Harmonic Analysis

Abstract: This chapter investigates the issue of the role of the computer,in musical analysis. Starting with a survey of the main approaches in computer analysis, we focus on the particular problem of Jazz chord sequences harmonic analysis. We propose a theory of chord sequence analysis, based on an explicit conceptual hierarchy of analysis objects. We discuss the implementation,of the theory

By means of an artificial neural network (ANN) model, higher measurement accuracy of integer harmonics can be obtained. Combining the windowed fast Fourier transform (FFT) algorithm with the improved ANN model, we present a new precise algorithm for non-integer harmonics analysis. According to the result obtained from the Hanning-windowed FFT algorithm, we choose the initial values of orders of harmonics for the neural network. Through such processing, the time of iterations is shortened and the convergence rate of neural network is raised thereby. The simulation results show that close non-integer harmonics can be separated from a signal with higher accuracy and better real-time by using the algorithm presented in the paper. Key w o r d s : fast Fourier transform (FFT)r artificial neural network (ANN) ; Hanniug-window; harmonics analysis

The regional and interanual variability of daily extreme temperature frequencies in Argentina from 1959 to 1998 was analysed. Maximum and minimum daily temperature series from more than 60 weather stations of all the country were used for this purpose. A quality control of the data was previously done. The results pointed out an important diminution of cold minimum temperature frequencies

In this paper is analyzing the current operating conditions of one electric arc furnace (EAF) in order to evaluate the best option to solve the energy consumption problem. Experimental results show that EAFs represent a substantial source of electric disturbances, such as voltage fluctuations, flicker, harmonics, and unbalance between phases. Improvement of the energetic performances of an EAF imposes a careful technical and economical analysis. The possible compensation solutions include passive filter, SVC (static var compensator) and STATCOM (static synchronous compensator).Finally, the guideline for compensator selection and performance estimation is obtained.

We present an analytical solution for the magnetic field, induced eddy currents, and the corresponding losses generated in the rotor of a slotless permanent-magnet (PM) motor. The field excitation is a current sheet placed at the stator interior surface. The solution is based on an analytical solution of the diffusion equation using double Fourier series and in the complex domain. The first and the second Fourier series correspond to the time and space harmonics, respectively. We have analyzed the effect of each time harmonic in detail, and verified the results with FEM software.

Magnetic field distributions from flat conductor electromagnetic surface acoustic wave transducers have been investigated for meander and grating line geometries. Expressions are derived for magnetic fields and inductance of electromagnetic transducers, and for space harmonic amplitudes of surface currents induced in a metal ground plane. Lift off, that is, separation gap between conductors and ground plane, and transducer geometry are accounted for in the theory. Experimental measurements of inductance are presented and compared with predicted inductance values, and good agreement is found.

The dynamic characteristics of an edge-emitting laser under large-signal modulation are analyzed in the frequency domain using a harmonic balance method on device level. The simulations reveal the nonlinearities of the carrier dynamics in the quantum well region which strongly influence the optical power in the higher harmonics.

This paper presents a new method to measure motor speed by means of frequency estimation of rotor slot spectral components in the supply current of squirrel single-cage induction motors. The novelty of the method consists in the harmonic analysis of the supply current by means of the chirp-Z transform (CZT). The advantages are improved accuracy due to better spectral resolution and resolvability. Moreover, a shorter observation window is required, thus reducing errors related to nonstationary current signals. The experimental results are presented to validate the proposed method and to make a comparison with a similar method based on the fast Fourier transform (FFT).

The rapid increase in the size of databases required to store power quality monitoring data has demanded new techniques for analysing and understanding the data. One suggested technique to assist in analysis is data mining. Data mining is a process that uses a variety of data analysis tools to identify hidden patterns and relationships within large samples of data. This paper presents several data mining tools and techniques that are applicable to power quality data analysis to enable efficient reporting of disturbance indices and identify network problems through pattern recognition. This paper also presents results of data mining techniques applied to power quality data from an MV electrical distribution system to identify disturbance patterns.

By means of the model results, important harmonic constants of the tidal heights and currents, as well as the form factor, were computed. These results have revealed that there is a phase delay and an increase in amplitude of the major constituents as the tide ...

