Clock skew caused by variation is one of the most important problems in clock network synthesis today. Even if a clock network is designed to have zero skew, variation such as capacitive load and power supply will cause differences in arrival time of a clock signal. Non-tree clock network is considered to be an effective way to address the skew variation problem. Due to its inherent redundancy, clock mesh is very tolerant to variation. However, it costs much excessive amount of power compared to a clock tree. Link based non-tree clock network is an economic way to reduce clock skew caused by variation. Instead of using a dense mesh, only a number of links are inserted into a tree, so the power increase is small. Several existing works focus on the effect of cross link as well as the construction of such cross link structure. However, it is still not very clear where cross links should be inserted to achieve the most clock skew reduction with small wire resources. In this thesis, we propose a new method using linear program to solve this problem. In our approach, clock skew in a non-tree clock network is computed using an idea of load redistribution and non-tree decomposition. The delay information obtained is then used to select the node pairs for cross link insertion. Our methodology tries to insert cross links where skew can be reduced most effectively. Our method also considers tradeoff between cross link length and skew reduction effect. We compare our result with the most similar work on this problem [1] and a recent work [4] which inserts links between internal nodes of a tree. Experiments show that our method can reduce skew under variation effectively. We achieve 28% clock skew reduction with only 40% link resources. / Qian, Fuqiang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 51-55). / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Clock Distribution Network --- p.1 / Chapter 1.2 --- Our Contributions --- p.6 / Chapter 1.3 --- Organization of the Thesis --- p.8 / Chapter 2 --- Literature Review --- p.9 / Chapter 2.1 --- Exact Zero Skew --- p.9 / Chapter 2.2 --- DME Algorithm --- p.11 / Chapter 2.3 --- Combinatorial Algorithms for Fast Clock Mesh Optimization --- p.12 / Chapter 2.4 --- MeshWorks: An Efficient Framework for Planning, Synthesis and Optimization of Clock Mesh Networks --- p.14 / Chapter 2.5 --- Reducing Clock Skew variability via Cross Links --- p.16 / Chapter 2.6 --- Statistical Based Link Insertion for Robust Clock Network Design --- p.18 / Chapter 2.7 --- Variation Tolerant Buffered Clock Network Synthesis with Cross Links --- p.20 / Chapter 2.8 --- Cross Link Insertion for Improving Tolerance to Variations in Clock Network Synthesis --- p.22 / Chapter 3 --- Clock Network Construction with Cross Links --- p.24 / Chapter 3.1 --- Signal Delay and Clock Skew in Non-tree Clock Network --- p.24 / Chapter 3.1.1 --- Computing Delay in Non-tree Network --- p.25 / Chapter 3.1.2 --- Effect of a Cross Link on Clock Skew --- p.27 / Chapter 3.2 --- Link Insertion for Non-tree Clock Network --- p.28 / Chapter 3.2.1 --- Motivation of Computing Delay for Link Insertion --- p.29 / Chapter 3.2.2 --- Overall Flow for Cross Link Insertion --- p.30 / Chapter 3.2.3 --- Linear Program for Selecting Node Pairs --- p.31 / Chapter 3.2.4 --- Reducing the Number of Optimizations --- p.35 / Chapter 3.2.5 --- Experimental Results --- p.37 / Chapter 4 --- Buffered Clock Network with Cross Links --- p.41 / Chapter 4.1 --- Link Insertion in Buffered Clock Network --- p.41 / Chapter 4.1.1 --- Delay Calculation in Buffered Clock Network --- p.42 / Chapter 4.1.2 --- Linear Program Formulation for Buffered Clock Network --- p.43 / Chapter 4.2 --- Experimental Results and Comparison --- p.44 / Chapter 4.3 --- Possible Extensions --- p.46 / Chapter 4.3.1 --- Link Insertion at Internal Nodes --- p.46 / Chapter 4.3.2 --- Modeling Clock Buffer Delay Variation --- p.47 / Chapter 5 --- Conclusion --- p.49 / Bibliography --- p.51

In this analysis, I investigate the causes of early elections in four parliamentary democracies across the world: Great Britain, Australia, Japan, and New Zealand. While I consider a number of explanations for the decisions to hold early elections, I find most theoretical and statistical support for Smith's (2003; 2004) informational thesis. He maintains that governments look to future economic conditions when making their timing decision. This approach, however, also leaves open the possibility that other, non-economic factors can explain why prime ministers call elections earlier than is necessary. I argue that the degree of disproportionality, the measured gap between a party's vote share and seat share, is a key attribute to explain the early election decision. When prime ministers weigh their decision to dissolve government, they cannot assess the effect of changes in their support in the population as accurately when a high degree of disproportionality is present. Using survival analysis, I find some support for a comprehensive attributes and events approach. New Zealand proves an exception; governments tend to fail sooner when high levels of disproportionality are present. This appears to be a result of particular factors related to disproportionality as a political issue, leading to electoral reform in 1996.

