Design of Multistage Decimation Filters Using Cyclotomic Polynomials: Optimization and Design Issues

This paper focuses on the design of multiplier-less decimation filters suitable for oversampled digital signals. The aim is twofold. On one hand, it proposes an optimization framework for the design of constituent decimation filters in a general multistage decimation architecture. The basic building blocks embedded in the proposed filters belong, for a simple reason, to the class of cyclotomic polynomials (CPs): the first 104 CPs have a z-transfer function whose coefficients are simply {-1,0,+1}. On the other hand, the paper provides a bunch of useful techniques, most of which stemming from some key properties of CPs, for designing the proposed filters in a variety of architectures. Both recursive and non-recursive architectures are discussed by focusing on a specific decimation filter obtained as a result of the optimization algorithm. Design guidelines are provided with the aim to simplify the design of the constituent decimation filters in the multistage chain.Comment: Submitted to CAS-I, July 07; 11 pages, 5 figures, 3 table

On the Polyphase Decomposition for Design of Generalized Comb Decimation Filters

Generalized comb filters (GCFs) are efficient anti-aliasing decimation filters with improved selectivity and quantization noise (QN) rejection performance around the so called folding bands with respect to classical comb filters. In this paper, we address the design of GCF filters by proposing an efficient partial polyphase architecture with the aim to reduce the data rate as much as possible after the Sigma-Delta A/D conversion. We propose a mathematical framework in order to completely characterize the dependence of the frequency response of GCFs on the quantization of the multipliers embedded in the proposed filter architecture. This analysis paves the way to the design of multiplier-less decimation architectures. We also derive the impulse response of a sample 3rd order GCF filter used as a reference scheme throughout the paper.Comment: Submitted to IEEE TCAS-I, February 2007; 11 double-column pages, 9 figures, 1 tabl

Connection Between System Parameters and Localization Probability in Network of Randomly Distributed Nodes

This article deals with localization probability in a network of randomly distributed communication nodes contained in a bounded domain. A fraction of the nodes denoted as L-nodes are assumed to have localization information while the rest of the nodes denoted as NL nodes do not. The basic model assumes each node has a certain radio coverage within which it can make relative distance measurements. We model both the case radio coverage is fixed and the case radio coverage is determined by signal strength measurements in a Log-Normal Shadowing environment. We apply the probabilistic method to determine the probability of NL-node localization as a function of the coverage area to domain area ratio and the density of L-nodes. We establish analytical expressions for this probability and the transition thresholds with respect to key parameters whereby marked change in the probability behavior is observed. The theoretical results presented in the article are supported by simulations.Comment: To appear on IEEE Transactions on Wireless Communications, November 200

A Model of the IEEE 802.11 DCF in Presence of Non Ideal Transmission Channel and Capture Effects

In this paper, we provide a throughput analysis of the IEEE 802.11 protocol at the data link layer in non-saturated traffic conditions taking into account the impact of both transmission channel and capture effects in Rayleigh fading environment. Impacts of both non-ideal channel and capture become important in terms of the actual observed throughput in typical network conditions whereby traffic is mainly unsaturated, specially in an environment of high interference. We extend the multi-dimensional Markovian state transition model characterizing the behavior at the MAC layer by including transmission states that account for packet transmission failures due to errors caused by propagation through the channel, along with a state characterizing the system when there are no packets to be transmitted in the buffer of a station.Comment: Accepted for oral presentation to IEEE Globecom 2007, Washington D.C., November 200

On The Linear Behaviour of the Throughput of IEEE 802.11 DCF in Non-Saturated Conditions

We propose a linear model of the throughput of the IEEE 802.11 Distributed Coordination Function (DCF) protocol at the data link layer in non-saturated traffic conditions. We show that the throughput is a linear function of the packet arrival rate (PAR) $\lambda$ with a slope depending on both the number of contending stations and the average payload length. We also derive the interval of validity of the proposed model by showing the presence of a critical $\lambda$, above which the station begins operating in saturated traffic conditions. The analysis is based on the multi-dimensional Markovian state transition model proposed by Liaw \textit{et al.} with the aim of describing the behaviour of the MAC layer in unsaturated traffic conditions. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed linear model.Comment: To appear on IEEE Communications Letters, November 200

On the Behavior of the Distributed Coordination Function of IEEE 802.11 with Multirate Capability under General Transmission Conditions