This paper proposes an analytical procedure for computation of all pairs of valid switching angles used in pattern generation in five-level H-bridge cascaded inverters. The proposed procedure eliminates harmonic components from inverter output voltage and, for each harmonic, returns the exact boundaries of all valid modulation index intervals. Due to its simple mathematical formulation, it can be easily implemented in real time using a digital signal processor or a field-programmable gate array. In this paper, after a detailed description of the method, simulation and experimental results demonstrate the high quality of achievable results. Since 1997, she has been a Researcher in numerical analysis with the University of L'Aquila. Her research interests deal with analytical and numerical methods for control and management of power converters, function approximation techniques, and modulation algorithms for multilevel converters.

Present day power systems invariably have nonlinear loads, which inject harmonics into the system and give rise to nonsinusoidal voltages and currents. Power quality issues are a prime concern of the power industries as well as of customers. Thus under these conditions, it becomes imperative to study these nonlinear loads; their characteristics and effects. Accordingly, the harmonic analyses have become a regularly used tool in predicting the effects of harmonic producing loads on power systems. State of power system can be obtained in respect to the results of these analyses. The accuracy of these results depends on the modeling of harmonic producing loads. There are a large number of harmonic analysis methods that are in widespread use. In these analyses, the harmonic producing loads are widely modeled by various techniques namely; Constant Current Sources, Norton and Crossed Frequency Admittance Matrix.

A new dynamic harmonic estimator is presented as an extension of the fast Fourier transform (FFT), which assumes a fluctuating complex envelope at each harmonic. This estimator is able to estimate harmonics that are time varying inside the obser- vation window. The extension receives the name "Taylor-Fourier transform (TFT)" since it is based on the McLaurin series expan- sion of

This paper presents the design and analysis of a parallel connected inverter configuration of. The configuration consists of parallel connected three-phase dc/ac inverter. Series resistors added to the inverter output to maintain same current in each inverter of the two parallel inverters, and to reduce the circulating current in the parallel inverters to the minimum. High frequency third harmonic injection PWM (THIPWM) employed to reduce the total harmonic distortion and to make maximum use of the voltage source. DSP was used to generate the THIPWM and the control algorithm for the converter. Selected experimental results have been shown to validate the proposed system.

According to growth of electricity demand and the increased number of non-linear loads in power grids, providing a high quality electrical power should be considered. In this paper, voltage sag and swell of the power quality issues are studied and distributed power flow controller (DPFC) is used to mitigate the voltage deviation and improve power quality. The DPFC is a new FACTS device, which its structure is similar to unified power flow controller (UPFC). In spite of UPFC, in DPFC the common dc-link between the shunt and series converters is eliminated and three-phase series converter is divided to several single-phase series distributed converters through the line. The case study contains a DPFC sited in a single-machine infinite bus power system including two parallel transmission lines, which simulated in MATLAB/Simulink environment. The presented simulation results validate the DPFC ability to improve the power quality.

Within the past decade, music-theoretical analysis of popular music has become increasingly common. Nonetheless, until quite recently the purview of such research has been relatively limited, focusing mainly on classic and art rock from the 1960s and 70s. While these repertoires have provided fertile ground for analytical exploration, several more recent genres and styles raise interesting structural, semiotic, and aesthetic questions that also merit study. One of the most distinctive types of contemporary popular music is electronic dance music, a broad category that includes styles such as techno, house, drum-n-bass, and trance. Electronic dance music differs from both rock and art music in a number of ways, all of which suggest avenues for productive theoretical investigation. While many genres of popular music are distinguished from each other on the basis of "surface" differences such as instrumentation or lyrical content, electronic dance music presents a distinctive overall formal structure in addition to its characteristic instrumentation. It also differs from most other types of Western music in its rejection of harmony as a primary musical parameter. Its use of pitch is typically restricted, with the majority of musical development taking place instead in the realms of rhythm, meter, texture, and timbre. Consequently, these areas should be principal concerns for the analyst wishing to pursue a close examination of musical sound in this repertoire. Rhythm provides an ideal starting point, as it seems to be the element to which listeners and fans of EDM relate most directly. This connection is most immediately apparent on the dance floor, where audiences physically enact the rhythms of the music. Written discussions of electronic dance music also tend to highlight its rhythmic qualities-references to its "unrelenting rhythm," "pulsing dance rhythms," and "irresistible tribal rhythm" are common (and fans often refer to the music simply as "beats" (as in, "let's go to the club and hear some beats"). Yet EDM poses a challenge to the analyst, for it differs in many ways from the repertoires that current music-theoretical models of rhythm and meter were developed to address. Transcription can give the impression that it is less complex rhythmically than these other bodies of music: although it typically consists of many different textural layers, each of which has a different rhythmic pattern, these patterns can appear quite simple when considered individually, and they repeat for long periods of time without changing. The

