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.

Affect analysis of FFT algorithm length on traffic self-similarity in NOC

Abstract: With network performance being highly dependent on the actual traffic, studies have shown that traffic is self-similar and long-range correlation in Network on Chip (NoC). The self-similarity of NoC traffic depends not only on the input sequence, but also changes with the processor algorithm on chip. In this paper, we improved firstly the existing method for generating sample traces of self-similar processes to suit Fast Fourier Transform (FFT) Algorithm. Then, Mainly studied the effects of FFT algorithm length for network traffic self-similarity in NoC by simulations. Experimental results show that the self-similarity of output sequence raised with the increasing of FFT length, and the output sequence is not self-similar when the length is long enough.

Input-adaptive parallel sparse fast fourier transform for stream processing

Abstract: Fast Fourier Transform (FFT) is frequently invoked in stream processing, e.g., calculating the spectral representation of audio/video frames, and in many cases the inputs are sparse, i.e., most of the inputs' Fourier coefficients being zero. Many sparse FFT algorithms have been proposed to improve FFT's efficiency when inputs are known to be sparse. However, like their "dense" counterparts, existing sparse FFT implementations are input oblivious in the sense that how the algorithms work is not affected by the value of input. The sparse FFT computation on one frame is exactly the same as the computation on the next frame. This paper improves upon existing sparse FFT algorithms by simultaneously exploiting the input sparsity and the similarity between adjacent inputs in stream processing. Our algorithm detects and takes advantage of the similarity between input samples to automatically design and customize sparse filters that lead to better parallelism and performance. More specifically, we develop an efficient heuristic to detect the similarity between the current input to its predecessor in stream processing, and when it is found to be similar, we novelly use the spectral representation of the predecessor to accelerate the sparse FFT computation on the current input. Given a sparse signal that has only $k$ non-zero Fourier coefficients, our algorithm utilizes sparse approximation by tuning several adaptive filters to efficiently package the non-zero Fourier coefficients into a small number of bins which can then be estimated accurately. Therefore, our algorithm has runtime sub-linear to the input size and gets rid of recursive coefficient estimation, both of which improve parallelism and performance. Furthermore, the new heuristic can detect the discontinuities inside the streams and resumes the input adaptation very quickly. We evaluate our input-adaptive sparse FFT implementation on Intel i7 CPU and three NVIDIA GPUs, i.e., NVIDIA GeForce GTX480, Tesla C2070 and Tesla C2075. Our algorithm is faster than previous FFT implementations both in theory and implementation. For inputs with size N=2^{24}, our parallel implementation outperforms FFTW for k up to 2^{18}, which is an order of magnitude higher than prior sparse algorithms. Furthermore, our input adaptive sparse FFT on Tesla C2075 GPU achieves up to 77.2x and 29.3x speedups over 1-thread and 4-thread FFTW, 10.7x, 6.4x, 5.2x speedups against sFFT 1.0, sFFT 2.0, CUFFT, and 6.9x speedup over our sequential CPU performance, respectively.

Increasing the Efficiency of Using Hardware Resources for Time-Frequency Correlation Function Computation

Abstract: In the article the techniques of increasing efficient of using multi-core processors for the task of calculating the fast Fourier transform were considered. The fast Fourier transform is led on the basis of calculating a time time-frequency correlation function. The time-frequency correlation function allows increasing the information content of the analysis as compared with the classic correlation function. The significant computational capabilities are required to calculate the time-frequency correlation function, that by reason of the necessity of multiple computing fast Fourier transform. For computing the fast Fourier transform the Cooley-Tukey algorithm with fixed base two is used, which lends itself to efficient parallelization and is simple to implement. Immediately before the fast Fourier transform computation the procedure of bit-reversing the input data sequence is used. For algorithm of calculating the time-frequency correlation function parallel computing technique was used that experimentally allowed obtaining the data defining the optimal number of iterations for each core of the CPU, depending on the sample size. The results of experiments allowed developing special software that automatically select the effective amount of subtasks for parallel processing. Also the software provides the choice of sequential or parallel computations mode, depending on the sample size and the number of frequency intervals in the calculation of time-frequency correlation function.

Recursive calculation of Fourier transform of discrete signal

Abstract: Two algorithms for the calculation of Fourier transform of a discrete signal are derived from the known recursive method for polynomial evaluation. The first algorithm processes the elements of the discrete signal in a natural order of elements and the second one in the reverse order. Both algorithms are modified for operation with real numbers only. The relation of these algorithms to the well known Goertzel algorithm and the Collatz's rule is demonstrated. Moreover, the application of the recursive algorithm to repeated DFT calculation is described.