Simulation and Spectral Analysis of Inharmonic Tones of Musical Instruments

Total Page:16

File Type:pdf, Size:1020Kb

Simulation and Spectral Analysis of Inharmonic Tones of Musical Instruments Proceedings of the 7th WSEAS International Conference on SIGNAL PROCESSING, ROBOTICS and AUTOMATION (ISPRA '08) University of Cambridge, UK, February 20-22, 2008 Simulation and Spectral Analysis of Inharmonic Tones of Musical Instruments VARSHA SHAH 1, Dr.REKHA S. PATIL 2 Asst. Prof., Rizvi College of Engineering 1, Principal, J.J.Magdum College of Engineering 2 University of Mumbai 1, Shivaji University 2 INDIA Abstract: - Simulation and spectral analysis of harmonic and inharmonic pure tones of musical instruments is undertaken. It is shown how the basic wave such as sine can be used to simulate various harmonic and inharmonic sound signals of different instruments generating different timbres. It is shown that even the modest value of inharmonicity coefficient is sufficient to raise the frequency of inharmonic spectrum by a partial step more than that of the harmonic spectrum thus deviating the spectrum from strictly harmonic case. Listening tests of the simulated tones are also conducted which proves that the perception of inharmonicity depends on the number of partials present in the sound. Keywords: - Inharmonic Signal, Inharmonicity, Partial, Synthesis, Spectrum Analysis. 1. Introduction iv) Wavetable Synthesis: It is used in Basic wave shape such as sine, square and digital musical instruments (synthesizers) to triangle play an important role in digital produce natural sounds. The sound of a signal processing applications. Various existing instrument sampled and stored synthesizing techniques use these waves to inside a wavetable. By repeatedly playing simulate the sound wave. samples from this table in a loop the Various synthesizing techniques are original sound is imitated classified in the following manner [2] Additive synthesis method is widely i) Additive Synthesis: In this method used in synthesizing musical simple each sound signal is represented by linear musical tones. We have used the said combination of sinusoids i.e. with variable method to generate simple as well as frequency and amplitude over time. complex harmonic and inharmonic musical ii) Frequency modulation synthesis (or tones by incorporating the inharmonicity FM synthesis): It is a form of audio coefficient. synthesis where the timbre of a simple waveform is changed by frequency modulating it with a modulating frequency2 2 Difference Harmonic and that is also in the audio range, resulting in a Inharmonic Tones more complex waveform and a different- sounding tone.[3] A simple tone has only one frequency, iii) Subtractive synthesis: It is technique while the complex tone consists of one or which creates musical timbres by filtering more simple tones. A complex tone can be complex waveforms generated by harmonic or inharmonic. oscillators. Subtractive synthesis is usually A complex signal is called the harmonic (but not exclusively) associated with analog signal if all the frequencies of partials are voltage controlled synthesizers. It can integer multiples of fundamental produce very natural changes in a sound, frequencies that is the lowest frequency of owing to the intuitive way in which it the signal. Various harmonics of this signal works. can be calculated using following equation: ISSN: 1790-5117 261 ISBN: 978-960-6766-44-2 Proceedings of the 7th WSEAS International Conference on SIGNAL PROCESSING, ROBOTICS and AUTOMATION (ISPRA '08) University of Cambridge, UK, February 20-22, 2008 fn = nf0 equation (1) coefficient was varied in the range of 50. Where n = number of harmonic 10-6 to 600. 10-6. The numbers of partials present in the sound were also varied in the In case of inharmonic signal the range of 5 to 25. Different fundamental frequencies of harmonics are not exact frequencies in the range of 30 Hz to integral multiples of the fundamental 1500Hz were used to simulate harmonic frequencies. Hence they are called as and inharmonic signals. To simulate and partials [7] .For e.g. the sound waves analyze signals and their spectrums generated from the struck or plucked type MATLAB 6.5 software and its toolboxes of musical instruments such as piano. This are used. is due to the stiffness of the strings of the instrument. The various partials can be calculated using the equation of the 4 Spectrum Analysis of stretching partials of piano tones which Simulated Tones relates the partial frequency, fn, with the Various simulated sounds are analyzed by fundamental frequency f0 in the presence of plotting their frequency spectrums using an inharmonicity coefficient B [1]. DSP technique. Graphical representation of 2 0.5 various spectrums is shown. They are as fn=nf0(1+Bn ) equation (2) follows: 3 4 2 1. Figure 1 to 4 show frequency spectrums B = π Qd / ( 64l T) equation (3) of 2 different sets of harmonic and Where n = partial number inharmonic signals. In this the tones are Q = Young’s modulus, generated by keeping inharmonicity d = the diameter coefficient constant = 300*10^-6, number l = the length of partials=25 for two different fundamental T = the tension of the string frequencies of 100Hz and 200Hz. f0 = fundamental frequency Typical values of B for piano strings lie roughly between 0.00005 for low bass tones and 0.015 for the high treble tones.