T I. INTRODUCTION HIS paper deals with some mathematical aspects of the discrete Fourier transform (DFT), studied with linear algebra and matrix theory methods. The vast majority of papers on the DFT have concerned computational issues, most notably the extensive literature ...

Regional and interannual variations of the rainy season over Indonesia are investigated using daily rainfall data during 1961-90. Pentad-mean rainfall data, with a relatively better continuity have been obtained for 46 stations, and the annual and semi-annual cycles of rainfall at these stations have been objectively analyzed by harmonic analysis. The onset of southern-hemispheric spring/summer (SON/ DJF) rainy season starts from the Indian Ocean side of Jawa in the middle September, and propagates northward (in Jawa) and eastward (to Nusa Tenggara in middle December). Another route of rainy sea-

For a three-phase buck-type pulsewidth modulation rectifier input stage of a high-power telecommunications power supply module, a differential-mode (DM) electromagnetic compatibility (EMC) filter is designed for compliance to CISPR 22 Class B in the frequency range of 150 kHz-30 MHz. The design is based on a harmonic analysis of the rectifier input current and a mathematical model of the measurement procedure including the line impedance stabilization network (LISN) and the test receiver. Guidelines for a successful filter design are given, and components for a 5-kW rectifier prototype are selected. Furthermore, formulas for the estimation of the quasi-peak detector output based on the LISN output voltage spectrum are provided. The damping of filter resonances is optimized for a given attenuation in order to facilitate a higher stability margin for system control. Furthermore, the dependence of the filter input and output impedances and the attenuation characteristic on the inner mains impedance are discussed. As experimentally verified by using a three-phase common-/Differential-Mode separator, this procedure allows accurate prediction of the converter DM conducted emission levels and therefore could be employed in the design process of the rectifier system to ensure compliance to relevant EMC standards.

—The aim of this paper is to establish the boundedness of certain sublinear operators with rough kernel generated by Calder´on–Zygmund operators and their commutators on generalized Morrey spaces under generic size conditions which are satisfied by most of the operators in harmonic analysis. The Marcinkiewicz operator which satisfies the conditions of these theorems can be considered as an example.

In this paper, the transient overvoltage suppression capability and harmonic filtering performance of C-type 2nd harmonic filters (HFs) are optimized by using two-stage damping resistors; one is permanently connected to the filter circuit, while the other one is switched on by back-to-back connected thyristors during furnace transformer and HF energization periods. However, in conventional C-type 2nd HFs, there is only one damping resistor, which is permanently connected to the filter circuit. In conventional designs, either the filtering performance is maximized or transient overvoltage suppression capability is enhanced or a compromise is made between these two objectives. This new configuration of C-type 2nd HFs has been applied to a sample iron and steel plant in which two ladle refining furnaces are in operation. For this purpose, an static var compensation system has been designed and installed, which is composed of a thyristor-controlled reactor, a 3rd HF, and the new C-type 2nd HF configuration proposed in this paper. The results of field tests and simulation studies show that the proposed C-type 2nd HF configuration gives much better results than conventional designs. Index Terms-C-type harmonic filter (HF), electric arc furnace (EAF), harmonics, interharmonics, ladle furnace, static var compensator (SVC). E LECTRIC arc furnaces (EAFs) and ladle refining fur- naces (LFs) in iron and steel plants are operated together with static var compensation systems. Static var compensators (SVCs) are mostly composed of thyristor-controlled reactors (TCRs) and passive shunt harmonic filters (HFs). These SVC Manuscript

This paper aims to develop a system for estimating a vehicle's speed by analyzing its drive by acoustics with a passive audio microphone. Analysis of the vehicle"s acoustics would primarily use the phenomenon of Doppler shift, and the instant at which vehicle is at closest-point-of approach. This approach uses a technique called Seam carving to track harmonics formed by vehicle particularly its engine noise. The method proposed is computationally inexpensive and can very easily be developed into mobile application.

