Single Fast Fourier Transform Research Articles

A fast Fourier transformation algorithm for parallel computers

A new algorithm is presented for using the fast Fourier transform (FFT) in a very efficient mode. This algorithm is ideal for a parallel computer such as the ICL Distributed Array Processor (DAP), though it can be used with benefit on any serial computer. For a two- or three-dimensional electron density Fourier map the Fourier coefficients are arranged in a one-dimensional vector form of the chosen length and the whole map is obtained by a single FFT operation. To obtain a higher density of calculated points in the map a number of FFT operations is required, each entailing a phase modification of the one-dimensional Fourier coefficients. A three-dimensional map using 1429 crystal reflections and giving the density at 32768 points takes roughly 2 s in the ICL DAP.

Efficient Parameter Identification for a Class of Bilinear Differential Systems *

Using sinusoidal probing signals on sequential time intervals of finite duration, a least squares parameter identification technique is developed for a class of bilinear differential systems which avoids the usual point-wise-in-time cross multiplication between the input-output data and avoids dealing with all unknown initial (boundary) conditions over each finite time interval. The basis of the technique is Shinbrot's method of moment functionals using commensurable sinusoids as the modulating functions. The main result is the demonstration that the sequential least squares procedure for the bilinear system parameters with sinusoidal inputs can be set up using a single Fast Fourier Transform of the output data over each finite time interval which is essentially the same computational requirement as attends the formulation for a linear system model

A VLSI Network for Variable Size FFT's

A network for the evaluation of the fast Fourier transform (FFT) is presented. Such a network is able to compute, in parallel, the FFT's of arbitrary partitions in powers of two of the N input elements. It is shown that, under a VLSI model of computations, such a design requires the same asymptotical area and attains the same throughput as the corresponding network for the evaluation of a single N-element FFT.

A Storage Efficient Way to Implement the Discrete Cosine Transform

Ahmed has shown that a discrete cosine transform can be implemented by doing one double length fast Fourier transform (FFT). In this correspondence, we show that the amount of work can be cut to doing two single length FFT's.