This work presents a new methodology for the formulation of discrete chirp Fourier transform (DCFT) algorithms and it discusses performance measures pertaining to the mapping of these algorithms to hardware computational structures (HCS) as well as the extraction of chirp rate estimation parameters of multicomponent nonstationary signals arriving from point targets. The methodology centers on the use of Kronecker products algebra, a branch of finite dimensional multilinear algebra, as a language to present a canonical formulation of the DCFT algorithm and its associated properties. The methodology also explains how to search for variants of this canonical formulation that contribute to enhance the mapping process to a target HCS. The parameter extraction technique uses time-frequency properties of the DCFT in a modeled delay-Doppler synthetic aperture radar (SAR) remote sensing and surveillance environment to treat multicomponent return signals of prime length, with additive Gaussian noise as background clutter, and extract associated chirp rate parameters. The fusion of time-frequency information, acquired from transformed chirp or linear frequency modulated (FM) signals using the DCFT, with information obtained when the signals are treated using the discrete ambiguity function acting as point target response, point spread function, or impulse response, is used to further enhance the estimation process. For the case of very long signals, parallel algorithm implementations have been obtained on cluster computers. A theoretical computer performance analysis was conducted on the cluster implementation based on a methodology that applies well-defined design of experiments methods to the identification of relations among different levels in the process of mapping computational operations to high-performance computing systems. The use of statistics for identification of relationships among factors has formalized the search for solutions to the mapping problem and this approach allows unbiased conclusions about results.
This work deals with the development of Kronecker products algorithms for fast synthetic aperture radar (SAR) image formation operations. A methodology has been developed to serve as a tool aid in the analysis, design, and efficient implementation of one-dimensional and two-dimensional fast Fourier transform (FFT) algorithms prevalent in SAR image formation operations with the idea in mind of reducing the computational effort and improving the hardware implementation process for real time on board SAR imaging applications. Kronecker products algebra, a branch of finite dimensional multilinear algebra, has been demonstrated to be a useful tool aid in the development of fast algorithms for unitary transformations and in the identification of similarities and differences among FFT computational frameworks.
This work presents modified variants, in a recursive format, of the Kahaner's additive fast Fourier transform algorithm. The variants are presented in Kronecker products algebra language. The language serves as a tool for the analysis, design, modification and implementation of the FFT variants on re-configurable field programmable gate array computational structures. The target for these computational structures are discrete Fourier transform beamforming algorithms for space-time-frequency applications in wireless.
This work concentrates on the analysis of radar signature signals for the characterization and efficient computational of finite discrete 2D point spread functions. A general simple model for ground penetrating raw data image formation is assumed in order to concentrate on the efficient computation of point spread functions. The point spread functions are used as impulse response functions for the simulation of high resolution image of 2D synthetic aperture imaging kernels. A methodology has been developed to serve as a tool aid in the analysis, design, and efficient implementation of 1D and 2D fast Fourier transform (FFT) algorithms prevalent in SAR image formation operations with the idea in mind of reducing the computational effort and improving the hardware implementation process. Kronecker products algebra, a branch of finite dimensional multilinear algebra, has been demonstrated to be a useful tool aid in the development of fast algorithms for unitary transformations and in the identification of similarities and differences among FFT computational frameworks.
Proc. SPIE. 3752, Subsurface Sensors and Applications
KEYWORDS: Point spread functions, Data modeling, Synthetic aperture radar, Remote sensing, Fourier transforms, Data processing, Signal processing, Surface properties, Convolution, Algorithm development
Synthetic aperture radar (SAR) imaging technologies are increasingly finding applications in the geosciences and are becoming instrumental in enhancing the fundamental understanding of the physical processes pertaining to the earth and the environment. Of particular importance are studies conducted about the earth surface property characteristics using SAR remote sensing techniques. These studies are relevant for the better understanding of concepts such as soil moisture content, backscattering from crops, nearshore ocean surface currents, and subsurface imaging in hyperarid regions. In this work, impulse response or point spread functions are used as ambiguity functions in the efficient computation of raw data generation operations and efficient filtering techniques are presented for imaging kernel operations. The efficiency in these operations is obtained through the use of Kronecker products algebra as a basis for the mathematical formulation of multidimensional fast Fourier transform algorithms.
This work deals with the use of artificial neural networks (ANN) for the digital processing of finite discrete time signals. The effort concentrates on the efficient replacement of fast Fourier transform (FFT) algorithms with ANN algorithms in certain engineering and scientific applications. The FFT algorithms are efficient methods of computing the discrete Fourier transform (DFT). The ubiquitous DFT is utilized in almost every digital signal processing application where harmonic analysis information is needed. Applications abound in areas such as audio acoustics, geophysics, biomedicine, telecommunications, astrophysics, etc. To identify more efficient methods to obtain a desired spectral information will result in a reduction in the computational effort required to implement these applications.