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.

We investigate when a trigonometric polynomial p of degree M in d variables is uniquely determined by its sampled values p(xj) on a random set of points xj in the unit cube (the “sampling problem for trigonometric polynomials”) and estimate the probability distribution of the condition number for the associated Vandermonde-type and Toeplitz-like matrices. The results provide a solid theoretical foundation for some efficient numerical algorithms that are already in use.

Time-encoding is a real-time asynchronous mechanism of mapping the information contained in the amplitude of a bandlimited signal into a time sequence. Time decoding algorithms recover the signal from the time sequence. Under an appropriate Nyquist-type rate condition the signal can be perfectly recovered. The algorithm for perfect recovery calls, however, for the computation of a pseudo-inverse of an infinite dimensional matrix. We present a simple algorithm for local signal recovery and construct a stitching algorithm for real-time signal recovery. We also provide a recursive algorithm for computing the pseudo-inverse of a family of finitedimensional matrices. 1.

this article, we discuss the problem of reconstructing a function f in a lattice-invariant subspace of L (IR ) from a family of non-uniformly distributed, weighted-averages fhf; x j i : j 2 Jg using an approximationprojection iterative algorithm

mapping amplitude information into a time sequence. We investigate fast algorithms for the recovery of time encoded bandlimited signals and construct an algorithm that has provably low computational complexity. We also devise a fast algorithm that is parameter-insensitive.

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