Showing papers on "Twiddle factor published in 1991"

Self-sorting in-place fast fourier transforms

Abstract: It has recently been shown that the familiar radix-2 Fast Fourier Transform (FFT) algorithm can be made both self-sorting and in-place—two useful properties which were previously thought to be mutually exclusive. In this paper the procedure is demonstrated and it is shown how it can be extended toradix-3, radix-4, radix-5, and finally to mixed-radix FFTs. These new versions of the FFT algorithm require neither an unscrambling step nor work space. Implementation on vector computers (for the case of multiple transforms) is discussed. Timing experiments on the Cray X-MP demonstrate that these new variants of the FFT run just as fast as older self sorting routines which required work space.

A better FFT bit-reversal algorithm without tables

Abstract: The bit-reversal counteralgorithm of B. Gold and C.M. Radar (1969) bit reverses a continuous sequence of N numbers by running a loop N -1 times. The heuristic approach presented repeats a similar loop only N/4 times. >

Pipelined Fast Fourier Transform (FFT) architecture

Abstract: A pipelined Fast Fourier Transform (FFT) architecture includes a memory for storing complex number data. A pipelined data path is coupled to the memory for accessing R complex number data therefrom, for computing an FFT butterfly, and storing R results from the FFT butterfly computation in the memory during one pipeline cycle.

Radix-12 DFT/FFT building block

Abstract: Using classic Fast Fourier Transform (FFT) rules, a radix-12 FFT is composed of a first tier of 2 multiplierless radix-6 transformers followed by multiplierless radix-2 transformers, or by its transpose configuration. Complex data are represented in a 1, W 3 coordinate system rather than in a classic 1,j coordinate system. The only multiplicative scaler in the complex twiddle factors is the reciprocal of the square root of 3 which appears six times and which by conversion to canonical signed digit code, can be accurately expressed by 5 adds. As a consequence the complex twiddle factor multipliers and ancillary address reduce to a total of 144 real adds required to perform the entire complex 12-point FFT.

Application of the fast Fourier number theoretic transform to radar

Abstract: Radar applications of the multiple radix fast Fourier number theoretic transform (FFT/NTT) are discussed. The FFT/NTT performs a prime length discrete Fourier transform (DFT) efficiently and accurately using NTTs. The FFT/NTT produces an output without any internal truncation or rounding; therefore, it follows that use of the FFT/NTT for radar processing should yield improvements in the radar's detection performance over some FFT implementations. It is shown that a FFT/NTT computed with n bits yielded equivalent performance to a 2/sup m/-point FFT which processed n+m bits. The FFT/NTT can be easily reconfigured to process additional input bits, thus allowing for increased clutter rejection. >

Implementation of 'multiply-add' FFT algorithms for complex and real data sequences

Abstract: Multiply-add FFT algorithms are FFT algorithms that take advantage of computer architectures with a multiply-add feature. Various FFT algorithms can be implemented on this type of architecture to give the multiplications for free. In the present work, some of these FFT algorithms are reviewed: the split-radix FFT algorithm for 2/sup k/ transform sizes, the multiplicative algorithms for prime transform sizes, and the prime factor algorithm for transform sizes with relatively prime factors. Both complex and real data sequences are considered, and operational counts are evaluated in terms of total floating-point operations. Tensor product formulation is used throughout for producing variants of algorithms matching to computer architecture. >

The multidimensional phase-rotation FFT: a new parallel architecture

Abstract: A new multidimensional FFT (fast Fourier transform) algorithm and processor architecture is introduced. The FFT architecture is based on a multidimensional parallel pipeline, sized to carry data into one d-dimensional kernel FFT of vector radix r/sup d/ completely in parallel. Inter-stage shuffling is confined to individual channels of the pipeline, and has constant geometry. The simplicity of the design is well-suited to VLSI implementation. >

A general in-place and in-order prime factor FFT algorithm

Abstract: Starting from an index mapping for one to multi-dimensions, a general in-place and in-order prime factor FFT algorithm is proposed in this paper. In comparing with existing prime factor FFT algorithms, this algorithm saves about half of the required storage capacity and possesses a higher efficiency. In addition, this algorithm can easily implement the DFT and IDFT in a single subroutine.

Parallelisation of a 2-D Fast Fourier Transform Algorithm

Abstract: The calculation of two and higher-dimension Fast Fourier Transforms (FFT’s) are of great importance in many areas of data analysis and computational physics. The two-dimensional FFT is implemented for a parallel network using a master-slave approach. In-place performance is good, but the use of this technique as an “accelerator” is limited by the communications time between the host and the network. The total time is reduced by performing the host-master communications in parallel with the master-slave communications. Results for the calculation of the two-dimensional FFT of real-valued datasets are presented.

System implementation of look up table FFT

Abstract: The implementation of a fast Fourier transform (FFT) look-up table is developed. Radix 2 is selected to work on a large range of data. The system is constructed to generate a series of tables depending on the input data. Each table has N/4 values of cosines and sines depending on the value of N. This system provides a fast method of FFT implementation. The flow chart and software provided for testing the result are discussed. >

The new algorithms for 2-dimensional FFT with prime size

Abstract: Two algorithms for the 2D fast Fourier transform (FFT) are developed, where the prime size p identical to 3 mod 4 and p identical to 2 mod 3. The indexing set in each case forms a field, and the computation of the 2D FFT can be completely transferred into one dimension which is identical to the computational structure of the 1D FFT with prime size. Instead of the row-column algorithm which was designed based on the 1D FFT, an algorithm based on 1D cyclic convolution is designed. It is shown that this algorithm is efficient for some sample points and flexible for parallel or vector processing. >