The Experts below are selected from a list of 270 Experts worldwide ranked by ideXlab platform
Balazs Bank - One of the best experts on this subject based on the ideXlab platform.
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converting infinite impulse response filters to parallel form tips tricks
IEEE Signal Processing Magazine, 2018Co-Authors: Balazs BankAbstract:Discrete-time rational transfer functions are often converted to parallel second-order sections due to better numerical performance compared to direct form infinite impulse response (IIR) implementations. This is usually done by performing partial fraction expansion over the original transfer function. When the order of the Numerator Polynomial is greater or equal to that of the denominator, Polynomial long division is applied before partial fraction expansion resulting in a parallel finite impulse response (FIR) path.
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Converting Infinite Impulse Response Filters to Parallel Form [Tips & Tricks]
IEEE Signal Processing Magazine, 2018Co-Authors: Balazs BankAbstract:Discrete-time rational transfer functions are often converted to parallel second-order sections due to better numerical performance compared to direct form infinite impulse response (IIR) implementations. This is usually done by performing partial fraction expansion over the original transfer function. When the order of the Numerator Polynomial is greater or equal to that of the denominator, Polynomial long division is applied before partial fraction expansion resulting in a parallel finite impulse response (FIR) path.
Karen Belkic - One of the best experts on this subject based on the ideXlab platform.
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the general concept of signal noise separation sns mathematical aspects and implementation in magnetic resonance spectroscopy
Journal of Mathematical Chemistry, 2009Co-Authors: Dževad Belkic, Karen BelkicAbstract:Magnetic resonance spectroscopy (MRS) and spectroscopic imaging (MRSI) are increasingly recognized as potentially key modalities in cancer diagnostics. It is, therefore, urgent to overcome the shortcomings of current applications of MRS and MRSI. We explain and substantiate why more advanced signal processing methods are needed, and demonstrate that the fast Pade transform (FPT), as the quotient of two Polynomials, is the signal processing method of choice to achieve this goal. In this paper, the focus is upon distinguishing genuine from spurious (noisy and noise-like) resonances; this has been one of the thorniest challenges to MRS. The number of spurious resonances is always several times larger than the true ones. Within the FPT convergence is achieved through stabilization or constancy of the reconstructed frequencies and amplitudes. This stabilization is a veritable signature of the exact number of resonances. With any further increase of the partial signal length N, towards the full signal length N, i.e., passing the stage at which full convergence has been reached, it is found that all the fundamental frequencies and amplitudes “stay put”, i.e., they still remain constant. Moreover, machine accuracy is achieved here, proving that when the FPT is nearing convergence, it approaches straight towards the exact result with an exponential convergence rate (the spectral convergence). This proves that the FPT is an exponentially accurate representation of functions customarily encountered in spectral analysis in MRS and beyond. The mechanism by which this is achieved, i.e., the mechanism which secures the maintenance of stability of all the spectral parameters and, by implication, constancy of the estimate for the true number of resonances is provided by the so-called pole-zero cancellation, or equivalently, the Froissart doublets. This signifies that all the additional poles and zeros of the Pade spectrum will cancel each other, a remarkable feature unique to the FPT. The FPT is safe-guarded against contamination of the final results by extraneous resonances, since each pole due to spurious resonances stemming from the denominator Polynomial will automatically coincide with the corresponding zero of the Numerator Polynomial, thus leading to the pole-zero cancellation in the Polynomial quotient of the FPT. Such pole-zero cancellations can be advantageously exploited to differentiate between spurious and genuine content of the signal. Since these unphysical poles and zeros always appear as pairs in the FPT, they are viewed as doublets. Therefore, the pole-zero cancellation can be used to disentangle noise as an unphysical burden from the physical content in the considered signal, and this is the most important usage of the Froissart doublets in MRS. The general concept of signal–noise separation (SNS) is thereby introduced as a reliable procedure for separating physical from non-physical information in MRS, MRSI and beyond.
