This paper analyses the use of hybrid continuous-time/discrete-time cascade Σ∆ modulators for the implementation of power-efficient analog-to-digital converters in broadband wireless communication systems. Two alternative implementations of multi-rate cascade architectures are studied and compared with conventional single-rate continuous-time topologies, taking into account the impact of main c...

This paper discusses certain types of tempo-spatial models constructed from Lévy bases. The dynamics are described by a field of stochastic processes X = {Xt(σ)}, on a set S of sites σ, defined as integrals Xt(σ) = ∫ t −∞ ∫ S ft(ρ, s;σ)Z(dρ× ds) where Z denotes a Lévy basis. The integrands f are deterministic functions of the form ft(ρ, s;σ) = ht(ρ, s;σ)1At(σ)(ρ, σ) where ht(ρ, s;σ) is of a spe...

In this paper, The difference between getting the output spectrum directly using spectrum analyzer and obtaining the spectrum digitally in measuring clock jitter effect on continuous-time Σ∆ modulator is analyzed. It is shown that clock jitter can be seen as input-referred or output-referred, depending on the nature of the measurement tool. Quantization noise and jitter noise are analyzed and c...

Sine-shaping of feedback DAC current in continuous-time Σ∆ ADCs is an effective solution to enhance their immunity to clock jitter. In this paper, a simple mixer circuit for producing a sine-shaped output in continuous-time Σ∆ ADCs is introduced. The proposed solution does not need extra clock source or synchronization circuit, as the mixer utilizes the same clock applied to the comparator. It ...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...

Let p be a prime > 3 and consider the Tate algebra A := Q p z defined to be the Banach algebra of formal power series over Q p that converge on the closed unit disk B[0, 1] ⊆ C p with the supremum norm ||f || := sup z∈B[0,1] |f (z)| for f ∈ A. Equivalently, we have (0.1) A = f (z) = ∞ k=0 a k z k a k ∈ Q p and lim k→∞ a k = 0 and the norm is given by (0.2) ||f || = sup k |a k |, for f = ∞ k=0 a...

Abstract Based on the recent work [4] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator Hφ = (−∆+ V )φ = −(φn+1 + φn−1 − 2φn) + Vnφn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicit...

We show that if X is a Σ 1 separable metrizable space which is not σ-compact then C p (X), the space of bounded real-valued continuous functions on X with the topology of pointwise convergence, is Borel-Π 1 -complete. Assuming projective determinacy we show that if X is projective not σ-compact and n is least such that X is Σ1n then Cp(X), the space of real-valued continuous functions on X with...

In this paper, we study the existence of three positive solutions for the second-order two-point boundary value problem on a measure chain, x∆∆(t)+ p(t) f ( t, x(σ (t)), x∆(t) ) = 0, t ∈ [t1, t2], a1x(t1)− a2x (t1) = 0, a3x(σ (t2))+ a4x ∆(σ (t2)) = 0, where f : [t1, σ (t2)]× [0,∞)× R → [0,∞) is continuous and p : [t1, σ (t2)] → [0,∞) a nonnegative function that is allowed to vanish on some subi...

Let Γ be a discrete subgroup of a simply connected, solvable Lie group G, such that AdG Γ has the same Zariski closure as AdG. If α : Γ → GLn(R) is any finite-dimensional representation of Γ, we show that α virtually extends to a continuous representation σ of G. Furthermore, the image of σ is contained in the Zariski closure of the image of α. When Γ is not discrete, the same conclusions are t...