The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformly-spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

Passive radar systems that exploit illuminators of opportunity, such as FM radio and television broadcasts, to detect and track airborne targets have been under development for over a decade. This paper reviews efforts to add radar imaging and target recognition capabilities to such systems. We discuss recent developments along two parallel threads: 1) Target recognition via radar cross section (RCS) profiles: In this approach, databases of the RCS of targets at different incident and observed angles are created using method-of-moments computational electromagnetics codes. The extracted RCS profiles for different targets, scaled to account for antenna patterns and atmospheric propagation, are compared to the collected data. A coordinated flight model is used to estimate the aircraft's orientation along its flight path. The low frequencies used in passive radar naturally give stable features well suited for automatic target recognition. 2) Radar imaging: A traditional inverse synthetic aperture approach to forming images with passive radar data results in severe artefacts due to the sparse and irregular Fourier sampling patterns resulting from realistic data collection scenarios. We review the application of a recent optimization-based, regionenhancing imaging algorithm to passive radar imaging that effectively suppresses these artefacts, and illustrate the difficulties posed by the underlying multidimensional autofocus problem.