On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

A new optimization approach to the design of one-dimensional and two-dimensional finite impulse response digital filters

The theory for designing finite impulse response (FIR) frequency sampling digital filters can be extended to two-dimensions. The linear phase frequency response can be represented as a linear combination of individual frequency responses corresponding to the filter\u27s bands. The design of two-dimensional frequency sampling filters (FSF) has been treated in the past by using the technique of linear programming to find the optimal values of the transition samples. Although in theory the method guarantees an optimal solution, convergence problems occurred; This paper will introduce some detail of a one-dimensional FSF design technique and then extend these concepts to the two-dimensional problem. The mean of the squared error in both the stopband and the passband is minimized subject to constraints on the filter\u27s stopband. The filter\u27s coefficients can be calculated by solving a linear system of equations

Lecture notes on the design of low-pass digital filters with wireless-communication applications

The low-pass filter is a fundamental building block from which digital signal-processing systems (e.g. radio and radar) are built. Signals in the electromagnetic spectrum extend over all timescales/frequencies and are used to transmit and receive very long or very short pulses of very narrow or very wide bandwidth. Time/Frequency agility is the key for optimal spectrum utilization (i.e. to suppress interference and enhance propagation) and low-pass filtering is the low-level digital mechanism for manoeuvre in this domain. By increasing and decreasing the bandwidth of a low-pass filter, thus decreasing and increasing its pulse duration, the engineer may shift energy concentration between frequency and time. Simple processes for engineering such components are described and explained below. These lecture notes are part of a short course that is intended to help recent engineering graduates design low-pass digital filters for this purpose, who have had some exposure to the topic during their studies, and who are now interested in the sending and receiving signals over the electromagnetic spectrum, in wireless communication (i.e. radio) and remote sensing (e.g. radar) applications, for instance. The best way to understand the material is to interact with the spectrum using receivers and or transmitters and software-defined radio development-kits provide a convenient platform for experimentation. Fortunately, wireless communication in the radio-frequency spectrum is an ideal application for the illustration of waveform agility in the electromagnetic spectrum. In Parts I and II, the theoretical foundations of digital low-pass filters are presented, i.e. signals-and-systems theory, then in Part III they are applied to the problem of radio communication and used to concentrate energy in time or frequency.Comment: Added Slepian ref. Added arXiv ID to heade

Efficient Fast-Convolution-Based Waveform Processing for 5G Physical Layer

This paper investigates the application of fast-convolution (FC) filtering schemes for flexible and effective waveform generation and processing in the fifth generation (5G) systems. FC-based filtering is presented as a generic multimode waveform processing engine while, following the progress of 5G new radio standardization in the Third-Generation Partnership Project, the main focus is on efficient generation and processing of subband-filtered cyclic prefix orthogonal frequency-division multiplexing (CP-OFDM) signals. First, a matrix model for analyzing FC filter processing responses is presented and used for designing optimized multiplexing of filtered groups of CP-OFDM physical resource blocks (PRBs) in a spectrally well-localized manner, i.e., with narrow guardbands. Subband filtering is able to suppress interference leakage between adjacent subbands, thus supporting independent waveform parametrization and different numerologies for different groups of PRBs, as well as asynchronous multiuser operation in uplink. These are central ingredients in the 5G waveform developments, particularly at sub-6-GHz bands. The FC filter optimization criterion is passband error vector magnitude minimization subject to a given subband band-limitation constraint. Optimized designs with different guardband widths, PRB group sizes, and essential design parameters are compared in terms of interference levels and implementation complexity. Finally, extensive coded 5G radio link simulation results are presented to compare the proposed approach with other subband-filtered CP-OFDM schemes and time-domain windowing methods, considering cases with different numerologies or asynchronous transmissions in adjacent subbands. Also the feasibility of using independent transmitter and receiver processing for CP-OFDM spectrum control is demonstrated