Solitary bees in seasonal environments have to align their life-cycles with favorable environmental conditions and resources. Therefore, a proper timing of their seasonal activity is highly fitness relevant. Most species in temperate environments use temperature as a trigger for the timing of their seasonal activity. Hence, global warming can disrupt mutualistic interactions between solitary bees and plants if increasing temperatures differently change the timing of interaction partners. The objective of this dissertation was to investigate the mechanisms of timing in spring-emerging solitary bees as well as the resulting fitness consequences if temporal mismatches with their host plants should occur. In my experiments, I focused on spring-emerging solitary bees of the genus Osmia and thereby mainly on O. cornuta and O. bicornis (in one study which is presented in Chapter IV, I additionally investigated a third species: O. brevicornis). Chapter II presents a study in which I investigated different triggers solitary bees are using to time their emergence in spring. In a climate chamber experiment I investigated the relationship between overwintering temperature, body size, body weight and emergence date. In addition, I developed a simple mechanistic model that allowed me to unite my different observations in a consistent framework. In combination with the empirical data, the model strongly suggests that solitary bees follow a strategic approach and emerge at a date that is most profitable for their individual fitness expectations. I have shown that this date is on the one hand temperature dependent as warmer overwintering temperatures increase the weight loss of bees during hibernation, which then advances their optimal emergence date to an earlier time point (due to an earlier benefit from the emergence event). On the other hand I have also shown that the optimal emergence date depends on the individual body size (or body weight) as bees adjust their emergence date accordingly. My data show that it is not enough to solely investigate temperature effects on the timing of bee emergence, but that we should also consider individual body conditions of solitary bees to understand the timing of bee emergence. In Chapter III, I present a study in which I investigated how exactly temperature determines the emergence date of solitary bees. Therefore, I tested several variants degree-day models to relate temperature time series to emergence data. The basic functioning of such degree-day models is that bees are said to finally emerge when a critical amount of degree-days is accumulated. I showed that bees accumulate degree-days only above a critical temperature value (~4°C in O. cornuta and ~7°C in O. bicornis) and only after the exceedance of a critical calendar date (~10th of March in O. cornuta and ~28th of March in O. bicornis). Such a critical calendar date, before which degree-days are not accumulated irrespective of the actual temperature, is in general less commonly used and, so far, it has only been included twice in a phenology model predicting bee emergence. Furthermore, I used this model to retrospectively predict the emergence dates of bees by applying the model to long-term temperature data which have been recorded by the regional climate station in Würzburg. By doing so, the model estimated that over the last 63 years, bees emerged approximately 4 days earlier. In Chapter IV, I present a study in which I investigated how temporal mismatches in bee-plant interactions affect the fitness of solitary bees. Therefore, I performed an experiment with large flight cages serving as mesocosms. Inside these mesocosms, I manipulated the supply of blossoms to synchronize or desynchronize bee-plant interactions. In sum, I showed that even short temporal mismatches of three and six days in bee-plant interactions (with solitary bee emergence before flower occurrence) can cause severe fitness losses in solitary bees. Nonetheless, I detected different strategies by solitary bees to counteract impacts on their fitness after temporal mismatches. However, since these strategies may result in secondary fitness costs by a changed sex ratio or increased parasitism, I concluded that compensation strategies do not fully mitigate fitness losses of bees after short temporal mismatches with their food plants. In the event of further climate warming, fitness losses after temporal mismatches may not only exacerbate bee declines but may also reduce pollination