V. Ramachandran - One of the best experts on this subject based on the ideXlab platform.
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CCECE - Analysis of Product-Separable Discrete Filters with Feedbacks for Variable Characteristics
2006 Canadian Conference on Electrical and Computer Engineering, 2006Co-Authors: J. Xiao, V. RamachandranAbstract:A structure containing two one-dimensional discrete filters connected in cascade is considered in order to obtain variable magnitude and contour characteristics. Each filter has an independent multiplier to vary the characteristics. Different classes are possible depending on the Numerator Polynomial chosen. The limits on the value of the multiplier is determined starting from the given filter. Various combinations are found to be possible. Some illustrations are given. A possible application in image processing is indicated.
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Generation of a class of two-dimensional (2-D) transfer functions yielding variable magnitude and contour characteristics
ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 2001Co-Authors: C.s. Gargour, V. Ramachandran, R.p. RamachandranAbstract:The properties of a two-dimensional (2-D) discrete transfer function with the degree of each variable being unity are discussed. The coefficients of the denominator Polynomial contain a parameter k (having real values) whose bounds are determined by stability considerations. These bounds are obtained by testing the overall Polynomial at only four points z/sub 1/=/spl plusmn/1 and z/sub 2/=/spl plusmn/1. A suitable Numerator Polynomial can be associated to get the overall transfer function. By varying the values of k, different magnitude and contour characteristics are obtained. Such structures can be cascaded so that the magnitude responses can be varied.
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ISCAS (2) - Generation of a class of two-dimensional (2-D) transfer functions yielding variable magnitude and contour characteristics
ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196), 1Co-Authors: C.s. Gargour, V. Ramachandran, Ravi P. RamachandranAbstract:The properties of a two-dimensional (2-D) discrete transfer function with the degree of each variable being unity are discussed. The coefficients of the denominator Polynomial contain a parameter k (having real values) whose bounds are determined by stability considerations. These bounds are obtained by testing the overall Polynomial at only four points z/sub 1/=/spl plusmn/1 and z/sub 2/=/spl plusmn/1. A suitable Numerator Polynomial can be associated to get the overall transfer function. By varying the values of k, different magnitude and contour characteristics are obtained. Such structures can be cascaded so that the magnitude responses can be varied.
Martina Kubitzke - One of the best experts on this subject based on the ideXlab platform.
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Spectra and eigenvectors of the Segre transformation
Advances in Applied Mathematics, 2014Co-Authors: Ilse Fischer, Martina KubitzkeAbstract:Abstract Given two sequences a = ( a n ) and b = ( b n ) of complex numbers such that their generating series can be written as rational functions where the denominator is a power of 1 − t , we consider their Segre product a ⁎ b = ( a n b n ) . We are interested in the bilinear transformations that compute the coefficient sequence of the Numerator Polynomial of the generating series of a ⁎ b from those of the generating series of a and b . The motivation to study this problem comes from commutative algebra as the Hilbert series of the Segre product of two standard graded algebras equals the Segre product of the two individual Hilbert series. We provide an explicit description of these transformations and compute their spectra. In particular, we show that the transformation matrices are diagonalizable with integral eigenvalues. We also provide explicit formulae for the eigenvectors of the transformation matrices. Finally, we present a conjecture concerning the real-rootedness of the Numerator Polynomial of the r -th Segre product of the sequence a if r is large enough, under the assumption that the coefficients of the Numerator Polynomial of the generating series of a are non-negative.
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enumerative g theorems for the veronese construction for formal power series and graded algebras
Advances in Applied Mathematics, 2012Co-Authors: Martina Kubitzke, Volkmar WelkerAbstract:Let (an)n?0 be a sequence of integers such that its generating series satisfies ?n?0antn=h(t)(1-t)d for some Polynomial h(t). For any r?1 we study the coefficient sequence of the Numerator Polynomial h0(a{r})+?+hλ'(a{r})tλ' of the rth Veronese series a{r}(t)=?n?0anrtn. Under mild hypothesis we show that the vector of successive differences of this sequence up to its ?d2?th entry is the f-vector of a simplicial complex for large r. In particular, the sequence (h0(a{r}),?,hλ'(a{r})) satisfies the consequences of the unimodality part of the g-conjecture. We give applications of the main result to Hilbert series of Veronese algebras of standard graded algebras and the f-vectors of edgewise subdivisions of simplicial complexes.
