Showing papers on "Prime-factor FFT algorithm published in 1980"

A Quantitative Study of Pitfalls in the FFT

Abstract: The effects of aliasing (including pseudoaliasing), picket-fence effect, and leakage in the fast Fourier transform (FFT) are presented. A computer program was written to perform the FFT analysis of known inputs. The program has the capability of detecting aliasing by calculating an "aliasing coefficient" (Q), and will increase the sampling frequency and the number of points in the input sequence if aliasing occurs. The term "pseudoaliasing" is a phenomenon which is similar to aliasing (or fold-over) but related to the effects of picket fence and leakage. The "leakage coefficient" (ri) is a quantitative measure of the deviation from the fundamental frequency component with respect to the sampling frequency, when the input sequence has only one frequency component.

Computing the Waiting Time Distribution for the G/G/1 Queue by Signal Processing Methods

Abstract: Two methods, based on signal processing techniques, are presented for obtaining numerical solutions for the general single server queue with first-come, first-served discipline The first method is based on the use of the fast Fourier transform (FFT) for producing iterative solutions to a discrete version of Lindley's integral equation for both nonsteady state and equilibrium conditions The second method makes use of the complex cepstrum, implemented with the FFT, for providing direct solutions with the queue in equilibrium

High-resolution narrow-band spectra by FFT pruning

Abstract: A new method of computing high-resolution narrow-band spectra faster than the chirp z transform (CZT) and direct computation of discrete Fourier transform (DFT) is presented. This is achieved by a generalization of Markel's pruning algorithm and in combination with Skinner's pruning algorithm for the decimation-in-time FFT formulation. However, for very high resolutions it is shown that the CZT is selectively superior to the new method.

A stepwise approach to computing the multidimensional fast Fourier transform of large arrays

Abstract: We consider the problem of performing a two-dimensional fast Fourier transform (FFT) on a very large matrix in limited core memory. We propose a decomposition of the Cooley-Tukey algorithm to allow efficient utilization of core memory and mass storage. The number of input/output operations is greatly reduced, with no increase in the computational burden. The method is suitable for nonsquare matrices and arrays of three or more dimensions.

Fast computation of multidimensional discrete fourier transforms

Abstract: An algorithm is presented, for the computation of multidimensional Fourier and Fourier-like discrete transforms, which offers substantial savings in the number of multiplications over the conventional fast Fourier transform method Implementation of this algorithm, and the use of it to compute discrete Fourier transforms of real sequences, are also described

FFT as Nested Multiplication, with a Twist

Abstract: A simple, yet complete and detailed description of the fast Fourier transform for general N is given with the aim of making the underlying idea quite apparent. To help with this didactic goal, a simple twist, i.e., a shifting of information from rows to columns during the calculations, is introduced which allows us to give a simple meaning to intermediate results and assures that the final results need no further reordering.

Efficient Synthesis and Implementation of Large Discrete Fourier Transformations

Abstract: A systematic technique is presented for synthesizing and efficiently performing large discrete Fourier transformations (DFT’s) in the range from 60 to 5000 points. The technique is termed the mutual prime factor cyclic algorithm (MPFCA). The mutual prime factor portion of the algorithm is attributed originally to L. H. Thomas, with generalization supplied by I. J. Good; the cyclic aspect of the algorithm has recently been formalized by S. Winograd. Three methods are described for implementing the MPFCA; computational complexity (multiplications and additions) is estimated for each method and compared with the fast Fourier transform (FFT). For special purpose hardware, the MPFCA is at least twice as efficient as the FFT. A major result of importance is the realization that the three considerably different implementation methods presented lead to rather similar multiplication complexities for large size DFT’s; furthermore, the resulting multiplication complexity is considerably higher than that achieved for...

A note on the application of FFT to the solution of a system of Toeplitz normal equations

Abstract: This note presents an approach to the solution of a system of Toeplitz normal equations, based on using iterative techniques, the circulant matrices and the fast Fourier transform algorithm. The number of computations required and the roundoff errors associated with this method are discussed. The merits and demerits of this approach are compared with the Trench's algorithm.

On vectorizing the fast fourier transform

Abstract: A variant of the Cooley-Tukey algorithm due to Stockham is derived and vectorized and is shown to be on a par with the Pease algorithm. The Stockham algorithm is then proposed for the entire computation of the two-dimensional fast Fourier transform on a vector computer.

Computation of the discrete cosine transform via the arcsine transform

Abstract: A procedure is described for the computation of the discrete cosine transform (DCT) via the use of the arcsine transform. The approach eliminates time-consuming multiplications, the DCT being accomplished with only additions and table lookups. While a fast Fourier transform (FFT) approach to computing the DCT involves on the order of N\log_{2}2N "butterfly" computations to evaluate all N coefficients, the arcsine method requires only 4N - 1 real additions and 2N table lookups to evaluate each DCT coefficient. Thus, for applications in which M coefficients are desired or when N is reasonably small (say, N \leq 256 ), the arcsine approach is favored over that of the FFT. Some approaches to hardware implementation are presented.

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.

Implementation of prime transform algorithm using c.c.d. programmable transversal filter

Abstract: An economic scheme is proposed for implementing the prime transform algorithm using charge-coupled device programmable transversal filters.

Fourier Transform Faster Than Fast Fourier Transform (FFT)

Abstract: Because of the rapid advances in multiplication hardware, the most time consuming processing step inFourier Transform will be the number of memory accesses rather than the number of multiplications. Analgorithm of Continuous Fourier Transform (CFT) which minimizes memory access was developed. It can beimplemented with existing technology and is potentially faster than FFT, particularly for processing continuous, real -time signals. IntroductionSince its publication by Cooley and Tukey,l Fast Fourier Transform (FFT) has been the principal techniqueemployed in the computer realization of Fourier analysis for most applications. The success of FFT lies inthe fact that the number of multiplications, which until very recently has been the most time consumingoperation in the computation, is minimized to the order to N log2N from N2, where N is the number of datavalues to be transformed.As indicated by recent advancements in the LSI and computer technologies, multiplications can be done asfast as additions,2'3 and low cost CPU's can be ganged together in parallel to increase processing throughput.These developments point to new directions of signal processing which might achieve even greater throughputthan the FFT as implemented on a single CPU computer. Here I shall outline the theoretical justificationsof such a design and suggest ways of its hardware implementation with currently available LSI technology.This type of Fourier Transform processor is capable of processing signals sampled at a rate in excess of

System Identification Using Fast Fourier Transform

Abstract: Algorithms for system identification applying throughout Fast Fourier Transform (FFT) to the major calculating operations are introduced. It is shown that by using data of about as twice length as system settling time and by truncating the incorrect correlation functions resulting from them, errors owing to finiteness of data can be avoided. It is shown that so as to suppress the effects owing to statistical fluctuation of input data or output noise, superposition of data in frequency domain is effective, and also the damping terms of poles or zeros can be efficiently evaluated by utilizing the phase change of the spectra of the impulse response sequence. The proposed method can be efficiently applied to relatively higher order systems or relatively rapidly time-variant systems because of high accuracy and high speed processing of FFT. Moreover, it needs not to assume the order of the system a priori, and yields a reasonable lower order approximating system in itself.

Floating point error bound in the prime factor FFT

Abstract: The prime factor FFT