Narrow Results

A comprehensive analysis of the impact of the finite gain-bandwidth product (GBW) in amplifiers and the excess loop delay on a parallel multibit CT ΔΣ ADC for an orthogonal frequency division multiplexing OFDM ultra-wideband (UWB) receiver has been carried out in this paper. The overall converter consists of two CT ΔΣ modulators covering two sub-bands (each of them implemented by a third and a fourth order CT ΔΣ modulator) that are arranged to operate in parallel. Our study was based on the dependence of the noise transfer function (NTF) poles and zeroes locus in the z-plane on these two nonideal effects for both modulators from a theoretical approach. The corresponding STFs were also analytically evaluated. System-level simulations have been accomplished too. Amplifiers were modeled according to a single-pole transfer function. Using the modified Z-transform method the dependence of the NTF poles and zeroes locus in the z-plane on the finite GBW and on excess loop delay was obtained when the DAC pulse end occurs in the current ("early") or in the following ("late") clock cycle. NTF poles and zeroes loci were evaluated as a function of the two nonideal effects considered separately or combined.

A high-speed and high-accuracy continuous-time common-mode feedback block (CMFB) is presented. To satisfy speed and accuracy requirements, some modifications have been applied on differential difference amplifier (DDA) CMFB circuit. The proposed method is applied to a folded cascode op-amp with power supply of 3.3 V. In order to verify the proposed circuit, simulations are done in 0.35 μm standard CMOS technology. In the worst condition when the output common-mode (CM) voltage is initialized to VCC or GND, only 1.1 ns is required to set the output CM voltage on the desired level. Also in a wide range of input CM voltage variations, the deviation of the output CM voltage from reference voltage is less than 6 mV, so simulation results confirm the expected accuracy and speed while simultaneously the proposed CMFB circuit preserves other characteristics of DDA CMFB circuit such as unity gain frequency, 3-dB bandwidth, phase margin and linearity.

Portfolio optimization under downside risk is of crucial importance to asset managers. In this article we consider one such particular measure given by the notion of Capital at Risk (CaR), closely related to Value at Risk. We consider portfolio optimization with respect to CaR in the Black-Scholes setting with time dependent parameters and investment strategies, i.e., continuous-time portfolio optimization. We review the results from our previous work in unconstrained portfolio optimization, and then investigate and solve the corresponding problems with the additional constraint of no-short-selling. Analytical formulae are derived for the optimal strategies, and numerical examples are presented.

A classical lazy random walk on cycles is known to mix with the uniform distribution. In contrast, we show that a continuous-time quantum walk on cycles exhibits strong non-uniform mixing properties. First, we prove that the instantaneous distribution of a quantum walk on most even-length cycles is never uniform. More specifically, we prove that a quantum walk on a cycle C_n is not instantaneous uniform mixing, whenever n satisfies either: (a) n = 2^u, for u ≥ 3; or (b) n = 2^uq, for u ≥ 1 and q ≡ 3 (mod 4). Second, we prove that the average distribution of a quantum walk on any Abelian circulant graph is never uniform. As a corollary, the average distribution of a quantum walk on any standard circulant graph, such as the cycles, complete graphs, and even hypercubes, is never uniform. Nevertheless, we show that the average distribution of a quantum walk on the cycle C_n is O(1/n)-uniform.

We study continuous-time quantum walks on graphs which generalize the hypercube. The only known family of graphs whose quantum walk instantaneously mixes to uniform is the Hamming graphs with small arities. We show that quantum uniform mixing on the hypercube is robust under the addition of perfect matchings but not much else. Our specific results include:

• The graph obtained by augmenting the hypercube with an additive matching x ↦ x ⊕ η is instantaneous uniform mixing whenever |η| is even, but with a slower mixing time. This strictly includes the result of Moore and Russell¹ on the hypercube.

• The class of Hamming graphs H(n,q) is not uniform mixing if and only if q ≥ 5. This is a tight characterization of quantum uniform mixing on Hamming graphs; previously, only the status of H(n,q) with q < 5 was known.

• The bunkbed graph whose adjacency matrix is I ⊗ Q_n + X ⊗ A_f, where A_f is a -circulant matrix defined by a Boolean function f, is not uniform mixing if the Fourier transform of f has support of size smaller than 2^n-1. This explains why the hypercube is uniform mixing and why the join of two hypercubes is not.

Our work exploits the rich spectral structure of the generalized hypercubes and relies heavily on Fourier analysis of group-circulants.

The realization problem for positive, continuous-time linear single-input, single-output systems with delays is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for computation of positive minimal realizations is presented and illustrated by an example.

This paper presents a novel finite-and-quantized output feedback asymptotic tracking control method for a general class of continuous-time linear time-invariant systems. First, we construct a finite quantizer with time-varying thresholds and design a pole placement control law that exclusively utilizes the finite-and-quantized output signal and an external reference signal. Then, we establish the boundedness of all closed-loop signals and prove the asymptotic convergence of the output tracking error to zero. The proposed method combines the advantages of classical pole placement control technique and finite quantization feedback technique. It not only reduces the requirement for feedback information compared with existing tracking control methods but also effectively handles unstable poles and zeros in controlled systems, thereby achieving asymptotic output tracking. Finally, we provide a representative example to validate the effectiveness and new features of our proposed method.