FIR filters for systems with input clock jitter

A method of designing fixed-coefficient FIR filters whose input signals are sampled irregularly due to clock jitter is presented. The approach does not require direct measuring of the jitter. Instead it is assumed that the jitter is a strictly stationary stochastic process for which some statistical information is available. Preliminary analysis of degradation of filter performance due to presence of jitter is also presented. Some numerical analyses illustrate the main assertions of the paper

Digital filtering of band-limited signals using Periodic Nonuniform Sampling

We examine the problem of digital filtering of band-limited signals by means of a linear digital filter with one or more stopbands. The main target of the study is to filter the signals using lower than Landau sampling rates, where the Landau rate is defined as the total bandwidth of the input signal. In order to reach such low rates Periodic Nonuniform Sampling is employed. We derive necessary and sufficient conditions for perfect filtering, and propose a practical algorithm for constructing PNS grids that allow for sub-Landau sampling and filtering. Finally, we present a reconstruction system and provide a numerical result illustrating the proposed method

Design of IIR Digital Filters with Arbitrary Flatness Using Iterative Quadratic Programming

This paper presents a design method of Chebyshev-type and inverse-Chebyshev-type infinite impulse response (IIR) filters with an approximately linear phase response. In the design of Chebyshev-type filters, the flatness condition in the stopband is preincorporated into a transfer function, and an equiripple characteristic in the passband is achieved by iteratively solving the QP problem using the transfer function. In the design of inverse-Chebyshev-type filters, the flatness condition in the passband is added to the constraint of the QP problem as the linear matrix equality, and an equiripple characteristic in the stopband is realized by iteratively solving the QP problem. To guarantee the stability of the obtained filters, we apply the extended positive realness to the QP problem. As a result, the proposed method can design the filters with more high precision than the conventional methods. The effectiveness of the proposed design method is illustrated with some examples

A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design

IEEE Transactions on Signal Processing43551-558ITPR

IIR Digital Filter Design Using Convex Optimization

Digital filters play an important role in digital signal processing and communication. From the 1960s, a considerable number of design algorithms have been proposed for finite-duration impulse response (FIR) digital filters and infinite-duration impulse response (IIR) digital filters. Compared with FIR digital filters, IIR digital filters have better approximation capabilities under the same specifications. Nevertheless, due to the presence of the denominator in its rational transfer function, an IIR filter design problem cannot be easily formulated as an equivalent convex optimization problem. Furthermore, for stability, all the poles of an IIR digital filter must be constrained within a stability domain, which, however, is generally nonconvex. Therefore, in practical designs, optimal solutions cannot be definitely attained. In this dissertation, we focus on IIR filter design problems under the weighted least-squares (WLS) and minimax criteria. Convex optimization will be utilized as the major mathematical tool to formulate and analyze such IIR filter design problems. Since the original IIR filter design problem is essentially nonconvex, some approximation and convex relaxation techniques have to be deployed to achieve convex formulations of such design problems. We first consider the stability issue. A sufficient and necessary stability condition is derived from the argument principle. Although the original stability condition is in a nonconvex form, it can be appropriately approximated by a quadratic constraint and readily combined with sequential WLS design procedures. Based on the sufficient and necessary stability condition, this approximate stability constraint can achieve an improved description of the nonconvex stability domain. We also address the nonconvexity issue of minimax design of IIR digital filters. Convex relaxation techniques are applied to obtain relaxed design problems, which are formulated, respectively, as second-order cone programming (SOCP) and semidefinite programming (SDP) problems. By solving these relaxed design problems, we can estimate lower bounds of minimum approximation errors, which are useful in subsequent design procedures to achieve real minimax solutions. Since the relaxed design problems are independent of local information, compared with many prevalent design methods which employ local search, the proposed design methods using the convex relaxation techniques have an increased chance to obtain an optimal design

Diseño de filtros digitales FIR mediante técnicas de computación evolutiva y estudio de su aplicación al procesado de señales biomédicas

