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.

A fast algorithm for the computation of radon transforms1

Abstract: A fast algorithm is presented for numerical evaluation of forward and inverse Radon transforms. The algorithm does not perform exact one-to-one mapping as the discrete Fourier transform but, due to the use of band-limited basis functions, it is robust and sufficiently accurate for seismic applications. By rewriting the transform as a convolution, a computational speed is obtained similar to the speed of the 2D fast Fourier transform.

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.

Fast Fourier transform benchmark on X86 Xeon system for multimedia data processing

Abstract: I benchmarking the well-known Fast Fourier Transforms Library at X86 Xeon E5 2690 v3 system. Fourier transform image processing is an important tool that is used to decompose the image into sine and cosine components. If the input image represented by the equation in the spatial domain, output from the Fourier transform represents the image in the fourier or the frequency domain. Each point represents a particular frequency included in the spatial domain image in the Fourier domain image. Fourier transform is used widely for image analysis, image filtering, image compression and image reconstruction as a wide variety of applications. Fourier transform plays a important role in signal processing, image processing and speech recognition. It has been used in a wide range of sectors. For example, this is often a signal processing, is used in digital signal processing applications, such as voice recognition, image processing. The Discrete Fourier transform is a specific kind of Fourier transform. It maps the sequence over time to sequence over frequencies. If it implemented as a discrete Fourier transform, the time complexity is O (N2). It's actually not a better way to use. Alternatively, the Fast Fourier Transform is possible to easily perform a Discrete Fourier Transform of parallelism with only O (n log n) algorithm. Fast Fourier Transform is widely used in a variety of scientific computing program. If you are using the correct library can improve the performance of the program, without any additional effort. I have a well-known fast Fourier transform library was going to perform a benchmarking on X86 based Intel Xeon E5 2690 systems. In the machine's current Intel Xeon X86 Linux system. I have installed Intel IPP library, FFTW3 Library (West FFT), Kiss -FFT library and the numutils library on Intel X86 Xeon E5 based systems. The benchmark performed at C, and measuring the performance over a range of a transform size. It benchmarks both real and complex transforms in one dimension.

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.

An improved fast Radon transform algorithm for two-dimensional discrete Fourier and Hartley transform

Abstract: Presents a novel algorithm for the computation of the two-dimensional discrete Fourier transform and discrete Hartley transform. By using the discrete Radon transform (DRT), the algorithm essentially converts the two-dimensional transforms into a number of one-dimensional ones. By totally eliminating all redundant operations during the computation of the DRT, the algorithm can give an average of 20% reduction in the number of additions as compared to previous approaches which are also based on the DRT. In fact, it has the same arithmetic complexity as the fastest algorithms which use the polynomial transform for their decompositions. However, the present approach has the advantage over the ones using the polynomial transform in that it can easily be realized. >