services for later-flowering species and affect populations of animal-pollinated plants. In conclusion, I showed that spring-emerging solitary bees are susceptible to climate change as in response to warmer temperatures bees advance their phenology and show a decreased fitness state. As spring-emerging solitary bees not only consider overwintering temperature but also their individual body condition for adjusting emergence dates, this may explain differing responses to climate warming within and among bee populations which may also have consequences for bee-plant interactions and the persistence of bee populations under further climate warming. If in response to climate warming plants do not shift their phenologies according to the bees, bees may experience temporal mismatches with their host plants. As bees failed to show a single compensation strategy that was entirely successful in mitigating fitness consequences after temporal mismatches with their food plants, the resulting fitness consequences for spring-emerging solitary bees would be severe. Furthermore, I showed that spring-emerging solitary bees use a critical calendar date before which they generally do not commence the summation of degree-days irrespective of the actual temperature. I therefore suggest that further studies should also include the parameter of a critical calendar date into degree-day model predictions to increase the accuracy of model predictions for emergence dates in solitary bees. Although our retrospective prediction about the advance in bee emergence corresponds to the results of several studies on phenological trends of different plant species, we suggest that more research has to be done to assess the impacts of climate warming on the synchronization in bee-plant interactions more accurately. / Solitäre Bienen aus gemäßigten Breiten müssen ihre Lebenszyklen vorteilhaften Umweltbedingungen und –ressourcen angleichen. Deshalb ist ein gutes Timing ihrer saisonalen Tätigkeit von höchster Relevanz. Die meisten Arten aus gemäßigten Breiten nutzen Temperatur als Trigger um ihre saisonale Aktivität zeitlich abzustimmen. Aus diesem Grund kann der Klimawandel die mutualistischen Interaktionen zwischen Bienen- und Pflanzenarten stören, falls steigende Temperaturen das Timing der Interaktionspartner unterschiedlich verändern. Das Ziel dieser Doktorarbeit war es, die Timing-Mechanismen von Frühlingsbienenarten zu untersuchen, sowie die resultierenden Fitnessfolgen, falls zeitliche Fehlabstimmungen zu ihren Wirtspflanzen eintreten sollten. In meinen Experimenten konzentrierte ich mich auf Frühlingsbienenarten der Gattung Osmia (Mauerbienen) und dabei vor allem auf zwei spezielle Arten, nämlich O. cornuta und O. bicornis (in meiner Studie, die ich im Kapitel IV meiner Doktorarbeit präsentiere, untersuchte ich zusätzlich noch eine dritte Bienenart: O. brevicornis). Kapitel II präsentiert eine Studie, in der ich verschiedene Trigger untersuchte, die solitäre Bienen nutzen um ihren Schlupfzeitpunkt im Frühjahr festzulegen. Dazu untersuchte ich in einem Klimakammerexperiment den Zusammenhang zwischen Überwinterungstemperaturen, Körpergröße, Körpergewicht und Schlupftag. Zusätzlich entwickelte ich ein einfaches mechanistisches Modell, welches mir ermöglichte, meine verschiedenen Ergebnisse in einem einheitlichen Rahmen zusammenzufügen. In Kombination mit den empirischen Daten deutet das Modell stark darauf hin, dass Bienen einen strategischen Ansatz verfolgen und genau an dem Tag schlüpfen, der für ihre individuelle Fitnesserwartung am sinnvollsten ist. Ich konnte zeigen, dass dieser gewählte Schlupftag einerseits temperaturabhängig ist, da wärmere Temperaturen den Gewichtverlust der Bienen während der Überwinterung steigern, was wiederum den optimalen Schlupftag auf einem früheren Zeitpunkt verschiebt, andererseits konnte ich ebenfalls zeigen, dass der optimale Schlupfzeitpunkt von der individuellen Körpergröße bzw. dem Körpergewicht der Biene abhängt, da diese ihren Schlupftag danach abstimmen. Meine Daten zeigen, dass es nicht reicht alleinig Temperatureffekte auf das Timing der solitären Bienen zu untersuchen, sondern dass wir ebenfalls die Körperkonditionen der Bienen beachten sollten, um die zeitliche Abstimmung des Bienenschlupfes besser verstehen zu können. In Kapitel III präsentiere ich eine Studie, in der ich den Temperatureinfluss auf den Schlupftermin solitärer Bienen detailreicher untersuchte. Dazu habe ich verschiedene Varianten von Temperatursummen-Modellen