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Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
Abstract

Cited by 83 (13 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced 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 minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Modeling of Light Propagation in Skin, and an Application to Noninvasive Diagnostics
, 2002
"... ed upon changes of the light scattering coecient in the upper dermal regions of skin induced by glucose dissolved in the interstitial uid. We will focus on the identi cation of this coecient in vivo. As we want to probe our tissue with decoherent light of a single wavelength in the near infrared re ..."
Abstract
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ed upon changes of the light scattering coecient in the upper dermal regions of skin induced by glucose dissolved in the interstitial uid. We will focus on the identi cation of this coecient in vivo. As we want to probe our tissue with decoherent light of a single wavelength in the near infrared regime, the physical process is properly described by the radiative transfer equation. The modeling has to face the task of mapping a special measurement setting as well as spatial and temporal varying skin optical properties to a proper boundary value problem formulation for the radiative transfer equation and an eective solution of the inverse problem. As we will soon recognize, an eective solution of the forward and more urging of the inverse problem is necessarily based on approximations of the radiative transfer equation, especially the diusion approximation will be treated in detail. Moreover we will have to excurse to datadriven approaches in order to overcome the limitations of m