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61
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 ..."
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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.
METEOR: A constraintbased FIR filter design program
 IEEE Trans. on Signal Processing
, 1992
"... The usual way of designing a lter is to specify a lter length and a nominal response, and then to nd a lter of that length which best approximates that response. In this paper we propose a di erent approach: specify the lter only in terms of upper and lower limits on the response, nd the shortest lt ..."
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Cited by 15 (0 self)
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The usual way of designing a lter is to specify a lter length and a nominal response, and then to nd a lter of that length which best approximates that response. In this paper we propose a di erent approach: specify the lter only in terms of upper and lower limits on the response, nd the shortest lter length which allows these constraints to be met, and then nd a lter of that order which is farthest from the upper and lower constraint boundaries in a minimax sense. Previous papers have described methods for using an exchange algorithm for nding a feasible linearphase FIR lter of a given length if one exists, given upper and lower bounds on its magnitude response. The resulting lters touch the constraint boundaries at many points, however, and are not good nal designs because they do not make best use of the degrees of freedom in the coe cients. We use the simplex algorithm for linear programming to nd a best linearphase FIR lter of minimum length, as well as to nd the minimum feasible length itself. The simplex algorithm, while much slower than exchange algorithms, also allows us to incorporate more general kinds of constraints, such as concavity constraints (which can be used to achieve very at magnitude characteristics). We give examples that illustrate how the proposed and the usual approaches di er, and how the new approach can be used to design lters with at passbands, lters which meet point constraints, minimum phase lters, and bandpass lters with controlled transition band behavior. 1.
Generalized Plenoptic Sampling
, 2001
"... Imagebased rendering (IBR) has become a very active research area in recent years. The optimal sampling problem for IBR has not been completely solved. In this paper, we show that theoretically, the optimal sampling efficiency can be achieved by employing the generalized periodic sampling theory wi ..."
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Cited by 14 (2 self)
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Imagebased rendering (IBR) has become a very active research area in recent years. The optimal sampling problem for IBR has not been completely solved. In this paper, we show that theoretically, the optimal sampling efficiency can be achieved by employing the generalized periodic sampling theory with arbitrary geometry. When there is no occlusion in the scene and the scene is Lambertian, we show that the sampling density can be twice of that when we use rectangular sampling. We then propose a general framework for IBR sampling. Begin with an oversampled dataset, we downsample the data first in the discrete domain. To render an image from the downsampled data, two approaches are proposed, i.e., to reconstruct the oversampled dataset first through upsampling and then rendering, or to use a continuous interpolation filter to calculate the desired light rays directly. Eigenfilter method is employed to design filters during downsampling and upsampling. We show that if the proposed approach adopts the same downsampling density as the previous work, the reconstruction filter of the proposed approach is easier to design, and the reconstructed scene could have a higher quality.
An Approach to the Design of Sparse Array Systems
, 1994
"... Sparse arrays have been proposed for twodimensional arrays for threedimensional ultrasound imaging in order to reduce the number of channels in the system. Such arrays have been designed by picking array elements in a random fashion, either according to a uniform or a Gaussian distribution. A rand ..."
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Cited by 8 (6 self)
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Sparse arrays have been proposed for twodimensional arrays for threedimensional ultrasound imaging in order to reduce the number of channels in the system. Such arrays have been designed by picking array elements in a random fashion, either according to a uniform or a Gaussian distribution. A random array can have large variations in the level of the maximum sidelobe. A method for optimization of the sidelobe level of 1D sparse arrays has been demonstrated. This shows that weighting can give responses that resemble filled DolphChebyshev arrays. The initial thinning pattern is of less importance for the final result, but the less ideal the unweighted pattern is, the more dynamic range is required from the weight function.
Optimization of JPEG color image coding using a human visual system model
 SPIE conference on Human Vision and Electronic Imaging
, 1996
"... We introduce a new model that can be used in the perceptual optimization of standard color image coding algorithms (JPEG/MPEG). The human visual system model is based on a set of oriented filters and incorporates background luminance dependencies, luminance and chrominance frequency sensitivities, a ..."
