Systems Design by Continued Fraction Expansion
نویسندگان
چکیده
منابع مشابه
Beta-expansion and continued fraction expansion over formal Laurent series
Let x ∈ I be an irrational element and n 1, where I is the unit disc in the field of formal Laurent series F((X−1)), we denote by kn(x) the number of exact partial quotients in continued fraction expansion of x, given by the first n digits in the β-expansion of x, both expansions are based on F((X−1)). We obtain that lim inf n→+∞ kn(x) n = degβ 2Q∗(x) , lim sup n→+∞ kn(x) n = degβ 2Q∗(x) , wher...
متن کاملA Short Proof of the Simple Continued Fraction Expansion of
One of the most interesting proofs is due to Hermite; it arose as a byproduct of his proof of the transcendence of e in [5]. (See [6] for an exposition by Olds.) The purpose of this note is to present an especially short and direct variant of Hermite’s proof and to explain some of the motivation behind it. Consider any continued fraction [a0, a1, a2, . . .]. Its ith convergent is defined to be ...
متن کاملQuadratic Irrational Integers with Partly Prescribed Continued Fraction Expansion
We generalise remarks of Euler and of Perron by explaining how to detail all quadratic integers for which the symmetric part of their continued fraction expansion commences with prescribed partial quotients. I last saw Bela Brindza, my once postdoctoral student, in April, 2002. I was working on the paper below and attempted to enthuse him with its results, particularly those concerning periodic...
متن کاملPade table, continued fraction expansion, and perfect reconstruction filter banks
We investigate the relationships among the Pad e table, continued fraction expansions and perfect reconstruction (PR) lter banks. We show how the Pad e table can be utilized to develop a new lattice structure for general two-channel bi-orthogonal perfect reconstruction (PR) lter banks. This is achieved through characterization of all two-channel bi-orthogonal PR lter banks. The parameterization...
متن کاملA Wirsing-type approach to some continued fraction expansion
The Gauss 1812 problem gave rise to an extended literature. In modern times, the socalled Gauss-Kuzmin-Lévy theorem is still one of the most important results in the metrical theory of regular continued fractions (RCFs). A recent survey of this topic is to be found in [10]. From the time of Gauss, a great number of such theorems followed. See, for example, [2, 6, 7, 8, 18]. Apart from the RCF e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the Society of Instrument and Control Engineers
سال: 1979
ISSN: 0453-4654
DOI: 10.9746/sicetr1965.15.895