getestet, um Temperaturzeitreihen auf Schlupftermine zu beziehen. Die grundlegende Funktionsweise solcher Temperatursummen-Modelle ist, dass der Bienenschlupf auf den Tag prognostiziert wird an dem die Bienen eine bestimmte Menge an Temperatursummen aufsummiert haben. Ich konnte zeigen, dass Bienen Temperatursummen erst ab bestimmten Temperaturen bilden (ab circa 4°C bei O. cornuta und circa 7°C bei O. bicornis) und erst nach Erreichen eines bestimmten Kalendertages (circa 10.März bei O. cornuta und circa 28.März bei O. bicornis). Solch ein bestimmter Kalendertag, vor dessen Erreichen und unabhängig von der aktuellen Temperatur keine Temperatursummen gebildet werden, wird grundsätzlich recht selten verwendet und in Phänologie-Modellen zur Vorhersage des Bienenschlupfes, bis heute auch nur zwei Mal. Zusätzlich benutzte ich mein Modell, um rückwirkend den Bienenschlupf über die letzten Jahrzehnte vorherzusagen. Dazu wandte ich das Modell auf Langzeit-Temperaturdaten an, die von der regionalen Wetterstation in Würzburg aufgezeichnet wurden. Das Modell prognostizierte rückwirkend, dass im Verlauf der letzten 63 Jahre die Bienen ungefähr 4 Tage früher schlüpfen. In Kapitel IV präsentiere ich eine Studie, in der ich untersuchte, inwieweit zeitliche Fehlabstimmungen in Bienen-Pflanzen-Interaktionen die Fitness der solitären Bienen beeinflussen. Dazu führte ich ein Experiment mit großen Flugkäfigen durch, die als Mesokosmos dienten. Innerhalb jedes dieser Mesokosmen manipulierte ich das Angebot an Blüten um Bienen-Pflanzen-Interaktionen wahlweise zu synchronisieren oder zu desynchronisieren. Zusammengefasst konnte ich dabei aufzeigen, dass sogar kurze zeitliche Fehlabstimmungen von drei oder sechs Tagen bereits genügen (Bienen schlüpften zeitlich vor dem Erscheinen der Pflanzen) um bei den Bienen fatale Fitnessfolgen zu verursachen. Nichtsdestotrotz konnte ich bei den Bienen verschiedene Strategien erkennen, mit denen sie Auswirkungen auf ihre Fitness nach zeitlichen Fehlabstimmungen entgegenwirken wollten. Allerdings könnten diese Strategien zu sekundären Fitnessverlusten folgen da sie zu einem veränderten Geschlechterverhältnis oder einem stärkeren Prasitierungsgrad führen. Deshalb konnte ich zusammenfassend feststellen, dass nach zeitlichen Fehlabstimmungen zu den entsprechenden Wirtspflanzen, die Kompensationsstrategien der Bienen nicht ausreichen, um Fitnessverlusste zu minimieren. Im Falle des weiter voranschreitenden Klimawandel könnten die Fitnessverluste der Bienen nicht nur das momentane Bienensterben weiter verschärfen, sondern auch ihren Bestäubungsdienst an später blühenden Arten minimieren und dadurch Populationen von tierbestäubten Pflanzen beeinträchtigen. Zusammenfassend konnte ich zeigen, dass Frühlingsbienenarten anfällig für Klimawandel sind, da sie nach warmen Überwinterungstemperaturen früher schlüpfen und einen geringeren Fitnesszustand aufweisen. Da Frühlingsbienenarten bei der zeitlichen Abstimmung ihres Schlupftages nicht nur Überwinterungstemperaturen, sondern auch ihren individuellen Fitnesszustand beachten, könnte dies unterschiedliche Reaktionen innerhalb oder zwischen Bienenpopulationen auf den Klimawandel erklären. Dies könnte ebenfalls Folgen für Bienen-Pflanzen Interaktionen haben und das weitere Bestehen von Bienenpopulationen gefährden. Falls, durch den Klimawandel bedingt, Pflanzenarten ihre Phänologie nicht in Einklang mit der Phänologie der Bienen verschieben, dann könnten Bienen zeitliche Fehlabstimmungen mit ihren Wirtspflanzen erleben. Da Bienen keine einzige Kompensationsmaßnahme aufzeigen, die erfolgreich Fitnessverlusten entgegenwirken konnte, wären in einem solchen Fall die Folgen für Frühlingsbienenarten fatal. Darüber hinaus konnte ich feststellen, dass Frühlingsbienen einen bestimmten Starttag im Jahr beachten, vor dessen Erreichen sie keine Temperatursummen bilden, unabhängig von der aktuellen Temperatur. Ich schlage deshalb vor, dass weitere Studien ebenfalls einen solchen Starttag in Temperatursummen-Modelle einbauen sollten, um die Genauigkeit zur Berechnung des Bienenschlupfes weiter zu verbessern. Obwohl meine retrospektive Vorhersage zum verfrühten Bienenschlupf ziemlich genau den Ergebnissen von verschiedenen Studien zu den phänologischen Verschiebungen von Pflanzenarten entspricht, schlagen wir vor, dass zusätzliche Untersuchungen konzipiert werden müssen um präzisere Aussagen über die Folgen des Klimawandels auf die Synchronisation der Bienen-Pflanzen-Interaktionen liefern zu können.