The aim of this paper is threefold. First, it presents a multi-dimensional Markovian state transition model characterizing the behavior of the IEEE 802.11 protocol at the Medium Access Control layer which accounts for packet transmission failures due to channel errors modeling both saturated and non-saturated traffic conditions. Second, it provides a throughput analysis of the IEEE 802.11 protocol at the data link layer in both saturated and non-saturated traffic conditions taking into account the impact of both the physical propagation channel and multirate transmission in Rayleigh fading environment. The general traffic model assumed is M/M/1/K. Finally, it shows that the behavior of the throughput in non-saturated traffic conditions is a linear combination of two system parameters; the payload size and the packet rates, $\lambda^{(s)}$, of each contending station. The validity interval of the proposed model is also derived. Simulation results closely match the theoretical derivations, confirming the effectiveness of the proposed models.Comment: Submitted to IEEE Transactions on Wireless Communications, October 21, 200

On the Throughput Allocation for Proportional Fairness in Multirate IEEE 802.11 DCF

This paper presents a modified proportional fairness (PF) criterion suitable for mitigating the \textit{rate anomaly} problem of multirate IEEE 802.11 Wireless LANs employing the mandatory Distributed Coordination Function (DCF) option. Compared to the widely adopted assumption of saturated network, the proposed criterion can be applied to general networks whereby the contending stations are characterized by specific packet arrival rates, $\lambda_s$, and transmission rates $R_d^{s}$. The throughput allocation resulting from the proposed algorithm is able to greatly increase the aggregate throughput of the DCF while ensuring fairness levels among the stations of the same order of the ones available with the classical PF criterion. Put simply, each station is allocated a throughput that depends on a suitable normalization of its packet rate, which, to some extent, measures the frequency by which the station tries to gain access to the channel. Simulation results are presented for some sample scenarios, confirming the effectiveness of the proposed criterion.Comment: Submitted to IEEE CCNC 200

Bayesian Approach for dimensionality reduction of compartmental model parameters of the PET [18F]FDG tracer

