Topic
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.
Papers published on a yearly basis
Papers
More filters
01 Apr 1981
TL;DR: This paper presents an approach to calculating the discrete Fourier transform (DFT) using a prime factor algorithm (PFA) that results in a flexible, modular program that very efficiently calculates the DFT in-place.
Abstract: This paper presents an approach to calculating the discrete Fourier transform (DFT) using a prime factor algorithm (PFA). A very simple indexing scheme is employed that results in a flexible, modular program that very efficiently calculates the DFT in-place. A modification of this indexing scheme gives a new algorithm with the output both in-place and in-order at a slight cost in flexibility. This means only 2N data storage is needed for a length N complex FFT and no unscrambling is necessary. The basic part of a FORTRAN program is given. A speed comparison shows the new algorithm to be faster than both the Cooley-Tukey and the nested Winograd algorithms.
8 citations
TL;DR: In this paper, the analysis of rounding error in the one-dimensional fast Fourier transform (FFT) is extended to a class of generalized orthogonal transforms with a common fast algorithm similar to the FFT algorithm.
Abstract: The analysis of rounding error in the one-dimensional fast Fourier transform (FFT) is extended to a class of generalized orthogonal transforms [1] with a common fast algorithm similar to the FFT algorithm. This class includes the BInary FOurier REpresentation (BIFORE) transform (BT) [2], the complex BT (CBT) [3], and the discrete Fourier transform (DFT). Expressions for the mean square error (MSE) in the two-dimensional BT, CBT, and FFT are derived. In the case of white input data, the mean square error-to-signal ratio is derived for the multidimensional generalized transforms. The error-to-signal ratio for the one-dimensional FFT derived by Kaneko and Liu is modified with improvement. Some comparisons among BIFORE, DFT, and Haar transforms are also included. The theoretical results for the two-dimensional FFT and BIFORE have been verified experimentally. The experimental results are in good agreement with the theoretical results for lower order sequences, but deviate as the order increases due to the actual manner of rounding in the digital computer.
8 citations
TL;DR: The technique of pre-calculation process for real-time FFT, which simultaneously constructs and computes the butterfly modules while the incoming data is collected, is presented and is a better choice for a critical mission requiring a shorter time to complete the FFT calculation.
8 citations
01 Nov 2015
TL;DR: This paper describes the development of decimation-in-time radix-2 FFT algorithm with 16 and 32 points, which was used as a description language, and ISE Design Suite as an Integrated Development Environment (IDE).
Abstract: The Fast Fourier Transform (FFT) is an important algorithm used in the field of Digital Signal Processing and Communication Systems. The FFT has applications in a wide variety of areas, such as linear filtering, correlation, and spectrum analysis, among many others. This paper describes the development of decimation-in-time radix-2 FFT algorithm with 16 and 32 points. VHDL was used as a description language, and ISE Design Suite as an Integrated Development Environment (IDE).
8 citations
TL;DR: A method is presented for converting the m-dimensional discrete Fourier transform (MD-DFT) into a number of one-dimensional DFTs (1D-DFTs) by rearranging the order of the input sequence, which results in a considerable saving in the number of addition operations.
Abstract: A method is presented for converting the m-dimensional discrete Fourier transform (MD-DFT) into a number of one-dimensional DFTs (1D-DFTs) by rearranging the order of the input sequence. The result of this conversion is that the number of multiplications for computing an m-dimensional DFT is only 1/m times that of the usually used row-column DFT algorithm. To reduce the number of additions, a multidimensional polynomial transform (MD-PT) is then used and a considerable saving in the number of addition operations is also achieved.
8 citations