This paper examines the time lag between the peak in the arrival rate and the peaks in the mean and variance for the number of customers in an M(t)/M(t)/1l system. We establish a necessary condition for the time at which the peak in the mean is achieved. In cases in which system utilization exceeds one during some period, we show that the peak in the mean occurs after the end of this period. / Revised October 1994

The recent pollution norms have brought a strong emphasis on the reduction of diesel engine emissions. Low temperature combustion technology such as premixed compression ignition (PCI) has the capability to significantly and simultaneously reduce nitric oxides (NOx) and particulate matter (PM), thus meeting these specific pollution norms. There has been, however, observed loss in fuel conversion efficiency in some cases. This study analyzes how energy transfer and brake fuel conversion efficiency alter with (or are affected by) injection timings and exhaust gas recirculation (EGR) rate. The study is conducted for PCI combustion for four injection timings of 9°, 12°, 15° and 18° before top dead center (BTDC) and for four exhaust gas recirculation (EGR) rates of 39%, 40%, 41% and 42%. The data is collected from the experimental apparatus located in General Motors Collaborative Research Laboratory at the University of Michigan. The heat release is calculated to obtain various in-cylinder energy transfers. The brake fuel conversion efficiency decreases with an increase in EGR. The decrease in the brake fuel conversion efficiency is due to the decrease in work output. This decrease is due to an increase in the pumping work and an increase in friction and decrease in gross indicated work. The decrease in the combustion efficiency is because of the increased formation of unburnt products due to increased ignition delay caused by the application of EGR and decreasing air-fuel (A/F) ratio. A definite trend is not obtained for the contribution of heat transfer to the total energy distribution. However the total heat transfer decreases with retardation of injection timing because of decreasing combustion temperature. As the injection timing is retarded, the brake fuel conversion efficiency is found to decrease. This decrease is because of a decrease in net work output. This is because the time available for utilization of the energy released is less because of late combustion. The total heat transfer decreases with retardation of injection timing because of decreasing combustion temperature. The contribution of heat transfer to the total energy distribution decreases with increase in EGR.

Digital resampling is a process that converts a digital signal from one sampling rate to another. This process is performed by means of interpolating between the input samples to produce output samples at an output sampling rate. The digital interpolation process is accomplished with an interpolation filter.<p> The problem of resampling digital signals at an output sampling rate that is incommensurate with the input sampling rate is the first topic of this thesis. This problem is often encountered in practice, for example in multiplexing video signals from different sources for the purpose of distribution. There are basically two approaches to resample the signals. Both approaches are thoroughly described and practical circuits for hardware implementation are provided. A comparison of the two circuits shows that one circuit requires a division to compute the new sampling times. This time scaling operation adds complexity to the implementation with no performance advantage over the other circuit, and makes the 'division free' circuit the preferred one for resampling.<p> The second topic of this thesis is performance analysis of interpolation filters for Quadrature Amplitude Modulation (QAM) signals in the context of timing recovery. The performance criterion of interest is Modulation Error Ratio (MER), which is considered to be a very useful indicator of the quality of modulated signals in QAM systems. The methodology of digital resampling in hardware is employed to describe timing recovery circuits and propose an approach to evaluate the performance of interpolation filters. A MER performance analysis circuit is then devised. The circuit is simulated with MATLAB/Simulink as well as implemented in Field Programmable Gate Array (FPGA). Excellent agreement between results obtained from simulation and hardware implementation proves the validity of the methodology and practical application of the research works.