Techniques to Improve the Efficiency of Data Transmission in Cable Networks

The cable television (CATV) networks, since their introduction in the late 1940s, have now become a crucial part of the broadcasting industry. To keep up with growing demands from the subscribers, cable networks nowadays not only provide television programs but also deliver two-way interactive services such as telephone, high-speed Internet and social TV features. A new standard for CATV networks is released every five to six years to satisfy the growing demands from the mass market. From this perspective, this thesis is concerned with three main aspects for the continuing development of cable networks: (i) efficient implementations of backward-compatibility functions from the old standard, (ii) addressing and providing solutions for technically-challenging issues in the current standard and, (iii) looking for prospective features that can be implemented in the future standard. Since 1997, five different versions of the digital CATV standard had been released in North America. A new standard often contains major improvements over the previous one. The latest version of the standard, namely DOCSIS 3.1 (released in late 2013), is packed with state-of-the-art technologies and allows approximately ten times the amount of traffic as compared to the previous standard, DOCSIS 3.0 (released in 2008). Backward-compatibility is a must-have function for cable networks. In particular, to facilitate the system migration from older standards to a newer one, the backward compatible functions in the old standards must remain in the newer-standard products. More importantly, to keep the implementation cost low, the inherited backward compatible functions must be redesigned by taking advantage of the latest technology and algorithms. To improve the backward-compatibility functions, the first contribution of the thesis focuses on redesigning the pulse shaping filter by exploiting infinite impulse response (IIR) filter structures as an alternative to the conventional finite impulse response (FIR) structures. Comprehensive comparisons show that more economical filters with better performance can be obtained by the proposed design algorithm, which considers a hybrid parameterization of the filter's transfer function in combination with a constraint on the pole radius to be less than 1. The second contribution of the thesis is a new fractional timing estimation algorithm based on peak detection by log-domain interpolation. When compared with the commonly-used timing detection method, which is based on parabolic interpolation, the proposed algorithm yields more accurate estimation with a comparable implementation cost. The third contribution of the thesis is a technique to estimate the multipath channel for DOCSIS 3.1 cable networks. DOCSIS 3.1 is markedly different from prior generations of CATV networks in that OFDM/OFDMA is employed to create a spectrally-efficient signal. In order to effectively demodulate such a signal, it is necessary to employ a demodulation circuit which involves estimation and tracking of the multipath channel. The estimation and tracking must be highly accurate because extremely dense constellations such as 4096-QAM and possibly 16384-QAM can be used in DOCSIS 3.1. The conventional OFDM channel estimators available in the literature either do not perform satisfactorily or are not suitable for the DOCSIS 3.1 channel. The novel channel estimation technique proposed in this thesis iteratively searches for parameters of the channel paths. The proposed technique not only substantially enhances the channel estimation accuracy, but also can, at no cost, accurately identify the delay of each echo in the system. The echo delay information is valuable for proactive maintenance of the network. The fourth contribution of this thesis is a novel scheme that allows OFDM transmission without the use of a cyclic prefix (CP). The structure of OFDM in the current DOCSIS 3.1 does not achieve the maximum throughput if the channel has multipath components. The multipath channel causes inter-symbol-interference (ISI), which is commonly mitigated by employing CP. The CP acts as a guard interval that, while successfully protecting the signal from ISI, reduces the transmission throughput. The problem becomes more severe for downstream direction, where the throughput of the entire system is determined by the user with the worst channel. To solve the problem, this thesis proposes major alterations to the current DOCSIS 3.1 OFDM/OFDMA structure. The alterations involve using a pair of Nyquist filters at the transceivers and an efficient time-domain equalizer (TEQ) at the receiver to reduce ISI down to a negligible level without the need of CP. Simulation results demonstrate that, by incorporating the proposed alterations to the DOCSIS 3.1 down-link channel, the system can achieve the maximum throughput over a wide range of multipath channel conditions