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Cited by 8 (2 self)
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We introduce a new model that can be used in the perceptual optimization of standard color image coding algorithms (JPEG/MPEG). The human visual system model is based on a set of oriented filters and incorporates background luminance dependencies, luminance and chrominance frequency sensitivities, and luminance and chrominance masking effects. The main problem in using oriented filterbased models for the optimization of coding algorithms is the difference between the orientation of the filters in the model domain and the DCT block transform in de coding domain. We propose a general method to combine these domains by calculating a local sensitivity for each DCT (color) block. This leads to a perceptual weighting factor for each DCT coefficient in each block. We show how these weighting factors allow us to use advanced techniques for optimal bit allocation in JPEG (e.g. custom quantization matrix design and adaptive thresholding). With the model we propose it is possible to calculate a perceptually weighted mean squared error (WMSE) directly in the DCT color domain, although the model itself is based on a directional frequency band decomposition. 1.
Green’s functions for multiply connected domains via conformal mapping
 SIAM Review
, 1999
"... Abstract. A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the pa ..."
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Cited by 8 (2 self)
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Abstract. A method is described for the computation of the Green’s function in the complex plane corresponding to a set of K symmetrically placed polygons along the real axis. An important special case is a set of K real intervals. The method is based on a Schwarz–Christoffel conformal map of the part of the upper halfplane exterior to the problem domain onto a semiinfinite strip whose end contains K − 1 slits. From the Green’s function one can obtain a great deal of information about polynomial approximations, with applications in digital filters and matrix iterations. By making the end of the strip jagged, the method can be generalized to weighted Green’s functions and weighted approximations. Key words. Green’s function, conformal mapping, Schwarz–Christoffel formula, polynomial approximation,
Comparison of Command Shaping Methods for Reducing Residual Vibration
 Third European Control Conf
, 1995
"... This paper compares command shaping techniques for controlling residual vibration of highperformance machines. Input shaping generates vibrationreducing shaped commands through convolution of an impulse sequence with the desired command. Because input shaping has similarities to notch filtering, i ..."
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Cited by 7 (0 self)
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This paper compares command shaping techniques for controlling residual vibration of highperformance machines. Input shaping generates vibrationreducing shaped commands through convolution of an impulse sequence with the desired command. Because input shaping has similarities to notch filtering, it is compared here with a variety of FIR and IIR filters. Several types of input shapers are presented and shown to be more effective than any of the conventional filters. Introduction Control of machine vibration becomes very important as designers attempt to push the state of the art with faster, lighter machines. Many researchers have examined different controller configurations in order to control machines without exciting resonances. Even with a sophisticated controller it is difficult to rapidly move flexible machines without deflections and vibrations. A more achievable goal is to eliminate residual vibration once the machine has achieved a desired setpoint. Input shaping is a comm...
Exchange Algorithms that Complement the ParksMcClellan Algorithm for LinearPhase FIR Filter Design
 IEEE TRANS. ON CIRCUITS AND SYSTEMS II
, 1996
"... This paper describes an exchange algorithm for the frequency domain design of linearphase FIR equiripple filters where the Chebyshev error in each band is specified. The algorithm is a hybrid of the algorithm of Hofstetter, Oppenheim and Siegel and the ParksMcClellan algorithm. The paper also desc ..."
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Cited by 5 (3 self)
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This paper describes an exchange algorithm for the frequency domain design of linearphase FIR equiripple filters where the Chebyshev error in each band is specified. The algorithm is a hybrid of the algorithm of Hofstetter, Oppenheim and Siegel and the ParksMcClellan algorithm. The paper also describes a modification of the ParksMcClellan algorithm where either the passband or the stopband ripple size is specified and the other is minimized.
Nonlinear Phase FIR Filter Design according to the L 2 Norm with Constraints for the Complex Error
, 1994
"... We examine the problem of approximating a complex frequency response by a realvalued FIR filter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the KuhnTucker optimality conditions which specialize to a system of nonlinear equati ..."
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Cited by 5 (2 self)
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We examine the problem of approximating a complex frequency response by a realvalued FIR filter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the KuhnTucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iteration step. The algorithm allows arbitrary tradeoffs between an L 2 and an L1 design. The L 2 and the L1 solution result as special cases. Wir untersuchen das Problem der Approximation eines komplexen Frequenzganges mittels eines reellwertigen nichtrekursiven Filters nach der L 2 Norm mit zusatzlichen Ungleichungsbedingungen fur die komplexe Fehlerfunktion. Ausgehend von den KuhnTucker Optimalitatsbedingungen, die auf ein nichtlineares Gleichungssystem fuhren, leiten wir einen iterativen Algorithmus her. Diese Gleichungen werden in jedem Iterationsschritt mittels des NewtonVerfahrens gelost. D...