FFT Scheme Research Articles

Fast Acquisition Scheme of the Spread Spectrum Signals for Satellite Communications

A four-channel parallel acquisition scheme combining partial matched filters and fast Fourier transforms (PMF-FFT) is proposed for the fast acquisition of the spread spectrum signals in satellite communication terminals installed into the offshore buoys with the high-dynamic movement, which is used tofinish data communication missions between the buoys and the satellite. Compared with traditional code phase FFT scheme, the new scheme reduces the maximum acquisition time to 26.5% and the maximum computation amount to 46.9%. It also improves about 4 times in the frequency resolution and 1.6 dB in the receiving sensitivity at the expense of computation complexity compared to PMF-FFT scheme. The parallel PMF-FFT scheme greatly reduces scallop loss, thus ensuring acquisition sensitivity. The parallel PMF-FFT scheme within the satellite communication terminal can ensure the fast and stable tracking of satellite signal by the violently moving antenna within 20 ms under level-4 sea state.

A Novel VLSI Architecture for Multi-Constellation and Multi-Frequency GNSS Acquisition Engine

This paper proposes a novel VLSI architecture of GNSS acquisition engine based on short-time correlation combined with an FFT scheme. The architecture supports multi-constellation systems and multi-frequency satellite signals flexibly by the manner of time-division multiplexing. The supported signals include GPS, BDS, GLONASS, GALILEO, QZSS, IRNSS, and SBAS. Compared with other direct acquisition structures, the search efficiency of the acquisition engine is improved by using the IF playback structure. Based on the characteristics of L1C and B1C signal spread spectrum codes, an efficient generation method and the circuit structure of Legendre sequence which is compatible with L1C and B1C spread spectrum codes are proposed. It can effectively reduce the die area of the spread spectrum code generator and the generation time of the L1C/B1C spread spectrum code. Combining with the acquisition scheme adopted in this paper, the structure of the short-time correlators’ array is optimized, and the maximum clock frequency of the acquisition engine is significantly improved. The acquisition engine proposed in this paper is implemented in a 55-nm CMOS technology. The system occupied a silicon area of 2.1 mm2 and consumes only 72.02-mW power while realizing the maximum clock frequency at about 333.33 MHz.

Signal Detection Performance of Overlapped FFT Scheme with Additional Frames Consisting of Non-continuous Samples in Indoor Environment

Overlapped FFT has been proposed as a signal detection scheme in dynamic spectrum access to reduce the variance of the noise and improve the detection probability. However, the improvement of the detection probability in the conventional overlapped FFT is bounded with the upper limit of the overlap ratio. This paper proposes a new overlapped FFT scheme using additional frames. In the proposed scheme, in addition to the original FFT frames, new frames that consist of multiple subframes with non-continuous samples are constructed and included. It can realize the increase of the number of the FFT frames and the improvement of the detection probability compared with the conventional scheme. Numerical results through computer simulation show that the proposed scheme improves the detection probability by up to 0.07. On indoor channel models the proposed scheme also improves the detection probability. In addition, it is clarified that as the delay spread increases the detection probability reduces due to the correlation between the frames.

Fast Fourier transforms for the evaluation of convolution products: CPU versus GPU implementation

In a large variety of research areas, convolution products that relate a physical quantity in some observation points with their sources are encountered. When the sources and the observation points coincide, the numerical evaluation of the physical quantity typically leads to order N2 numerical problems. Here, fast Fourier transforms are widely used to reduce the computations to order Nlog N complexity. When adopting Fourier transforms FFT for finite physical problems, zero padding is required. Hence, in 2D and 3D problems, an optimization of the evaluation of the convolution product includes a non-execution of Fourier transforms on arrays containing only zeros in the forward 2D or 3D FFT scheme and their corresponding arrays in the inverse 2D or 3D FFT scheme. This paper describes the implementation of such an approach on graphical processing units GPUs and compares the time gains on GPU and on CPU. It is found that on CPU, the speedup corresponds with the theoretical limit, while in the GPU implementation, the memory bandwidth limits the speedup ratio. Copyright © 2013 John Wiley & Sons, Ltd.

Experimental Investigation of Signal Sensing with Overlapped FFT Based Energy Detection

Overlapped FFT based energy detection has been proposed as a signal detection scheme in dynamic spectrum access. The overlapped FFT scheme increases the number of FFT frames to reduce the variance of squared noise and improve the detection probability. This paper evaluates the performance of the energy detection with overlapped FFT through experiments. In the experiments, different from the assumption in computer simulation of previous researches, a fixed distortion component caused by a direct current offset is observed. It is shown that the overlapped FFT scheme also works effectively under the existence of the fixed distortion. Numerical results obtained through the experiments show that the overlapped FFT scheme improves the detection probability by up to 0.15 with the noise and the fixed distortion component. The variance of the squared noise also reduces with the overlapped FFT scheme as it is expected in theoretical analysis when the fixed distortion is negligible.

