This paper presents the design of an image-reject continuous-time (CT) quadrature bandpass (QBP) ∆Σ modulator using a tailored signal-transfer-function (STF) design. The quadrature delta-sigma noise shaping with polyphase filter implementations and strategic IF placement effectively improve image rejection internally. The Fifth-order CT QBP ∆Σ modulator planned for WiMAX and Bluetooth standards...

The modern small devices of today require cheap low power radio frequency (RF) transceivers that can provide reliable connectivity at all times. In an RF transceiver, the analog-to-digital converter (ADC) is one of the most important parts and it is also one of the main power consumers. There are several architectures for implementing an ADC, but in the last decade, continuoustime ∆Σ modulators...

In this paper we propose a way to design continuous time Σ∆ modulators. The method is based on the Nyquist stability criterion. Based on this criterion we propose to use the vector gain margin as a robust stability margin. Using this margin as a design criterion we design a robustly stable modulator. Finally, we also show how this margin can be used to evaluate the relative stability of a desig...

1. 1.1. Loops and Fundamental group. Let X be an arcwise connected topological space. Consider the homotopy classes of loops starting at a fixed point b 0 ∈ X : Ω(X, b 0). Recall that a loop is a continuous mapping σ : (I, ∂I) → (X, b 0). Composition σ * τ of two loops σ, τ is defined as (σ * τ)(t) =    σ(2t), 0 ≤ t ≤ 1/2 τ (2t − 1), 1/2 ≤ t ≤ 1 Let c be the constant loop at b 0 and σ −1 be ...

Let (X,Y, Z) be a triple of payoff processes defining a Dynkin game R̃(σ, τ) = E [ Xσ1{τ>σ} + Yτ1{τ<σ} + Zτ1{τ=σ} ] , where σ and τ are stopping times valued in [0, T ]. In the case Z = Y , it is well known that the condition X ≤ Y is needed in order to establish the existence of value for the game, i.e., infτ supσ R̃(σ, τ) = supσ infτ R̃(σ, τ). In order to remove the condition X ≤ Y , we introduc...

Let E be a set of inequalities between finite Σ-terms. Let Vω and Vr denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying E, respectively. We prove that the free Vr-algebra R(X) on generators X is the subalgebra of the corresponding free Vω-algebra Fω(X) determined by those elements of Fω(X) denoted by the regular Σ-coterms. We actually establish...

We consider the three-point even order boundary value problem on time scales, (−1)y (2n) (t) = f(t, y(t)), t ∈ [a, c], αi+1y ∆(2i)(b) + βi+1y ∆(2i+1)(a) = y (2i) (a), γi+1y ∆(2i)(b) = y (2i) (σ(c)), 0 ≤ i ≤ n− 1, where n ≥ 1, a < b < σ(c), σ(c) is right-dense and f : [a, σ(c)] × R → R is continuous. First, we establish the existence of at least three positive solutions by using the well-known L...

Let E be an ideal of Lo over a σ-finite measure space (Ω,Σ, μ), and let (X, ‖ ·‖X) be a real Banach space. Let E(X) be a subspace of the space Lo(X) of μ-equivalence classes of all strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ Lo(X) for which the scalar function ‖f(·)‖X belongs to E. Let E(X)n stand for the order continuous dual of E(X). In this paper we characteriz...

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this fr...