Design of a digital FIR filter with minimum delay for BCI applications

The present thesis-work focuses on the BCI system implemented at the San Camillo Hospital (Venice) as a rehabilitative treatment. It is an alternative rehabilitative strategy, that applies an operant conditioning based on neuroplasticity to operate external devices. The aim of this thesis work is designing a digital FIR filter for this BCI application. Herein, the approach and criterion used are explained in detail, finally are exposed the outcomes and possible future strategies and approachesope

A novel parametrization of α-spline functions: application to digital filter design

α-spline functions, which are a generalization of conventional B-splines, are defined with several parameters which provide more flexibility in terms of the variety of shapes that the functions can adopt. Because of this feature, the α-spline spline functions have shown improvements in the performance of several applications, including the design of digital filters. This article proposes a novel parametrization to generate new families of α-spline functions that allows a more efficient control of the shape of these functions. Different combinations of parameters are presented, and a detailed analysis of the properties of the new functions is carried out. In addition, the new α-spline functions are applied to the design of digital filters, providing an appropriate design procedure. The characteristics of the new filters are analysed and compared with previous design techniques, demonstrating the remarkable superiority of their performance

Efficient Algorithms for Immersive Audio Rendering Enhancement

Il rendering audio immersivo è il processo di creazione di un’esperienza sonora coinvolgente e realistica nello spazio 3D. Nei sistemi audio immersivi, le funzioni di trasferimento relative alla testa (head-related transfer functions, HRTFs) vengono utilizzate per la sintesi binaurale in cuffia poiché esprimono il modo in cui gli esseri umani localizzano una sorgente sonora. Possono essere introdotti algoritmi di interpolazione delle HRTF per ridurre il numero di punti di misura e per creare un movimento del suono affidabile. La riproduzione binaurale può essere eseguita anche dagli altoparlanti. Tuttavia, il coinvolgimento di due o più gli altoparlanti causa il problema del crosstalk. In questo caso, algoritmi di cancellazione del crosstalk (CTC) sono necessari per eliminare i segnali di interferenza indesiderati. In questa tesi, partendo da un'analisi comparativa di metodi di misura delle HRTF, viene proposto un sistema di rendering binaurale basato sull'interpolazione delle HRTF per applicazioni in tempo reale. Il metodo proposto mostra buone prestazioni rispetto a una tecnica di riferimento. L'algoritmo di interpolazione è anche applicato al rendering audio immersivo tramite altoparlanti, aggiungendo un algoritmo di cancellazione del crosstalk fisso, che considera l'ascoltatore in una posizione fissa. Inoltre, un sistema di cancellazione crosstalk adattivo, che include il tracciamento della testa dell'ascoltatore, è analizzato e implementato in tempo reale. Il CTC adattivo implementa una struttura in sottobande e risultati sperimentali dimostrano che un maggiore numero di bande migliora le prestazioni in termini di errore totale e tasso di convergenza. Il sistema di riproduzione e le caratteristiche dell'ambiente di ascolto possono influenzare le prestazioni a causa della loro risposta in frequenza non ideale. L'equalizzazione viene utilizzata per livellare le varie parti dello spettro di frequenze che compongono un segnale audio al fine di ottenere le caratteristiche sonore desiderate. L'equalizzazione può essere manuale, come nel caso dell'equalizzazione grafica, dove il guadagno di ogni banda di frequenza può essere modificato dall'utente, o automatica, la curva di equalizzazione è calcolata automaticamente dopo la misurazione della risposta impulsiva della stanza. L'equalizzazione della risposta ambientale può essere applicata anche ai sistemi multicanale, che utilizzano due o più altoparlanti e la zona di equalizzazione può essere ampliata misurando le risposte impulsive in diversi punti della zona di ascolto. In questa tesi, GEQ efficienti e un sistema adattativo di equalizzazione d'ambiente. In particolare, sono proposti e approfonditi tre equalizzatori grafici a basso costo computazionale e a fase lineare e quasi lineare. Gli esperimenti confermano l'efficacia degli equalizzatori proposti in termini di accuratezza, complessità computazionale e latenza. Successivamente, una struttura adattativa in sottobande è introdotta per lo sviluppo di un sistema di equalizzazione d'ambiente multicanale. I risultati sperimentali verificano l'efficienza dell'approccio in sottobande rispetto al caso