This paper presents harmonic analysis in a multiple adjustable speed drive system. In a system where multiple drives are fed from the same bus, harmonic currents produced by the various drives can reflect back to the power source and to the other drives causing distortion of the voltage waveform. If these harmonic currents are significant, they can potentially cause problems for the given system. Therefore studying the harmonics at various points in the system and comparing the values of total harmonic distortion can provide guidance in choosing appropriate filtering solutions. A two ac drive system was setup in a laboratory environment and the total harmonic distortion of the voltage and current was measured at several points within the system to observe how the harmonics interact with each other. The frequency of the drives and the torque of the motors were also varied to achieve a variable torque relationship to model heating, ventilation, and air condition loads.

The growing demand for electricity makes the power grid ever expanding day by day and more and more complex. There is a potential requirement to continuously monitor the power grid and thus making it smarter and reliable. Traditional measurement systems are getting replaced by PMUs, which enables the online monitoring of the power system. With the aid of GPS, PMUs can measure the phasor values of voltages at the bus, where it is placed and the current through the branches connected to that bus. The Current measurement enables us to estimate the voltages at the neighbouring buses. Because of this, placing PMUs at all buses for the complete monitoring of the power system is redundant. Finding the optimal locations of PMUs to make the power system completely observable is of great research interest. This paper proposes the optimal locations of PMU in Tamil Nadu state of Indian power grid using ILP. PMU placement problem has been formulated and optimization has been carried out. Results showing the various optimal locations are tabulated.

At the point of common coupling (PCC), the summation of two harmonic voltage vectors at same frequency is only certain if their amplitudes and phase angles are well known. Therefore, there are many cases where the phase angle difference between harmonic voltage vectors is unknown. In practice, for example, in calculating the steady state rating of the a.c. passive harmonic filter, arithmetic summation method is often used in determining maximal harmonic level. This summation law is very conservative as it may result in high cost of equipment ratings. Actually, a compromise should be made in taking into account the equipment safety and the risk of overrating as well as excessive costs. Based on uniform distribution of difference in phase angles, the paper provides an algorithm to calculate the probability upon which the magnitude of summation vector of two harmonic voltages may exceed a given value. On the basis of the probability and the given harmonic value, harmonic summation can be assessed. This may also result in a recommendation of another harmonic summation method for the standard IEC/TR 61000-3-6.

We define a q-analog of the modified Bessel and Bessel-Macdonald functions. As for the q-Bessel functions of Jackson there is a couple of functions of the both kind. They are arisen in the Harmonic analysis on quantum symmetric spaces similarly to their classical counterpart. Their definition is based on the power expansions. We derive the recurrence relations, difference equations, q-Wronskians, and an analog of asymptotic expansions which turns out is exact in some domain if q = 1. Some relations for the basic hypergeometric function which follow from this fact are discussed.

This paper presents an algorithm to perform online tremor characterization from motion sensors measurements, while filtering the voluntary motion performed by the patient. In order to estimate simultaneously both nonstationary signals in a stochastic filtering framework, pathological tremor was represented by a time-varying harmonic model and voluntary motion was modeled as an auto-regressive moving-average (ARMA) model. Since it is a nonlinear problem, an extended Kalman filter (EKF) was used. The developed solution was evaluated with simulated signals and experimental data from patients with different pathologies. Also, the results were comprehensively compared with alternative techniques proposed in the literature, evidencing the better performance of the proposed method. The algorithm presented in this paper may be an important tool in the design of active tremor compensation systems.

Musical genres are categorical labels characterizing pieces of music. Automatically classifying music into genres is gaining importance as a way to structure and organize the increasingly large numbers of music files available digitally on the web. In this work such a classification algorithm is developed and examined. The algorithm uses a vector of features based on the timbral texture of the music, and maps it into a new Euclidean space, by a non-linear method called “Diffusion Maps”, before the classification stage itself. This method allows dimensionality reduction while preserving and emphasizing the distinction between different genres. The proposed classifier classifies accurately 97% when classifying 2 musical genres, and 52% when classifying 10 musical genres. This is compared to an accuracy of 88% and 28% respectively, when classifying without the proposed mapping.