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enumerative g theorems for the veronese construction for formal power series and graded algebras
arXiv: Combinatorics, 2011Co-Authors: Martina Kubitzke, Volkmar WelkerAbstract:Let $(a_n)_{n \geq 0}$ be a sequence of integers such that its generating series satisfies $\sum_{n \geq 0} a_nt^n = \frac{h(t)}{(1-t)^d}$ for some Polynomial $h(t)$. For any $r \geq 1$ we study the coefficient sequence of the Numerator Polynomial $h_0(a^{ }) +...+ h_{\lambda'}(a^{ }) t^{\lambda'}$ of the $r$\textsuperscript{th} Veronese series $a^{ }(t) = \sum_{n \geq 0} a_{nr} t^n$. Under mild hypothesis we show that the vector of successive differences of this sequence up to the $\lfloor \frac{d}{2} \rfloor$\textsuperscript{th} entry is the $f$-vector of a simplicial complex for large $r$. In particular, the sequence satisfies the consequences of the unimodality part of the $g$-conjecture. We give applications of the main result to Hilbert series of Veronese algebras of standard graded algebras and the $f$-vectors of edgewise subdivisions of simplicial complexes.
Lorlynn A. Mateo - One of the best experts on this subject based on the ideXlab platform.
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Further results on Numerator Polynomial matrix for feedforward learning control of MIMO plant with finite zeros
2015 54th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), 2015Co-Authors: Lorlynn A. Mateo, Kenji SugimotoAbstract:In the implementation of feedforward learning control, a two-degree-of-freedom (2DOF) structure is assumed where both feedforward (FF) control and feedback (FB) control blocks are used. The two controllers have designated tasks, namely, response shaping by the FF controller and plant stabilization by the FB controller. This article specifically proposes a design for FF learning control considering an unknown multi-input multi-output (MIMO) linear time-invariant plant with finite zeros. To treat the difficulties in the plant introduced by finite zeros, a Numerator Polynomial matrix fractional representation approach is proposed. The proposed scheme aims to achieve faster error convergence compared to the conventional scheme.
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feedforward learning control for mimo plant with finite zeros parameterization of Numerator Polynomial matrix
Conference on Decision and Control, 2014Co-Authors: Kenji Sugimoto, Lorlynn A. MateoAbstract:This paper proposes a scheme for feedforward (FF) learning control for an unknown multi-input multi-output (MIMO) linear plant in the two-degree-of-freedom structure. Provided that a feedback (FB) control stabilizes the plant but gives a poor response property to reference signals, FF control with on-line learning of inverse dynamics improves the response significantly. In contrast to existing FF learning control schemes called feedback error learning, we propose a scheme that overcomes difficulties in MIMO plant with finite zeros. Numerical simulation is carried out to show the effectiveness of the proposed scheme.
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CDC - Feedforward learning control for MIMO plant with finite zeros: Parameterization of Numerator Polynomial matrix
53rd IEEE Conference on Decision and Control, 2014Co-Authors: Kenji Sugimoto, Lorlynn A. MateoAbstract:This paper proposes a scheme for feedforward (FF) learning control for an unknown multi-input multi-output (MIMO) linear plant in the two-degree-of-freedom structure. Provided that a feedback (FB) control stabilizes the plant but gives a poor response property to reference signals, FF control with on-line learning of inverse dynamics improves the response significantly. In contrast to existing FF learning control schemes called feedback error learning, we propose a scheme that overcomes difficulties in MIMO plant with finite zeros. Numerical simulation is carried out to show the effectiveness of the proposed scheme.
