SCALED AND SCALING-FREE McCLELLAN TRANSFORMATIONS FOR THE DESIGN OF 2-D DIGITAL FILTERS

1991 ◽  
Vol 01 (01) ◽  
pp. 105-124 ◽  
Author(s):  
N. NAGAMUTHU ◽  
M. N. S. SWAMY
Keyword(s):  
Real Time ◽  
Digital Filters ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Scaling Factors ◽  
Mcclellan Transformation ◽  
Real Time Applications ◽  
Necessary And Sufficient ◽  
New Formula ◽  
Analytical Expressions

In this paper, the scaling problem of McClellan transformation used for the design 2-D digital filters with elliptical and circular cutoff contours is critically analyzed. Several new and extremely simple formulas for calculating the maximum and minimum values of the transformation function are presented. Using these extreme values, simple formulas for scaling factors and scaled McClellan transformations are derived for the various cases of each type of contour. Using the necessary and sufficient conditions for a scaling-free transformation, the scaling-free McClellan transformations are also derived. It is shown that the number of independent coefficients in them to be optimized varies from 0 to 2 depending on the case, compared to 3 in the original transformation. They are very useful in deriving analytical expressions for the transformation coefficients, and the 2-D filters designed by employing them have a smaller number of multiplications per output sample and hence, attractive for real-time applications. A new scaling formula is presented and some of its properties and effects on the derived formulas are discussed. The major advantage of this new formula is that from the unscaled transformation coefficients for a given type of 2-D filter, we can generate the scaled transformation coefficients for a different type of 2-D filter. Some examples are presented to demonstrate the usefulness of the derived formulas.

Delay-independent Stability of Uncertain Control Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Mehdi Ahmadian
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Entire Family ◽  
Active Vibration ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Analytical Expressions

This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.

Analytical Expressions for Stability and Bifurcations of Turret Mooring Systems

1998 ◽  
Vol 42 (03) ◽  
pp. 216-232
Author(s):  
Luis O. Garza-Rios ◽  
Michael M. Bernitsas
Keyword(s):  
Parametric Design ◽  
Sufficient Conditions ◽  
Mooring Lines ◽  
Design Variables ◽  
Stability And Bifurcations ◽  
Dynamic Loss ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Fifth Order ◽  
Analytical Expressions

The eight necessary and sufficient conditions for stability of turret mooring systems (TMS) are derived analytically. Analytical expressions for TMS bifurcation boundaries where static and dynamic loss of stability occur are also derived. These analytical expressions provide physics-based means to evaluate the stability properties of TMS, find elementary singularities, and describe the morphogeneses occurring as a parameter (or design variable) or group of parameters are varied. They eliminate the need to compute numerically the TMS eigenvalues. Analytical results are verified by comparison to numerical results generated by direct computation of eigenvalues and their bifurcations. Catastrophe sets (design charts) are constructed in the two-dimensional parametric design space to show the dependence of design variables on the stability of the system. The TMS mathematical model consists of the nonlinear horizontal plane—surge, sway and yaw—fifth-order, large drift, low speed maneuvering equations. Mooring lines are modeled quasistatically by catenaries. External excitation consists of time independent current, steady wind, and second-order mean drift forces.

The inverse problem for the Euler-Bernoulli beam

1986 ◽  
Vol 407 (1832) ◽  
pp. 199-218 ◽  
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Sufficient Conditions ◽  
Sectional Area ◽  
Bernoulli Beam ◽  
Scaling Factors ◽  
Cross Sectional ◽  
End Conditions ◽  
Necessary And Sufficient ◽  
Euler Bernoulli Beam

It has long been known that two scaling factors and three spectra, corresponding to three different end-conditions, are required to determine the cross-sectional area A(x) and second moment of area I(x) of an Euler-Bernoulli beam. What has not been known are the necessary and sufficient conditions on the spectral data which will yield positive functions A(x), I(x) . Such a set of conditions is derived in this paper.

scholarly journals The Extreme Values of Young’s Modulus and the Negative Poisson’s Ratios of Rhombic Crystals

Crystals ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 863
Author(s):  
Valentin A. Gorodtsov ◽  
Dmitry S. Lisovenko
Keyword(s):  
Young’S Modulus ◽  
Poisson’S Ratio ◽  
Extreme Values ◽  
Young's Modulus ◽  
Sufficient Conditions ◽  
Poisson's Ratio ◽  
Cubic Crystals ◽  
Special Cases ◽  
Function Of Two Variables ◽  
Necessary And Sufficient

The extreme values of Young’s modulus for rhombic (orthorhombic) crystals using the necessary and sufficient conditions for the extremum of the function of two variables are analyzed herein. Seven stationary expressions of Young’s modulus are obtained. For three stationary values of Young’s modulus, simple analytical dependences included in the sufficient conditions for the extremum of the function of two variables are revealed. The numerical values of the stationary and extreme values of Young’s modulus for all rhombic crystals with experimental data on elastic constants from the well-known Landolt-Börnstein reference book are calculated. For three stationary values of Young’s modulus of rhombic crystals, a classification scheme based on two dimensionless parameters is presented. Rhombic crystals ((CH3)3NCH2COO·(CH)2(COOH)2, I, SC(NH2)2, (CH3)3NCH2COO·H3BO3, Cu-14 wt%Al, 3.0wt%Ni, NH4B5O8·4H2O, NH4HC2O4·1/2H2O, C6N2O3H6 and CaSO4) having a large difference between maximum and minimum Young’s modulus values were revealed. The highest Young’s modulus among the rhombic crystals was found to be 478 GPa for a BeAl2O4 crystal. More rigid materials were revealed among tetragonal (PdPb2; maximum Young’s modulus, 684 GPa), hexagonal (graphite; maximum Young’s modulus, 1020 GPa) and cubic (diamond; maximum Young’s modulus, 1207 GPa) crystals. The analytical stationary values of Young’s modulus for tetragonal, hexagonal and cubic crystals are presented as special cases of stationary values for rhombic crystals. It was found that rhombic, tetragonal and cubic crystals that have large differences between their maximum and minimum values of Young’s modulus often have negative minimum values of Poisson’s ratio (auxetics). We use the abbreviated term auxetics instead of partial auxetics, since only the latter were found. No similar relationship between a negative Poisson’s ratio and a large difference between the maximum and minimum values of Young’s modulus was found for hexagonal crystals.

Sign in / Sign up

Export Citation Format

Share Document