Nowadays, it is a general trend to increase the electricity production using distributed power generation systems (DPGS) based on renewable energy resources such as wind, sun or hydrogen. Jf these systems are not properly controlled, their connection to the utility network can generate problems on the grid side. Therefore, considerations about power generation, safe running and grid synchronization must be done before connecting these systems to the utility network. This paper is mainly dealing with the grid synchronization issues of distributed systems. An overview of the synchronization methods as well as their major characteristics is given. New solutions to optimize the synchronization methods when running on distorted grid conditions are discussed. Simulation and experimental results are used to evaluate the behavior of the synchronization methods under different kind of grid disturbances such as voltage dips, harmonics and notches.

This paper presents an application of Fortran Feasible Sequential Quadratic Programming optimization method for finding the optimum fixed shunt inductive-capacitive compensator for power factor correction of non-linear loads, where source voltage and load current harmonics are considered. Optimization minimizes the transmission line losses, and maximizes the load power factor. The performance of the proposed solution is discussed by means of numerical examples.

This paper focuses on I2R losses under nonsinusoidal conditions, mainly in cables and transformers. For this purpose, a mathematical development that takes in account the presence of harmonic components in the I2R losses calculation will be presented, so that the effects of the harmonic distortion in the power system components and consequently the impact on the power factor can be analyzed. Based on this study, a factor that evaluates the power quality performance in low voltage networks is presented. This factor is directly associated to the economical viability, once that it points when the losses minimization is interesting according to the cost/benefit ratio.

T he Seventh Student High-Effi ciency Power Amplifi er (PA) Design Competition was held at the IEEE Microwave Theory and Techniques Society (MTT-S) International Microwave Symposium (IMS) 2011 in Baltimore, Maryland. Every year, many students from all over the world participate in the competition and demonstrate their ability to design a high-effi ciency PA. Since IMS2008, in order to encourage students to explore PA design at a high-frequency, a weighting factor was introduced to the calculation of the score-the fi nal score being determined by multiplying the power-added-effi ciency (PAE) by the frequency weighting factor, PAE×(frequency (GHz)) 0.25 . Thus, while preparing the competition, participants are encouraged to carefully determine the device technology considering the operating frequency of the PA as well as their higheffi ciency PA topology.

A new digital signal processing approach to shaping intersymbol interference (ISI) and static mismatch errors simultaneously in oversampled multi-level digital to analog converters (DAC) has recently been proposed. In this paper, a mathematical framework is established for analyzing ISI errors as well as comparing the ISI sensitivities of different mismatch shaping algorithms. The framework is used to analyze the fundamental problems of popularly used algorithms such as data-weighted-averaging (DWA) in the presence of nonlinear ISI: Large-signal even-order distortion and frequency modulated harmonics at low signal levels. The new ISI-shaping algorithm results in significant improvement over previous schemes including the modified Mismatch Shaper (MMS) which also addresses ISI error. The new ISI shaper, while increasing the digital complexity, practically eliminates the need for conventional ISI mitigation techniques such as time consuming, layout-critical, non-automated and process specific analog design methods. The advantages of ISI shaping is further verified on an experimental audio DAC with simple non-return-to-zero (NRZ) current steering segments implemented in a 45 nm CMOS process and running off a single-phase clock of only 3.072 MHz.