This study develops an optimization methodology for signal timing at intersections to reduce emissions based on MOVES, the latest emission model released by U.S. Environmental Protection Agency (EPA). The primary objective of this study is to bridge the gap that the research on signal optimization at intersections lags behind the development of emissions models. The methodology development includes four levels: the vehicle level, the movement level, the intersection level, and the arterial level. At the vehicle level, the emission function with respect to delay is derived for a vehicle driving through an intersection. Multiple acceleration models are evaluated, and the best one is selected in terms of emission estimations at an intersection. Piecewise functions are used to describe the relationship between emissions and intersection delay. At the movement level, emissions are modeled if the green time and red time of a movement are given. To account for randomness, the number of vehicle arrivals during a cycle is assumed to follow Poisson distributions. According to the numerical results, the relative difference of emission estimations with and without considering randomness is usually smaller than 5.0% at a typical intersection of two urban arterials. At the intersection level, an optimization problem is formulated to consider emissions at an intersection. The objective function is a linear combination of delay and emissions at an intersection, so that the tradeoff between the two could be examined with the optimization problem. In addition, a convex approximation is proposed to approximate the emission calculation; accordingly, the optimization problem can be solved more efficiently using the interior point algorithm (IPA). The case study proves that the optimization problem with this convex approximation can still find appropriate optimal signal timing plans when considering traffic emissions. At the arterial level, emissions are minimized at multiple intersections along an arterial. First, discrete models are developed to describe the bandwidth, stops, delay, and emissions at a particular intersection. Second, based on these discrete models, an optimization problem is formulated with the intersection offsets as decision variables. The simulation results indicate that the benefit of emission reduction become more and more significant as the number of intersections along the arterial increases.

Enligt Market timing-teorin styr marknadens värdering av företag huruvida nya investeringar finansieras med lån eller med nytt eget kapital. Syftet med denna uppsats är att undersöka om teorin kan förklara svenska företags val av finansiering och således företagens kapitalstruktur. För att uppfylla syftet med uppsatsen har företagsdata insamlats kvartalsvis. Vidare har en regression genomförts mellan de beroende variablerna "Bokförd skuldsättningsgrad" och "Marknadsmässig skuldsättningsgrad" med diverse oberoende variabler för att analysera ifall Market timing-teorin stämmer överens med svenska företag. Av de oberoende variablerna anses marknadsvärdet dividerat med bokfört värde (M/B) bäst förklara Market timing-teorins korrekthet. Regressioner har även genomförts med både samtida oberoende variabler och tidslaggade oberoende variabler för att se ifall Market timing-teorin skiljer sig åt med tiden. Slutsatsen av undersökningen är att Market timing-teorin stämmer överens i förhållande till den marknadsmässiga skuldsättningsgraden vilken vi anser bäst överensstämmer med innehållet i Market timing-teorin. Vi har alltså statistiskt säkerställt att svenska företags kapitalstruktur påverkas av marknadens värdering av företagen och därigenom fastställt att market timing påverkar svenska företags kapitalstruktur.

Examensarbete 15 hp. Musiklärarexamen

Digital resampling is a process that converts a digital signal from one sampling rate to another. This process is performed by means of interpolating between the input samples to produce output samples at an output sampling rate. The digital interpolation process is accomplished with an interpolation filter.<p> The problem of resampling digital signals at an output sampling rate that is incommensurate with the input sampling rate is the first topic of this thesis. This problem is often encountered in practice, for example in multiplexing video signals from different sources for the purpose of distribution. There are basically two approaches to resample the signals. Both approaches are thoroughly described and practical circuits for hardware implementation are provided. A comparison of the two circuits shows that one circuit requires a division to compute the new sampling times. This time scaling operation adds complexity to the implementation with no performance advantage over the other circuit, and makes the 'division free' circuit the preferred one for resampling.<p> The second topic of this thesis is performance analysis of interpolation filters for Quadrature Amplitude Modulation (QAM) signals in the context of timing recovery. The performance criterion of interest is Modulation Error Ratio (MER), which is considered to be a very useful indicator of the quality of modulated signals in QAM systems. The methodology of digital resampling in hardware is employed to describe timing recovery circuits and propose an approach to evaluate the performance of interpolation filters. A MER performance analysis circuit is then devised. The circuit is simulated with MATLAB/Simulink as well as implemented in Field Programmable Gate Array (FPGA). Excellent agreement between results obtained from simulation and hardware implementation proves the validity of the methodology and practical application of the research works.