[7] Timber is that parameter of the sound wave which allows us to differentiate the sounds of two different instruments of same pith and the amplitude. 3 Implementation of Simulation of Musical tones Simulation of complex inharmonic tones: b=300 * 10^-6; No. of partials: 25 Harmonic and inharmonic signals were Fig.1: Harmonic with fun.freq. = 100; generated by varying number of partials, Fig2: Inharmonic with fun.freq. = 100; fundamental frequency & inharmonicity Fig.3: Harmonic with fun.freq. = 200; coefficient. Fig.4: Inharmonic with fun.freq. = 200; Initially simple tones of single frequency are simulated. Equation 1 is used 2. Figures 5 to 8 show the spectrum of one to simulate complex harmonic sound of a harmonic and 3 inharmonic spectrums in musical instrument viz. harmonium which which fundamental frequency is taken as consists of more than one frequency. 450Hz, inharmonicity coefficient is taken as Equation 2 is used to simulate complex 100 * 10^-6 and the number of partials are inharmonic pure tones of musical taken as 5, 15 and 30. instrument viz. piano. The inharmonicity ISSN: 1790-5117 262 ISBN: 978-960-6766-44-2 Proceedings of the 7th WSEAS International Conference on SIGNAL PROCESSING, ROBOTICS and AUTOMATION (ISPRA '08) University of Cambridge, UK, February 20-22, 2008 3. Figures 9-12 show the spectrums of 1 harmonic signal and 3 inharmonic signals. Inharmonicity coefficients of 3 different values are selected to generate inharmonic signals. In this number of partials are taken as 25 for all the four signals. 5 Perceptual Analysis Five subjects having musical training participated in listening tests of the simulated sounds. Different harmonic and inharmonic sounds were simulated and the wave files were played to find the effects of No.of partials=25; fun.freq.=80Hz. different inharmonicity coefficients, Fig.9 Harmonic signal fundamental frequencies and number of Fig10:Inharmonic with b=50 * 10^-6; partials present in the sound. Repeated tests Fig.11:Inharmonic with b=200 * 10^-6; were conducted to confirm the subjective Fig.12:Inharmonic with b=600 * 10^-6; effect of various sounds. iii. After listening to the inharmonic sounds the opinion of the subjects were as follows: a. when the inharmonicity coefficient was 6 Observations and results varied by keeping the fundamental frequency constant and keeping the number 6.1 Results of Audibility test of partials same the subjects heard the i.It is the opinion of all the subject listeners metallic touch to the sounds. that the simple notes timber sound like a b. They also felt that up to approximately broken note of any wind instrument. 600*10^-6 of inharmonicity coefficient ii. Subjects heard various harmonics sound with the fundamental frequency of 50 to and found them as the pure tones 450 Hz the inharmonic sound was pleasant generated from the wind instrument like to hear than harmonic one. harmonium. 6.2 Results of Spectral Analysis of the Simulated Signals i. It is observed that even the modest b of 300*10^-6 increases the frequency of the inharmonic spectrum by a partial step. It is observed from figure 1 and figure 2 that due to inharmonicity the frequency of the inharmonic spectrum deviates in such a way that frequency of 20th partial of harmonic signal is shifted to 21st partial in case of inharmonic signal. ii. It is observed from figures 5 to 8 that as the fundamental frequency increases [b=100 * 10^-6; fun.freq.=450Hz. keeping the inharmonicity coefficient Fig.5: Harmonic with no. of partials = 5; constant the deviation of the spectrum from Fig 6: Inharmonic with no. of partials= 5; the strictly harmonic case also increases. Fig.7: Harmonic with no. of partials=15; iii. It is observed in figures 9 to 12 that as Fig.8: Inharmonic with no. of partials=30; the inharmonicity coefficient increases the deviation of the frequencies of the spectrum of inharmonic signal also increase & the ISSN: 1790-5117 263 ISBN: 978-960-6766-44-2 Proceedings of the 7th WSEAS International Conference on SIGNAL PROCESSING, ROBOTICS and AUTOMATION (ISPRA '08) University of Cambridge, UK, February 20-22, 2008 spectrum moves away from the strictly [9] V. Valimaki, M. Karjalainen, T. Tolono, harmonic case. and C. Erkut, “Nonlinear modeling and synthesis of the kantele – a traditional Finnish string instrument,” in Proc. Int. 7 Conclusion Computer MusicConf., (Beijing, China), It was seen from the analysis of simulated pp. 220–223, 1999. musical tones that the inharmonic sound is [10] Serra, X. and Smith, J. O., 1990. found to be natural than the harmonic sound "Spectral Modeling Synthesis: A Sound if adequate amount of inharmonicity is Analysis/Synthesis System Based on a present.
