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STENCIL COEFFICIENT COMPUTATIONS FOR THE MULTIRESOLUTION TIME DOMAIN METHOD — A FILTERBANK APPROACH
"... Abstract—Multiresolution Time Domain (MRTD) techniques based on wavelet expansions can be used for adaptive refinement of computations to economize the resources in regions of space and time where the fields or circuit parameters or their derivatives are large. Hitherto, standard wavelets filter coe ..."
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coefficients have been used with the MRTD method but the design of such filter itself may enable to incorporate desired properties for different applications. Towards this, in this paper, a new set of stencil coefficients in terms of scaling coefficients starting from a half band filter, designed by window
DESIGN OF TWOCHANNEL FIR FILTERBANKS WITH RATIONAL SAMPLING FACTORS BY USING THE FREQUENCY RESPONSE MASKING TECHNIQUE
"... This paper considers the use of the frequency response masking (FRM) technique for designing finiteimpulse response (FIR) filters generating nearly perfectreconstruction (NPR) twochannel filterbanks with rational sampling factors in the case where the processing unit between the analysis and syn ..."
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This paper considers the use of the frequency response masking (FRM) technique for designing finiteimpulse response (FIR) filters generating nearly perfectreconstruction (NPR) twochannel filterbanks with rational sampling factors in the case where the processing unit between the analysis
Parametrized Biorthogonal Wavelets and FIR Filter Bank Design with Gröbner Bases
"... This paper builds upon the recent results of Regensburger and Scherzer on parametrization of orthonormal wavelets by discrete moments (and, therefore, also continuous moments) of scaling function followed by the solution of a parametrized set of polynomial equations in the FIR filter coefficients us ..."
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using Gröbner bases. First, parametrization of orthonormal filters with two discrete moments as parameters, instead of just one is considered followed by the generalization of the results to the case of biorthogonal wavelets. A characterization theorem for the continuous moments of the scaling function
Rational Coefficient DualTree Complex Wavelet Transform: Design and Implementation
 IEEE Trans. on Signal Processing
, 2008
"... The dualtree complex wavelet transform (CWT) has recently received significant interest in the wavelet community, owing primarily to its directional selective and nearshift invariant properties. It has been shown that with two separate maximallydecimated and dyadic decompositions where filters a ..."
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Cited by 6 (0 self)
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are offset by a half sample, the resulting CWT wavelet bases form an approximate Hilbert transform pair. In this paper, we present the design, implementation and applications of several families of orthogonal as well as biorthogonal rationalcoefficient wavelet filters that satisfy the Hilbert transform pair
1NonInvertible Gabor Transforms
"... Timefrequency analysis, such as the Gabor transform, plays an important role in many signal processing applications. The redundancy of such representations is often directly related to the computational load of any algorithm operating in the transform domain. To reduce complexity, it may be desirab ..."
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of the transform coefficients amounts to a 2D twisted convolution operation, which we show how to perform using a filterbank. When the undersampling factor is an integer, the processing reduces to standard 2D convolution. We provide simulation results to demonstrate the advantages and weaknesses of each
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"... The kinematic analyses, of manipulators and other robotic devices composed of mechanical links, usually depend on the solution of sets of nonlinear equations. There are a variety of both numerical and algebraic techniques available to solve such systems of equations and to give bounds on the number ..."
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of such systems are reviewed, and the three most useful solution techniques are summarized. The solution techniques are polynomial continuation, Gröbner bases, and elimination. We then discuss the results that have been obtained with these techniques in the solution of two basic problems, namely, the inverse
Volume I: Computer Science and Software Engineering
, 2013
"... Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations in Sc ..."
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Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matrices and polynomials is fundamental for modern computations
1Shannon Meets Nyquist: Capacity Limits of Sampled Analog Channels
"... We explore two fundamental questions at the intersection of sampling theory and information theory: how is channel capacity affected by sampling below the channel’s Nyquist rate, and what subNyquist sampling strategy should be employed to maximize capacity. In particular, we first derive the capaci ..."
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the capacity of sampled analog channels for two prevalent sampling mechanisms: filtering followed by sampling and sampling following filter banks. Connections between sampling and MIMO Gaussian channels are illuminated based on this analysis. Optimal prefilters that maximize capacity are identified for both
ALGEBRAIC ALGORITHMS1
, 2012
"... This is a preliminary version of a Chapter on Algebraic Algorithms in the up ..."
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This is a preliminary version of a Chapter on Algebraic Algorithms in the up
1SubNyquist Sampling: Bridging Theory and Practice
"... [ A review of past and recent strategies for subNyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely ..."
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[ A review of past and recent strategies for subNyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finelytuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuoustime signals to discrete streams of numbers. The famous ShannonNyquist theorem has become a landmark: a mathematical statement which has had one of the most profound impacts on industrial development of digital signal processing (DSP) systems. Over the years, theory and practice in the field of sampling have developed in parallel routes. Contributions by many research groups suggest a multitude of methods, other than uniform sampling, to acquire analog signals [1]–[6]. The math has deepened, leading to abstract signal spaces and innovative sampling techniques. Within generalized sampling theory, bandlimited signals have no special preference, other than historic. At the same time, the market adhered to the Nyquist paradigm; stateoftheart analog to digital conversion (ADC) devices provide values of their input at equalispaced time points [7], [8]. The footprints of ShannonNyquist are evident
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