Estimation of the modulation index of cpm signals using hos

Three simple methods are proposed for the estimation of the modulation index of continuous phase modulated signals in noise. These methods employ the estimated autocorrelation and fourth-order cumulant sequences of the received signal after sampling at the symbol rate. Analytic expressions are derived for the asymptotic mean and variance of the estimated parameters which are corroborated by means of Monte Carlo simulations. The performance of the methods is illustrated graphically and numerically. It is concluded that, under significant noise degradation, only the scheme based on the fourth-order cumulant sequence can be used to estimate consistently the modulation index h in the range 0(h(1.Peer ReviewedPostprint (published version

A 64-channel inductively-powered neural recording sensor array

This paper reports a 64-channel inductively powered neural recording sensor array. Neural signals are acquired, filtered, digitized and compressed in the channels. Additionally, each channel implements a local auto-calibration mechanism which configures the transfer characteristics of the recording site. The system has two operation modes; in one case the information captured by the channels is sent as uncompressed raw data; in the other, feature vectors extracted from the detected neural spikes are transmitted. Data streams coming from the channels are serialized by an embedded digital processor and transferred to the outside by means of the same inductive link used for powering the system. Simulation results show that the power consumption of the complete system is 377μW.Ministerio de Ciencia e Innovación TEC2009-0844

Blind multiuser deconvolution in fading and dispersive channels

An adaptive near-far resistant technique for the blind joint multiuser identification and detection in asynchronous CDMA systems is analyzed in fading and dispersive GSM channels.Peer ReviewedPostprint (published version

A relationship between the ideals of Fq[x,y,x−1,y−1]\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right] and the Fibonacci numbers

Let $C_n(q)$ be the number of ideals of codimension $n$ of $\mathbb{F}_q\left[x, y, x^{-1}, y^{-1} \right]$, where $\mathbb{F}_q$ is the finite field with $q$ elements. Kassel and Reutenauer [KasselReutenauer2015A] proved that $C_n(q)$ is a polynomial in $q$ for any fixed value of $n \geq 1$. For $q = \frac{3+\sqrt{5}}{2}$, this combinatorial interpretation of $C_n(q)$ is lost. Nevertheless, an unexpected connexion with Fibonacci numbers appears. Let $f_n$ be the $n$-th Fibonacci number (following the convention $f_0 = 0$, $f_1 = 1$). Define the series $$F(t) = \sum_{n \geq 1} f_{2n}\,t^n.$$ We will prove that for each $n \geq 1$, $$C_n\left( \frac{3+\sqrt{5}}{2}\right) = \lambda_n \, \left(f_{2n} \frac{3+\sqrt{5}}{2} - f_{2n-2} \right) ,$$ where the integers $\lambda_n \geq 0$ are given by the following generating function $$ \prod_{m \geq 1} \left(1+F\left( t^m\right)\right) = 1 + \sum_{n \geq 1} \lambda_n\,t^n. $

Middle divisors and σ\sigma-palindromic Dyck words

Given a real number $\lambda > 1$, we say that $d|n$ is a $\lambda$-middle divisor of $n$ if $$\sqrt{\frac{n}{\lambda}} < d \leq \sqrt{\lambda n}.$$ We will prove that there are integers having an arbitrarily large number of $\lambda$-middle divisors. Consider the word $$\langle\! \langle n \rangle\! \rangle_{\lambda} := w_1 w_2 ... w_k \in \{a,b\}^{\ast},$$ given by $$w_i := \left\{ \begin{array}{c l} a & \textrm{if } u_i \in D_n \backslash \left(\lambda D_n\right), \\ b & \textrm{if } u_i \in \left(\lambda D_n\right)\backslash D_n, \end{array} \right.$$ where $D_n$ is the set of divisors of $n$, $\lambda D_n := \{\lambda d: \quad d \in D_n\}$ and $u_1, u_2, ..., u_k$ are the elements of the symmetric difference $D_n \triangle \lambda D_n$ written in increasing order. We will prove that the language $$\mathcal{L}_{\lambda} := \left\{\langle\! \langle n \rangle\! \rangle_{\lambda} : \quad n \in \mathbb{Z}_{\geq 1} \right\}$$ contains Dyck words having an arbitrarily large number of centered tunnels. We will show a connection between both results

A power efficient neural spike recording channel with data bandwidth reduction

This paper presents a mixed-signal neural spike recording channel which features, as an added value, a simple and low-power data compression mechanism. The channel uses a band-limited differential low noise amplifier and a binary search data converter, together with other digital and analog blocks for control, programming and spike characterization. The channel offers a self-calibration operation mode and it can be configured both for signal tracking (to raw digitize the acquired neural waveform) and feature extraction (to build a first-order PWL approximation of the spikes). The prototype has been fabricated in a standard CMOS 0.13μm and occupies 400μm×400μm. The overall power consumption of the channel during signal tracking is 2.8μW and increases to 3.0μW average when the feature extraction operation mode is programmed.Ministerio de Ciencia e Innovación TEC2009-08447Junta de Andalucía TIC-0281

On prime numbers of the form 2n±k2^n \pm k

Consider the set $\mathcal{K}$ of integers $k$ for which there are infinitely many primes $p$ such that $p+k$ is a power of $2$. The aim of this paper is to show a relationship between $\mathcal{K}$ and the limits points of some set rational numbers related to a sequence of polynomials $C_n(q)$ introduced by Kassel and Reutenauer [KasselReutenauer]