Recommended publications
  • Echo-Enabled Harmonics up to the 75Th Order from Precisely Tailored Electron Beams E
    LETTERS PUBLISHED ONLINE: 6 JUNE 2016 | DOI: 10.1038/NPHOTON.2016.101 Echo-enabled harmonics up to the 75th order from precisely tailored electron beams E. Hemsing1*,M.Dunning1,B.Garcia1,C.Hast1, T. Raubenheimer1,G.Stupakov1 and D. Xiang2,3* The production of coherent radiation at ever shorter wave- phase-mixing transformation turns the sinusoidal modulation into lengths has been a long-standing challenge since the invention a filamentary distribution with multiple energy bands (Fig. 1b). 1,2 λ of lasers and the subsequent demonstration of frequency A second laser ( 2 = 2,400 nm) then produces an energy modulation 3 ΔE fi doubling . Modern X-ray free-electron lasers (FELs) use relati- ( 2) in the nely striated beam in the U2 undulator (Fig. 1c). vistic electrons to produce intense X-ray pulses on few-femto- Finally, the beam travels through the C2 chicane where a smaller 4–6 R(2) second timescales . However, the shot noise that seeds the dispersion 56 brings the energy bands upright (Fig. 1d). amplification produces pulses with a noisy spectrum and Projected into the longitudinal space, the echo signal appears as a λ λ h limited temporal coherence. To produce stable transform- series of narrow current peaks (bunching) with separation = 2/ limited pulses, a seeding scheme called echo-enabled harmonic (Fig. 1e), where h is a harmonic of the second laser that determines generation (EEHG) has been proposed7,8, which harnesses the character of the harmonic echo signal. the highly nonlinear phase mixing of the celebrated echo EEHG has been examined experimentally only recently and phenomenon9 to generate coherent harmonic density modu- at modest harmonic orders, starting with the 3rd and 4th lations in the electron beam with conventional lasers.
    [Show full text]
  • Generation of Attosecond Light Pulses from Gas and Solid State Media
    hv photonics Review Generation of Attosecond Light Pulses from Gas and Solid State Media Stefanos Chatziathanasiou 1, Subhendu Kahaly 2, Emmanouil Skantzakis 1, Giuseppe Sansone 2,3,4, Rodrigo Lopez-Martens 2,5, Stefan Haessler 5, Katalin Varju 2,6, George D. Tsakiris 7, Dimitris Charalambidis 1,2 and Paraskevas Tzallas 1,2,* 1 Foundation for Research and Technology—Hellas, Institute of Electronic Structure & Laser, PO Box 1527, GR71110 Heraklion (Crete), Greece; [email protected] (S.C.); [email protected] (E.S.); [email protected] (D.C.) 2 ELI-ALPS, ELI-Hu Kft., Dugonics ter 13, 6720 Szeged, Hungary; [email protected] (S.K.); [email protected] (G.S.); [email protected] (R.L.-M.); [email protected] (K.V.) 3 Physikalisches Institut der Albert-Ludwigs-Universität, Freiburg, Stefan-Meier-Str. 19, 79104 Freiburg, Germany 4 Dipartimento di Fisica Politecnico, Piazza Leonardo da Vinci 32, 20133 Milano, Italy 5 Laboratoire d’Optique Appliquée, ENSTA-ParisTech, Ecole Polytechnique, CNRS UMR 7639, Université Paris-Saclay, 91761 Palaiseau CEDEX, France; [email protected] 6 Department of Optics and Quantum Electronics, University of Szeged, Dóm tér 9., 6720 Szeged, Hungary 7 Max-Planck-Institut für Quantenoptik, D-85748 Garching, Germany; [email protected] * Correspondence: [email protected] Received: 25 February 2017; Accepted: 27 March 2017; Published: 31 March 2017 Abstract: Real-time observation of ultrafast dynamics in the microcosm is a fundamental approach for understanding the internal evolution of physical, chemical and biological systems. Tools for tracing such dynamics are flashes of light with duration comparable to or shorter than the characteristic evolution times of the system under investigation.
