Arbitrary Phase Characteristics Research Articles

Small gain versus positive real modeling of real parameter uncertainty

The authors shown by means of a lightly damped oscillator example with uncertain stiffness that small gain modeling of constant real parameter uncertainty can be extremely conservative. This example was chosen to highlight inherent drawbacks of small-gain principles applied to the analysis of robust controllers for lightly damped flexible structures. If, for this class of problems, uncertainty in the stiffness operator, which may be relatively large, is modeled as a small gain H/sub infinity / block, then the arbitrary phase characteristics of the uncertainty block can contribute to a significant perturbation of the damping operator, which may be relatively small. An alternative uncertainty modeling approach involving positive real transfer functions and the positivity theorem is shown to be significantly less conservative. >

Transfer functions with arbitrary phase characteristics

AbstractA simplified method—based on Thiele's continued fraction—is proposed for the derivation of transfer functions whose phase responses interpolate a desired phase characteristics at a set of prescribed frequencies, the maximally flat delay aproximation being recovered as a degenerate one. Illustrative examples showing the application of this procedure in the design of linear delay networks are also given.

Performance comparisons for nonrecursive digital filters with nonlinear phase characteristics

This letter presents a comparison between the performance, in terms of ripple and transition bandwidth, of nonrecursive digital filters with arbitrary phase characteristics and those with a linear phase response. Results are given which show that filters can be designed to have an arbitrary phase response, yet give as good a gain response as filters with linear phase.

Filters approximating ideal amplitude and arbitrary phase characteristics

The closed-form solution is derived for the scattering transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S_{12}(p)</tex> of a resistively terminated lossless reciprocal two-port prototype network of degree <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2n</tex> which satisfies the following constraints: <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|S_{12}(j\omega) | \leq 1</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">|S_{12}({\pm}j{\omega}_i) | = 1 , i = 1 \rightarrow n</tex> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\arg S_{12}({\pm}j{\omega}_i) = \pm \psi({\omega}_i), i = 1 \rightarrow n</tex> where the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega_i</tex> are arbitrary and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\psi(\omega)</tex> is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas.

Synthesis of electric filters with arbitrary phase characteristics

Synthesis of electric filters with arbitrary phase characteristics