FFT-based methods for the mechanics of composites: A general variational framework

For more than a decade, numerical methods for periodic elasticity, based on the fast Fourier transform, have been used successfully as alternatives to more conventional (fem, bem) numerical techniques for composites. These methods are based on the direct, point-wise, discretization of the Lippmann–Schwinger equation, and a subsequent truncation of underlying Fourier series required for the use of the fast Fourier transform. The basic FFT scheme is very attractive, because of its simplicity of implementation and use. However, it cannot handle pores or rigid inclusions, for which a specific (and significantly more involved) treatment is required. In the present paper, we propose a new FFT-based scheme which is as simple as the basic scheme, while remaining valid for infinite contrasts. Since we adopted an energy principle as an alternative to the Lippmann–Schwinger equation, our scheme is derived within a variational framework. As a by-product, it provides an energetically consistent rule for the homogenization of boundary voxels, a question which has been pending since the introduction of Fourier-based methods.

A Novel Three-Dimensional Wide-Angle Beam Propagation Method Based on Split-Step Fast Fourier Transform

A novel three-dimensional wide-angle beam propagation method based on the split-step fast Fourier transform is developed. The formulation is based on the three-dimensional Helmholtz wave equation. Each propagation step is performed by utilizing both the FFT and split-step scheme. The solution of Helmholtz wave equation does not make the slowly varying envelope and one-way propagation approximations. To validate the efficiency and accuracy, numerical results for a propagation beam in a tilted step-index optical waveguide are compared with other beam propagation algorithms.

Pruning fast Fourier transform algorithm design using group-based method

In this paper, we propose the grouped scheme, which can be specially applied to compute the pruning fast Fourier transform (pruning FFT) with power-of-two partial transformation length. The group-based pruning FFT algorithm applies the scheme of the grouped frequency indices to accelerate computations of selected discrete Fourier transform (DFT) outputs. The proposed pruning FFT algorithm has fewer complex multiplications than the other pruning FFT algorithms when the number of the partial transformed outputs is equal to or larger than 1/16 total FFT transform length. Whereas the number of the partial transformed outputs is equal to or smaller than 1/32 total FFT transform length, the arithmetic complexity of the proposed algorithm will be larger than the other pruning FFTs. To compute all transformed outputs of the DFT, the multiplication complexities of the proposed pruning FFT method are fewer than those of the radix-2 method. Meanwhile, the multiplication complexities of the proposed fast method approximate to those of the radix-4 FFT algorithm with the power-of-four length. For the comparison of data transfer costs in the pruning FFT cases, the proposed pruning FFT algorithm has smaller data transfer costs than the other pruning FFT algorithms when the number of the partial transformed outputs is equal to or larger than 1/4 total FFT transform length. By sharing coefficients of the twiddle factors in the same frequency group and using the radix-2 FFT scheme, the proposed pruning FFT algorithm can be implemented with properties of sharing hardware and regular structures.

Seismic Induced Nonlinear Rotor-Bearing-Casing Interaction of Rotating Nuclear Components

The study of the dynamics of turbomachinery during seismic events has been of continuous interest to both researchers and designers of large rotating equipment. Failure in such equipment, especially those associated with nuclear power generation, can lead to catastrophic consequences. Hence, there is a general trend for corporations to “overdesign” the equipment without any indepth understanding of the dynamical performance of the machine under extreme operating conditions. The overall objectives of this paper are fourfold, namely: (1) To study the nonlinear dynamics of rotor-bearing casing system during rub interactions; (2) To examine the effects of suddenly induced imbalance and base motion in the global dynamical behavior of the system: (3) To develop engineering insights through the modal parameters in both time and frequency domain; (4) To generate signature analysis on rub forces for pattern recognition. These goals are achieved through the development of a modal impact model. Accuracy and efficiency of this transient model are maintained using a self-adaptive integration scheme. A numerical FFT scheme is applied to examine the modal participations, bearing forces, and rub signatures in the frequency domain. A typical nuclear water pump will be used as an example for this approach.

Calculation of narrow-band spectra by direct decimation

The calculation of the spectrum of a narrow-band signal which is embedded in a broad-band sequence usually requites substantial computation and storage if executed by performing an FFT or DFT's directly on the broad-band sequence. In this paper a new scheme using direct decimation is proposed which computes the narrow-band spectrum with good resolution while requiring only modest computation and storage. The performance of the proposed scheme is analyzed. Examples are presented which demonstrate the efficiency of this scheme when compared with the FFT, DFT, zoom transform, and complex modulation scheme.