openPositron Emission Tomography (PET) con [18F]FDG (Fluorodeossiglucosio) è una tecnica di imaging nucleare ampiamente utilizzata in oncologia. Ha un ruolo cruciale nell'esaminare i processi fisiologici e patofisiologici in vivo, consentendo la misurazione quantitativa dei cambiamenti biochimici nel corpo. Ciò facilita la rilevazione di anomalie nel metabolismo dei tessuti d'interesse. Per stabilire una connessione tra i segnali PET e i processi biochimici interni, è richiesto l'utilizzo di un modello compartimentale. La stima dei parametri può essere eseguita a livello di regione di interesse (ROI) o a livello di voxel, sfruttando appieno la risoluzione spaziale dello scanner PET. In situazioni specifiche, ad esempio nello studio di una lesione, le informazioni fornite dall'analisi a livello di ROI potrebbero non essere sufficienti, e sarebbe richiesta un'analisi a livello di voxel. La sfida risiede nel tipo di segnale ottenuto a livello di voxel, caratterizzato da un basso rapporto segnale-rumore (SNR), in contrasto al segnale ottenuto dall'analisi a livello di ROI. Attualmente, i metodi comunemente utilizzati per la stima dei microparametri a livello di ROI non sono altrettanto efficaci a livello di voxel, a causa del basso SNR. Approcci semplificati, come il metodo grafico di Patlak, sono applicabili, ma generano parametri con informazioni fisiologiche meno dettagliate. Pertanto, c'è la necessità di un approccio in grado di produrre risultati affidabili a livello di voxel. Una soluzione potrebbe essere negli stimatori Bayesiani, che sfruttano informazioni a priori per performare meglio in presenza di dati rumorosi. Tuttavia, la stima dei microparametri nel modello è basata sull'assunzione di disporre di una funzione di input priva di rumore. Questo richiede tipicamente campionamenti arteriali, che possono essere scomodi e gravosi per il paziente. Un'alternativa è la Image-derived Input Function (IDIF), che estrae la funzione di input direttamente dall'immagine PET, utilizzando le arterie carotidi interne (ICA) o le arterie carotidi comuni (CCA), con correzioni applicate per correggere i Partial Volume Effect (PVE). Questa tesi si concentra sull'esplorazione di un approccio bayesiano per consentire una stima adeguata dei microparametri a livello di voxel. In particolare, è stato utilizzato il metodo di stima Maximum A Posteriori (MAP). Nella nostra implementazione, le informazioni a priori derivano dalle stime a livello di ROI, con l'obiettivo finale di ottenere stime precise a livello di voxel. Inoltre, la stima MAP è stata testata con un vincolo su un parametro del modello, il k3, basato sulla stima voxel-wise di Ki ottenuta utilizzando l'analisi grafica di Patlak, per ridurre ulteriormente la complessità. Inoltre, è stata esaminata l'influenza dell'utilizzo di diverse funzioni di input estratte da diverse ROI vascolari in questo studio. L'analisi è stata eseguita su un dataset composto da 10 soggetti affetti da glioma sottoposti ad una acquisizione con tracciante [18F]FDG su un sistema PET/MR presso l'Ospedale Universitario di Padova. Per valutare l'affidabilità dei risultati ottenuti con la stima MAP, le mappe parametriche sono state confrontate con quelle ottenute utilizzando un altro approccio bayesiano, ovvero il Variational Bayes (VB). Le stime a livello di voxel ottenute dai due diversi metodi presentano una correlazione elevata. Per quanto riguarda la funzione di input, osserviamo che si ottengono stime simili utilizzando l'IDIF delle ICA con correzione del PVE o utilizzando l'IDIF delle CCA senza alcuna correzione. Questo approccio apre la strada a futuri studi sulla gestione dei dati rumorosi in relazione all'errore di misura e sull'ispezione dell'influenza dei vincoli sul calcolo a posteriori del parametro k3.Positron Emission Tomography (PET) with [18F]FDG (Fluorodeoxyglucose) is a nuclear imaging technique widely utilized in oncology. It plays a crucial role in examining physiological and pathophysiological processes in vivo, enabling the quantitative measurement of biochemical changes in the body. This facilitates the detection of anomalies in the metabolism of tissues of interest. To establish a connection between PET signals and internal biochemical processes, compartmental modeling is required. Parameter estimation can be performed either at region-of-interest (ROI) level or at the voxel level, fully exploiting the PET scanner spatial resolution. In specific situations, for example when studying a lesion, the information provided by ROI level analysis may not be enough, and a voxel level analysis would be required. The challenge lies in the type of signal obtained at the voxel level, characterized by a low Signal-to-Noise Ratio (SNR), in contrast to regional analysis. Currently, commonly employed methods for microparameter estimation at ROI level are not equally effective at the voxel level, due to the low SNR. Simplified approaches, such as the Patlak Graphical method, are available, but they generate parameters with less detailed physiological information. Therefore, there is a need for an approach able to produce reliable voxel-level results. A solution may be found in Bayesian approaches, which leverage a priori information to perform better in the presence of noisy data. Nevertheless, microparameter estimation in the model is based on the assumption of having a noise-free Input function. This typically requires arterial sampling, which can be uncomfortable and burdensome for the patient. An alternative is the Image-Derived Input Function (IDIF), which extracts the Input function directly from the PET image, using the Internal Carotid Arteries (ICA) or the Common Carotid Arteries (CCA), with corrections applied for Partial Volume Effect (PVE). This thesis focuses on exploring a Bayesian approach to enable adequate voxel-level microparameter estimation. Specifically, the Maximum a Posteriori (MAP) estimation method is employed. In our implementation, the prior information is derived from ROI-level estimates with the ultimate goal of obtaining precise voxel-level estimates. Additionally, the MAP estimation was tested with a constraint on a model parameter, k3, based on the voxel-wise Ki estimate obtained using Patlak's graphical analysis, to further reduce complexity. Furthermore, the impact of using different input functions extracted from different vascular ROIs was examined in this study. The analysis was performed on a dataset consisting of 10 subjects affected by glioma who underwent [18F]FDG acquisition on a PET/MR system at the University Hospital of Padova. To assess the reliability of the results obtained with the MAP, the parametric maps were compared to the ones obtained using another bayesian approach, i.e. the Variational Bayes (VB). Voxel-level esimates coming from the two different methods exhibit a high correlation. As for the input function, we observe that similar estimates are obtained when using ICA's IDIF with PVE correction or when using CCA's IDIF without any correction. This approach opens doors for future research in handling data fitting with respect to measurement error and examining the influence of constraints on the posterior calculation of the k3 parameter