a banda singola. Infine, viene presentata una rete crossover a fase lineare per sistemi multicanale, mostrando ottimi risultati in termini di risposta in ampiezza, bande di transizione, risposta polare e risposta in fase. I sistemi di controllo attivo del rumore (ANC) possono essere progettati per ridurre gli effetti dell'inquinamento acustico e possono essere utilizzati contemporaneamente a un sistema audio immersivo. L'ANC funziona creando un'onda sonora in opposizione di fase rispetto all'onda sonora in arrivo. Il livello sonoro complessivo viene così ridotto grazie all'interferenza distruttiva. Infine, questa tesi presenta un sistema ANC utilizzato per la riduzione del rumore. L’approccio proposto implementa una stima online del percorso secondario e si basa su filtri adattativi in sottobande applicati alla stima del percorso primario che mirano a migliorare le prestazioni dell’intero sistema. La struttura proposta garantisce un tasso di convergenza migliore rispetto all'algoritmo di riferimento.Immersive audio rendering is the process of creating an engaging and realistic sound experience in 3D space. In immersive audio systems, the head-related transfer functions (HRTFs) are used for binaural synthesis over headphones since they express how humans localize a sound source. HRTF interpolation algorithms can be introduced for reducing the number of measurement points and creating a reliable sound movement. Binaural reproduction can be also performed by loudspeakers. However, the involvement of two or more loudspeakers causes the problem of crosstalk. In this case, crosstalk cancellation (CTC) algorithms are needed to delete unwanted interference signals. In this thesis, starting from a comparative analysis of HRTF measurement techniques, a binaural rendering system based on HRTF interpolation is proposed and evaluated for real-time applications. The proposed method shows good performance in comparison with a reference technique. The interpolation algorithm is also applied for immersive audio rendering over loudspeakers, by adding a fixed crosstalk cancellation algorithm, which assumes that the listener is in a fixed position. In addition, an adaptive crosstalk cancellation system, which includes the tracking of the listener's head, is analyzed and a real-time implementation is presented. The adaptive CTC implements a subband structure and experimental results prove that a higher number of bands improves the performance in terms of total error and convergence rate. The reproduction system and the characteristics of the listening room may affect the performance due to their non-ideal frequency response. Audio equalization is used to adjust the balance of different audio frequencies in order to achieve desired sound characteristics. The equalization can be manual, such as in the case of graphic equalization, where the gain of each frequency band can be modified by the user, or automatic, where the equalization curve is automatically calculated after the room impulse response measurement. The room response equalization can be also applied to multichannel systems, which employ two or more loudspeakers, and the equalization zone can be enlarged by measuring the impulse responses in different points of the listening zone. In this thesis, efficient graphic equalizers (GEQs), and an adaptive room response equalization system are presented. In particular, three low-complexity linear- and quasi-linear-phase graphic equalizers are proposed and deeply examined. Experiments confirm the effectiveness of the proposed GEQs in terms of accuracy, computational complexity, and latency. Successively, a subband adaptive structure is introduced for the development of a multichannel and multiple positions room response equalizer. Experimental results verify the effectiveness of the subband approach in comparison with the single-band case. Finally, a linear-phase crossover network is presented for multichannel systems, showing great results in terms of magnitude flatness, cutoff rates, polar diagram, and phase response. Active noise control (ANC) systems can be designed to reduce the effects of noise pollution and can be used simultaneously with an immersive audio system. The ANC works by creating a sound wave that has an opposite phase with respect to the sound wave of the unwanted noise. The additional sound wave creates destructive interference, which reduces the overall sound level. Finally, this thesis presents an ANC system used for noise reduction. The proposed approach implements an online secondary path estimation and is based on cross-update adaptive filters applied to the primary path estimation that aim at improving the performance of the whole system. The proposed structure allows for a better convergence rate in comparison with a reference algorithm