El diseño de filtros digitales eficientes es una rama esencial del procesado de señales. Los filtros FIR son empleados en numerosas aplicaciones debido a su naturaleza de fase lineal y estabilidad frecuencial. Los métodos de diseño tradicionales sufren el problema del escaso control sobre la respuesta en frecuencia del filtro diseñado. Por esto, en este documento, se presenta una técnica de optimización novedosa, denominada Algoritmo de Polinización de Flores (FPA), junto con una novedosa función de aptitud múltiple, para la obtención del filtro FIR deseado. El algoritmo FPA se basa en el proceso de polinización de las flores. Dadas las especificaciones del filtro FIR, el algoritmo FPA obtiene un conjunto de coeficientes óptimos del filtro que mejor se aproxima a las especificaciones ideales. Los resultados obtenidos se han comparado con los métodos tradicionales de enventanado y algoritmo Parks-MacClellan (PM) y con otros métodos algorítmicos. Estos resultados numéricos muestran la superioridad del método de computación natural (FPA), junto con la función de aptitud múltiple en el diseño de filtros FIR paso bajo, paso alto, paso banda y elimina banda. Concretamente: Se consigue un mejor ajuste a las especificaciones del filtro deseado, una mayor atenuación de la banda eliminada y menor ancho de banda de transición a costa de aumentar ligeramente el rizado en la banda de paso.Grado en Ingeniería de Tecnologías Específicas de Telecomunicació

Intelligent Tools for Multitrack Frequency and Dynamics Processing

PhDThis research explores the possibility of reproducing mixing decisions of a skilled audio engineer with minimal human interaction that can improve the overall listening experience of musical mixtures, i.e., intelligent mixing. By producing a balanced mix automatically musician and mixing engineering can focus on their creativity while the productivity of music production is increased. We focus on the two essential aspects of such a system, frequency and dynamics. This thesis presents an intelligent strategy for multitrack frequency and dynamics processing that exploit the interdependence of input audio features, incorporates best practices in audio engineering, and driven by perceptual models and subjective criteria. The intelligent frequency processing research begins with a spectral characteristic analysis of commercial recordings, where we discover a consistent leaning towards a target equalization spectrum. A novel approach for automatically equalizing audio signals towards the observed target spectrum is then described and evaluated. We proceed to dynamics processing, and introduce an intelligent multitrack dynamic range compression algorithm, in which various audio features are proposed and validated to better describe the transient nature and spectral content of the signals. An experiment to investigate the human preference on dynamic processing is described to inform our choices of parameter automations. To provide a perceptual basis for the intelligent system, we evaluate existing perceptual models, and propose several masking metrics to quantify the masking behaviour within the multitrack mixture. Ultimately, we integrate previous research on auditory masking, frequency and dynamics processing, into one intelligent system of mix optimization that replicates the iterative process of human mixing. Within the system, we explore the relationship between equalization and dynamics processing, and propose a general frequency and dynamics processing framework. Various implementations of the intelligent system are explored and evaluated objectively and subjectively through listening experiments.China Scholarship Council

Efficient algorithms for arbitrary sample rate conversion with application to wave field synthesis

