Hardware-efficient implementation of digital FIR filter using fast first-order moment algorithm

2018 ◽  
Author(s):  
Li Cao ◽  
jianguo Liu ◽  
jun Xiong ◽  
jing Zhang
Keyword(s):  
Fir Filter ◽  
Efficient Implementation ◽  
Order Moment ◽  
First Order

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

scholarly journals The Algorithm and Structure for Digital Normalized Cross-Correlation by Using First-Order Moment

Sensors ◽  
2020 ◽  
Vol 20 (5) ◽  
pp. 1353 ◽  
Author(s):  
Chao Pan ◽  
Zhicheng Lv ◽  
Xia Hua ◽  
Hongyan Li
Keyword(s):  
Systolic Array ◽  
Fast Algorithm ◽  
Cross Correlation ◽  
Inner Product ◽  
Order Moment ◽  
Mathematical Tool ◽  
Arbitrary Length ◽  
First Order ◽  
Normalized Cross Correlation ◽  
Systolic Structure

Normalized cross-correlation is an important mathematical tool in digital signal processing. This paper presents a new algorithm and its systolic structure for digital normalized cross-correlation, based on the statistical characteristic of inner-product. We first introduce a relationship between the inner-product in cross-correlation and a first-order moment. Then digital normalized cross-correlation is transformed into a new calculation formula that mainly includes a first-order moment. Finally, by using a fast algorithm for first-order moment, we can compute the first-order moment in this new formula rapidly, and thus develop a fast algorithm for normalized cross-correlation, which contributes to that arbitrary-length digital normalized cross-correlation being performed by a simple procedure and less multiplications. Furthermore, as the algorithm for the first-order moment can be implemented by systolic structure, we design a systolic array for normalized cross-correlation with a seldom multiplier, in order for its fast hardware implementation. The proposed algorithm and systolic array are also improved for reducing their addition complexity. The comparisons with some algorithms and structures have shown the performance of the proposed method.

Generalized stochastic resonance for a fractional harmonic oscillator with bias-signal-modulated trichotomous noise

2018 ◽  
Vol 32 (07) ◽  
pp. 1850072 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Xipei Huang ◽  
Yongxian Wen
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
External Excitation ◽  
First Order ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional Harmonic Oscillator ◽  
Amplitude Amplification

For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro–Loginov formula and generalized fractional Shapiro–Loginov formula are derived. Then, by using the generalized (fractional) Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.

scholarly journals New-type Hoeffding’s inequalities and application in tail bounds

2021 ◽  
Vol 5 (1) ◽  
pp. 248-261
Author(s):  
Pingyi Fan ◽  
Keyword(s):  
Information Processing ◽  
Random Variables ◽  
Order Moment ◽  
First Order ◽  
Hoeffding’S Inequalities ◽  
New Type ◽  
Hoeffding’S Inequality ◽  
Hoeffding Inequality ◽  
Moments Of Random Variables ◽  
Refined Version

It is well known that Hoeffding's inequality has a lot of applications in the signal and information processing fields. How to improve Hoeffding's inequality and find the refinements of its applications have always attracted much attentions. An improvement of Hoeffding inequality was recently given by Hertz [<a href="#1">1</a>]. Eventhough such an improvement is not so big, it still can be used to update many known results with original Hoeffding's inequality, especially for Hoeffding-Azuma inequality for martingales. However, the results in original Hoeffding's inequality and its refined version by Hertz only considered the first order moment of random variables. In this paper, we present a new type of Hoeffding's inequalities, where the high order moments of random variables are taken into account. It can get some considerable improvements in the tail bounds evaluation compared with the known results. It is expected that the developed new type Hoeffding's inequalities could get more interesting applications in some related fields that use Hoeffding's results.

scholarly journals Two-Dimensional Probabilistic Infiltration Analysis in a Hillslope Using First-Order Moment Approach

Ground Water ◽  
2018 ◽  
Vol 57 (2) ◽  
pp. 226-237 ◽  
Author(s):  
Rui-Xuan Tang ◽  
Jing-Sen Cai ◽  
Tian-Chyi Jim Yeh
Keyword(s):  
Order Moment ◽  
Two Dimensional ◽  
First Order ◽  
Moment Approach

scholarly journals Asymptotic behavior of projections of supercritical multi-type continuous-state and continuous-time branching processes with immigration

2021 ◽  
Vol 53 (4) ◽  
pp. 1023-1060
Author(s):  
Mátyás Barczy ◽  
Sandra Palau ◽  
Gyula Pap
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Time ◽  
Branching Process ◽  
Branching Processes ◽  
Order Moment ◽  
Moment Condition ◽  
First Order ◽  
Continuous State ◽  
Branching Process With Immigration ◽  
Continuous Time Branching Processes

AbstractUnder a fourth-order moment condition on the branching and a second-order moment condition on the immigration mechanisms, we show that an appropriately scaled projection of a supercritical and irreducible continuous-state and continuous-time branching process with immigration on certain left non-Perron eigenvectors of the branching mean matrix is asymptotically mixed normal. With an appropriate random scaling, under some conditional probability measure, we prove asymptotic normality as well. In the case of a non-trivial process, under a first-order moment condition on the immigration mechanism, we also prove the convergence of the relative frequencies of distinct types of individuals on a suitable event; for instance, if the immigration mechanism does not vanish, then this convergence holds almost surely.

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