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.

System design for a million channel digital spectrum analyzer /MCSA/

Abstract: The system design of a wideband (8 MHz) million-channel digital spectrum analyzer for use with a SETI receiver is presented. The analyzer makes use of a digital bandpass filter bank for transforming the wideband input signal into a specified number (120) of uniform narrowband output channels by the use of a Fourier transform digital processor combined with a prototype digital weighting network (finite impulse response filter). The output is then processed separately by 120 microprocessor-based discrete Fourier transform computers, each producing 8190 output channels of approximately 8 Hz bandwidth by the use of an 8190-point prime factor algorithm.

Comments on and extensions to "Evaluation of Fourier integrals using a FFT with improved accuracy and its applications"

Abstract: The evaluation of Fourier integrals using fast Fourier transform (FFT) employing the Narasimhan scheme is examined. It is observed to be a special case of spline interpolation. His method is effective when the sampling rate is sufficiently high and piecewise linear approximation between sampling points is adequate. If knowledge about the signal smoothness is available, further improvement in accuracy can be achieved by judicious choice of high degree spine interpolant.

Improvement of FFT-based cross-correlation algorithm for PIV

Abstract: An improved fast Fourier transform(FFT)-based cross-correlation algorithm is proposed to solve the computational efficiency problem of cross-correlation in particle image velocimetry(PIV).Based on the decimation in frequency theory,when the overlapping correlation window size is about 50%,the one-dimensional FFT values of overlapping windows are composed of their neighbor sub-window′s FFT values by using the frequency shift instead of implementing FFT and the repeating computation in FFT is greatly reduced.Finally,the proposed method was tested with the real particle images continuously acquired by CCD camera.The experimental results show about 12.25% increase in computational efficiency compared with the traditional method.

Design of Combined Radix-2, Radix- 4 and Radix-8 based Single Path Delay Feedback (SDF) FFT

Abstract: Objectives: FFT algorithm is used for enhancing the performance of DFT.In the previous years, various types of FFT algorithms have been introduced. Particularly, the pipeline algorithms have been reputed as proper algorithms for processing high-speed data. Some pipeline FFT algorithms like split radix, radix-2 and the mixed radix have been developed. Methods: In the existing method of Radix-2 SDF FFT has more hardware utilization and also computational stages are increased. Findings: To conquer this problem, we developed a combined radix-2, 4 & 8 butterfly elements based Single path Delay Feedback (SDF) fast fourier transform method for reducing the computational stages in this paper. The developed method has the identical number of multipliers and the smaller number of stages and butterfly elements than the existing radix-2 FFT. Improvements: This architecture offers 62.47% reduction in LUTs, 58.78% reduction in slices, and 37.85% reduction in delay and 30.86% reduction in power consumption than the existing method.

Tighter Fourier Transform Complexity Tradeoffs

Abstract: The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. Achieving a matching lower bound in a reasonable computational model is one of the most important open problems in theoretical computer science. In 2014, improving on his previous work, Ailon showed that if an algorithm speeds up the FFT by a factor of $b=b(n)\geq 1$, then it must rely on computing, as an intermediate "bottleneck" step, a linear mapping of the input with condition number $\Omega(b(n))$. Our main result shows that a factor $b$ speedup implies existence of not just one but $\Omega(n)$ $b$-ill conditioned bottlenecks occurring at $\Omega(n)$ different steps, each causing information from independent (orthogonal) components of the input to either overflow or underflow. This provides further evidence that beating FFT is hard. Our result also gives the first quantitative tradeoff between computation speed and information loss in Fourier computation on fixed word size architectures. The main technical result is an entropy analysis of the Fourier transform under transformations of low trace, which is interesting in its own right.