Arbitrary sample rate conversion (ASRC) is used in many fields of digital signal processing to alter the sampling rate of discrete-time signals by arbitrary, potentially time-varying ratios. This thesis investigates efficient algorithms for ASRC and proposes several improvements. First, closed-form descriptions for the modified Farrow structure and Lagrange interpolators are derived that are directly applicable to algorithm design and analysis. Second, efficient implementation structures for ASRC algorithms are investigated. Third, this thesis considers coefficient design methods that are optimal for a selectable error norm and optional design constraints. Finally, the performance of different algorithms is compared for several performance metrics. This enables the selection of ASRC algorithms that meet the requirements of an application with minimal complexity. Wave field synthesis (WFS), a high-quality spatial sound reproduction technique, is the main application considered in this work. For WFS, sophisticated ASRC algorithms improve the quality of moving sound sources. However, the improvements proposed in this thesis are not limited to WFS, but applicable to general-purpose ASRC problems.Verfahren zur unbeschränkten Abtastratenwandlung (arbitrary sample rate conversion,ASRC) ermöglichen die Änderung der Abtastrate zeitdiskreter Signale um beliebige, zeitvarianteVerhältnisse. ASRC wird in vielen Anwendungen digitaler Signalverarbeitung eingesetzt.In dieser Arbeit wird die Verwendung von ASRC-Verfahren in der Wellenfeldsynthese(WFS), einem Verfahren zur hochqualitativen, räumlich korrekten Audio-Wiedergabe, untersucht.Durch ASRC-Algorithmen kann die Wiedergabequalität bewegter Schallquellenin WFS deutlich verbessert werden. Durch die hohe Zahl der in einem WFS-Wiedergabesystembenötigten simultanen ASRC-Operationen ist eine direkte Anwendung hochwertigerAlgorithmen jedoch meist nicht möglich.Zur Lösung dieses Problems werden verschiedene Beiträge vorgestellt. Die Komplexitätder WFS-Signalverarbeitung wird durch eine geeignete Partitionierung der ASRC-Algorithmensignifikant reduziert, welche eine effiziente Wiederverwendung von Zwischenergebnissenermöglicht. Dies erlaubt den Einsatz hochqualitativer Algorithmen zur Abtastratenwandlungmit einer Komplexität, die mit der Anwendung einfacher konventioneller ASRCAlgorithmenvergleichbar ist. Dieses Partitionierungsschema stellt jedoch auch zusätzlicheAnforderungen an ASRC-Algorithmen und erfordert Abwägungen zwischen Performance-Maßen wie der algorithmischen Komplexität, Speicherbedarf oder -bandbreite.Zur Verbesserung von Algorithmen und Implementierungsstrukturen für ASRC werdenverschiedene Maßnahmen vorgeschlagen. Zum Einen werden geschlossene, analytischeBeschreibungen für den kontinuierlichen Frequenzgang verschiedener Klassen von ASRCStruktureneingeführt. Insbesondere für Lagrange-Interpolatoren, die modifizierte Farrow-Struktur sowie Kombinationen aus Überabtastung und zeitkontinuierlichen Resampling-Funktionen werden kompakte Darstellungen hergeleitet, die sowohl Aufschluss über dasVerhalten dieser Filter geben als auch eine direkte Verwendung in Design-Methoden ermöglichen.Einen zweiten Schwerpunkt bildet das Koeffizientendesign für diese Strukturen, insbesonderezum optimalen Entwurf bezüglich einer gewählten Fehlernorm und optionaler Entwurfsbedingungenund -restriktionen. Im Gegensatz zu bisherigen Ansätzen werden solcheoptimalen Entwurfsmethoden auch für mehrstufige ASRC-Strukturen, welche ganzzahligeÜberabtastung mit zeitkontinuierlichen Resampling-Funktionen verbinden, vorgestellt.Für diese Klasse von Strukturen wird eine Reihe angepasster Resampling-Funktionen vorgeschlagen,welche in Verbindung mit den entwickelten optimalen Entwurfsmethoden signifikanteQualitätssteigerungen ermöglichen.Die Vielzahl von ASRC-Strukturen sowie deren Design-Parameter bildet eine Hauptschwierigkeitbei der Auswahl eines für eine gegebene Anwendung geeigneten Verfahrens.Evaluation und Performance-Vergleiche bilden daher einen dritten Schwerpunkt. Dazu wirdzum Einen der Einfluss verschiedener Entwurfsparameter auf die erzielbare Qualität vonASRC-Algorithmen untersucht. Zum Anderen wird der benötigte Aufwand bezüglich verschiedenerPerformance-Metriken in Abhängigkeit von Design-Qualität dargestellt.Auf diese Weise sind die Ergebnisse dieser Arbeit nicht auf WFS beschränkt, sondernsind in einer Vielzahl von Anwendungen unbeschränkter Abtastratenwandlung nutzbar