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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.
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