Article

Le problème d’approximation dans la théorie des filtres electriques

Authors:
M.E. Stiefel
M.E. Stiefel
M.E. Stiefel
  • This person is not on ResearchGate, or hasn't claimed this research yet.
Download citation
To read the full-text of this research, you can request a copy directly from the author.

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the author.

Best multiband filter problem
Article
  • Sep 2024
This mini-review examines the problems of geometric function theory that arise in the synthesis of electric filters, and in particular the work of A. A. Gonchar on the generalisation of Zolotarev’s third problem. The modern development of this topic is described, in particular the method of algebro-geometric Ansatz.
View
Applications of Transformation Theory: A Legacy from Zolotarev (1847–1878)
Article
  • Jan 1984
What we are concerned with is, roughly, the generalization to the elliptic case of the familiar multiple angle formulas of elementary trigonometry such as cos⁡ 2θ=2cos⁡2 θ − 1; tan⁡ 2θ=2 tan⁡θ1−tan⁡2θ;sin⁡ 2θ=2 sin⁡ θcos⁡ ∈=2sin⁡ θ(1−sin⁡2θ)\begin{array}{l} \cos \,2\theta = 2{\cos ^2}\,\theta \, - \,1;\,\tan \,2\theta = \frac{{2\,\tan \theta }}{{1 - {{\tan }^2}\theta }};\\ \sin \,2\theta = 2\,\sin \,\theta \cos \, \in = 2\sin \,\theta \sqrt {\left( {1 - {{\sin }^2}\theta } \right)} \end{array} (which are respectively polynomial, rational, algebraic). More generally we have cos⁡ nθ=2n−1[cos⁡nθ−14 cos⁡n−2 θ + …]\cos \,{\rm{n}}\theta = {2^{n - 1}}\left[ {{{\cos }^n}\theta - \frac{1}{4}\,{{\cos }^{n - 2}}\,\theta \, + \, \ldots } \right] which we can also express as a Chebyshev polynomial: {{\rm{T}}_{\rm{n}}}\left( {\rm{x}} \right) = {\rm{cos}}\left( {{\rm{n}}\,{\rm{arccos}}\,{\rm{x}}} \right) = {{\rm{2}}^{{\rm{n}} - {\rm{1}}}}\left[ {{{\rm{x}}^{\rm{n}}} - \frac{{\rm{1}}}{{\rm{4}}}{\rm{n}}{{\rm{x}}^{{\rm{n}} - {\rm{2}}}}\,{\rm{ + }}\,{\rm{ \ldots }}} \right] = {{\rm{2}}^{{\rm{n}} - {\rm{1}}}}{\rm{ }}{{\rm{\tilde T}}_{\rm{n}}}\left( {\rm{x}} \right)
View
The Early Years of Computing in Switzerland
Article
  • Jul 1981
  • Ann Hist Comput
The computer-aided era in Switzerland started in 1950 with the relay machine Z4. Its main properties are described. and the numerical work carried out on it is presented. The ideas pursued and the basic discoveries realized are discussed. During the operation of the Z4, the staff of the Institute for Applied Mathematics at ETH designed the electronic computer ERMETH. Its properties as well as the most important numerical investigations of the years from 1956 to 1962 are outlined, including the work on algorithmic languages and compilers.
View
ResearchGate has not been able to resolve any references for this publication.