast Fourier Transform (FFT). The FFT algorithm involve multiplications of input data with appropriate coefficients, hence the best ordering of those operations can contribute for reducing the switching activity, what leads to the minimization of power consumption in FFTs. The heuristic algorithm named Bellmore and Nemhauser, and a proposed one named Anedma in both original and improved versions, are used to get as near as possible to the optimal solution for the ordering and partitioning of coefficients in FFTs. Data encoding methods are used for decreasing switching activity for transmitting information over buses, hence we have used some encoding techniques in the coefficients. As will be shown, the appropriate ordering of coefficients, based on the guidance given by the improved Anedma algorithm, can contribute for the reduction of Hamming distance of the encoded twiddle factors.

Fast method to detect specific frequencies in monitored signal

Abstract: The Discrete Fourier Transform (DFT) is a mathematical procedure that stands at the center of the processing that takes place inside a Digital Signal Processor. It has been known and argued through the literatures that the Fast Fourier Transform (FFT) is useless in detecting a specific frequency in a monitored signal because most of the computed results are ignored. In this paper we will present an efficient FFT based method to detect specific frequencies in a monitored signal which is compared to the most frequently used method “the Goertzel's Algorithm”. Parallel implementation structure show a fast computation method compared to the Goertzel's algorithm. Computational speedup gains of r using radix-r butterfly are shown.

Finding Significant Fourier Transform Coefficients Deterministically and Locally

Abstract: Computing the Fourier transform is a basic building block used in numerous applications. For data intensive applications, even the O(N log N) running time of the Fast Fourier Transform (FFT) algorithm may be too slow, and sub-linear running time is necessary. Clearly, outputting the entire F ourier transform in sub-linear time is infeasible, nevertheless, in many applications it suffices to find only the τ-significant Fourier transform coefficients, that is, the Fourier coefficients whose magnitude is at leas t τ-fraction (say, 1%) of the energy (i.e., the sum of squared Fourier coefficients). We call algorithm s achieving the latter SFT algorithms. In this paper we present a deterministic algorithm that finds the τ-significant Fourier coefficients of functions f over any finite abelian group G in time polynomial in log|G|, 1/τ and L1(b) (for L1(b) denoting the sum of absolute values of the Fourier coefficien ts of f ). Our algorithm is robust to random noise. Our algorithm is the first deterministic and efficient ( i.e., polynomial in log|G|) SFT algorithm to handle functions over any finite abelian groups, as well as th e first such algorithm to handle functions over ZN that are neither compressible nor Fourier-sparse. Our analysis is the first to show robustness to noise in the context of deterministic SFT algorithms. Using our SFT algorithm we obtain (1) deterministic (universal and explicit) algorithms for sparse Fourier approximation, compressed sensing and sketching; (2) an algorithm solving the Hidden Number Problem with advice, with cryptographic bit security implications; and (3) an efficient decoding algorithm in the random noise model for polynomial rate variants of Homomorphism codes and any other concentrated & recoverable codes.

Low-complexity twiddle factor generation for FFT processor

Abstract: A low-complexity twiddle factor generation structure for fast Fourier transform (FFT) is proposed. In FFT, twiddle faction generation and multiplication occupies more area than the other mathematical operations. The proposed structure reduces the twiddle factor generation part by removing the redundancies in the conventional structure and compressing the twiddle factor ROM contents. With the proposed structure, the twiddle factor generation part is reduced by 32–45% compared with that of the conventional structure.

Equivalent relationship and unified indexing of FFT algorithm

Abstract: The twiddle factor matrix of the discrete Fourier transform can be recursively factorized into the cascading of the basic butterfly stage matrices. It is shown that the matrix can be further partitioned into three matrices practically specifying the input data, twiddle factor, and output data sequences of the fast Fourier transform (FFT). The equivalent relationship of these matrices is introduced. Thus, the equivalent relationship for a variety of the FFT algorithms can be obtained by equivalent matrix transformation. It is shown that the multidimensional (M-D) FFT can be represented by the same vector-matrix form as the 1-D FFT. The addressing sequences of the M-D FFT is the subset of the 1-D FFT. Therefore, the signal flow graph of the 1-D FFT can be used to describe that of the M-D FFT and the 1-D FFT addressing sequences can be employed to implement the M-D FFT. The simulation results of the proposed FFT approach are given. >