How does rock harmony differ from that of the common practice? As several recent writings have shown, motions between individual chords-that is, functional behaviors-are often vastly different from that of the common practice. 1 Precisely how these and other harmonic differences coalesce to form surface-level progressions that depart from common-practice conventions, however, is a question that has been approached only peripherally. 2 With an emphasis on the classic-rock canon of the late 1960s through the 1980s, this article therefore investigates rock harmony from the larger perspective of the progression in an attempt to paint a more detailed picture of rock's idiosyncratic harmonic syntax. In particular, classifying triads as Tonic, Dominant, or Subdominant based largely on the similarity of their scale-degree content, or functional "kinship," reveals three central aspects of rock progressions. 3 First, they do not constrain the functional motion of their chords. In other words, unlike the TSDT paradigm of the common practice, the kinship functions of Subdominant and Dominant both move regularly to each other and to Tonic-functioned harmonies. Thus, there is no single kinship-functional paradigm that encompasses most rock progressions; rather, two paradigms appear more than any other: the authentic and plagal (described in more detail further below). Second, rock progressions that diverge from the common practice, which feature in the vast majority of songs, do so in two ways: by the ordering of the kinship functions into a form of the plagal paradigm, and/or by secondary triads that are unusual by common-practice norms, namely subtonic and mediant triads. Third, even when there appear secondary triads that are more typical by common-practice norms, namely submediant and supertonic triads, their behavior is often in opposition to those norms. This article will examine these elements of rock harmony in two parts. The first and larger part will establish a number of definitions necessary to parse progressions by their functional kinship. These include harmonic function, tonic perception, scale-degree assemblies, progressions, and types of progressions. The second part of the article will apply these definitions to a wide range of specific examples and generalizations in order to demonstrate how progressions in rock differ from those of the common practice. 1 See Nobile 2016, Quinn and White 2015, Doll 2007, and Stephenson 2002 (ch. 5). 2 Moore 2012 (71-79) views rock progressions as strongly modal, offering a flexible system for their analysis. Moore 1992 has also catalogued an extensive list of rock progressions by prominent root motions. Everett 2009 (214-301) offers a similarly-organized, comprehensive examination of rock progressions but, to categories based on root motions, he adds others based on contrapuntal motions, minor keys, modes, and chromaticism rather than by their distance from common-practice norms. De Clercq and Temperley 2011 provide a glimpse into some of rock's common "trigrams," which are three-chord successions that may occur across any perceptual boundaries rather than progressions that have a discernible beginning and end. And Biamonte 2010 is devoted to three rock-specific categories of harmonic progression: the double-plagal progression, the Aeolian progression, and modal scales thickened by harmonization in parallel triads. See also Biamonte 2012 for an extension of some of these ideas. 3 Following Harrison 1994, I capitalize the names of kinship functions (Tonic, Dominant, Subdominant) in order to distinguish them from specific triads with the same names, which remain uncapitalized.

Background One of the most important principles of tonal theory is that of harmonic syntax. This principle contains the norms of precise logical order in the succession of harmonic functions or chords in any harmonic progression in tonal music (Riemann 1893; Caplin 1998; Schenker 1954; Cadwallader and Gagne 1998; Aldwell, Schachter, and Cadwallader 2011). Such norms are shaped and determined by the frequency of specific harmonic progressions, which generate expectations in the listener acquainted with Western Classical tonal music; if the progression of chords tonic-dominant, for instance, is more common than the progressions tonic-subdominant and tonic-submediant, every occurrence of the tonic chord will generate the expectation of dominant rather than subdominant or submediant harmony. Tonal harmonic syntax is characterised by the distinct syntactical tendencies of each chord, determined principally by fifth and ascending-step (or half-step) root progressions.

In this paper, a high efficiency C-band GaN HEMT high power amplifier with internal harmonic manipulation circuits is presented. We employed a new circuit topology for simultaneous high efficiency matching at both fundamental and 2nd-harmonic frequencies. The developed GaN HEMT amplifier has achieved over 57% drain efficiency (50% power-added-efficiency) with 100 W output power at C-band. This is the state-of-the-art efficiency of GaN HEMT high power amplifier at C-band to the best of our knowledge.

Interior permanent magnet (IPM) motors are normally designed with two or more flux barriers per pole. The form of such flux barriers has a direct impact on the torque developed by the IPM motor, with regards to both its average value and ripple. The Machaon structure includes flux barriers of different shape, aimed at reducing the torque ripple. Their shape depends on the number of poles, number of slots, winding arrangements, and PM volume used in the rotor. An optimization technique is adopted in order to determine the best shape of the flux barriers with the objective of achieving a smooth torque with a high average value.

My purpose with the article is to help you to find your parameter settings and find the best way that can help you to utilize this very complex and complete indicator to prosper. See the list of its parameters below in this article. Enjoy! Starting from ZUP v 150 new addition; being able to mark Elliott waves on the chart and have an easier GUI (graphical user interface) helping users. The development of ZUP took place over a decade. There is no question about how much effort, hard work and contribution of lot of traders went into this development. Due to this, ZUP was and is one of the most popular harmonic pattern indicators.
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