    [Show full text]
  • Frequency Spectrum Generated by Thyristor Control J
    Electrocomponent Science and Technology (C) Gordon and Breach Science Publishers Ltd. 1974, Vol. 1, pp. 43-49 Printed in Great Britain FREQUENCY SPECTRUM GENERATED BY THYRISTOR CONTROL J. K. HALL and N. C. JONES Loughborough University of Technology, Loughborough, Leics. U.K. (Received October 30, 1973; in final form December 19, 1973) This paper describes the measured harmonics in the load currents of thyristor circuits and shows that with firing angle control the harmonic amplitudes decrease sharply with increasing harmonic frequency, but that they extend to very high harmonic orders of around 6000. The amplitudes of the harmonics are a maximum for a firing delay angle of around 90 Integral cycle control produces only low order harmonics and sub-harmonics. It is also shown that with firing angle control apparently random inter-harmonic noise is present and that the harmonics fall below this noise level at frequencies of approximately 250 KHz for a switched 50 Hz waveform and for the resistive load used. The noise amplitude decreases with increasing frequency and is a maximum with 90 firing delay. INTRODUCTION inductance. 6,7 Literature on the subject tends to assume that noise is due to the high frequency Thyristors are now widely used for control of power harmonics generated by thyristor switch-on and the in both d.c. and a.c. circuits. The advantages of design of suppression components is based on this. relatively small size, low losses and fast switching This investigation has been performed in order to speeds have contributed to the vast growth in establish the validity of this assumption, since it is application since their introduction, when they were believed that there may be a number of perhaps basically a solid-state replacement for mercury-arc separate sources of noise in thyristor circuits.
    [Show full text]
  • The Fusion and Layering of Noise and Tone: Implications for Timbre In
    The Fusion and Layering of Noise and Tone: Implications for Timbre in African Instruments Author(s): Cornelia Fales and Stephen McAdams Source: Leonardo Music Journal, Vol. 4 (1994), pp. 69-77 Published by: The MIT Press Stable URL: http://www.jstor.org/stable/1513183 Accessed: 03/06/2010 10:44 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=mitpress. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The MIT Press is collaborating with JSTOR to digitize, preserve and extend access to Leonardo Music Journal. http://www.jstor.org 4 A B S T R A C T SOUNDING THE MIND Since their earliest explora- The Fusion and Layering of Noise tions of Africanmusic, Western re- searchers have noted a fascination on the part of traditionalmusicians and Tone: Implicatons for Timbre for noise as a timbralelement.
    [Show full text]
  • Fixed Average Spectra of Orchestral Instrument Tones
    Empirical Musicology Review Vol. 5, No. 1, 2010 Fixed Average Spectra of Orchestral Instrument Tones JOSEPH PLAZAK Ohio State University DAVID HURON Ohio State University BENJAMIN WILLIAMS Ohio State University ABSTRACT: The fixed spectrum for an average orchestral instrument tone is presented based on spectral data from the Sandell Harmonic Archive (SHARC). This database contains non-time-variant spectral analyses for 1,338 recorded instrument tones from 23 Western instruments ranging from contrabassoon to piccolo. From these spectral analyses, a grand average was calculated, providing what might be considered an average non-time-variant harmonic spectrum. Each of these tones represents the average of all instruments in the SHARC database capable of producing that pitch. These latter tones better represent common spectral changes with respect to pitch register, and might be regarded as an “average instrument.” Although several caveats apply, an average harmonic tone or instrument may prove useful in analytic and modeling studies. In addition, for perceptual experiments in which non-time-variant stimuli are needed, an average harmonic spectrum may prove to be more ecologically appropriate than common technical waveforms, such as sine tones or pulse trains. Synthesized average tones are available via the web. Submitted 2010 January 22; accepted 2010 February 28. KEYWORDS: timbre, SHARC, controlled stimuli MOST modeling studies and experimental research in music perception involve the presentation or input of auditory stimuli. In many cases, researchers have aimed to employ highly controlled stimuli that allow other researchers to precisely replicate the procedure. For example, many experimental and modeling studies have employed standard technical waveforms, such as sine tones or pulse trains.
    [Show full text]
  • Specifying Spectra for Musical Scales William A
    Specifying spectra for musical scales William A. Setharesa) Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin 53706-1691 ~Received 5 July 1996; accepted for publication 3 June 1997! The sensory consonance and dissonance of musical intervals is dependent on the spectrum of the tones. The dissonance curve gives a measure of this perception over a range of intervals, and a musical scale is said to be related to a sound with a given spectrum if minima of the dissonance curve occur at the scale steps. While it is straightforward to calculate the dissonance curve for a given sound, it is not obvious how to find related spectra for a given scale. This paper introduces a ‘‘symbolic method’’ for constructing related spectra that is applicable to scales built from a small number of successive intervals. The method is applied to specify related spectra for several different tetrachordal scales, including the well-known Pythagorean scale. Mathematical properties of the symbolic system are investigated, and the strengths and weaknesses of the approach are discussed. © 1997 Acoustical Society of America. @S0001-4966~97!05509-4# PACS numbers: 43.75.Bc, 43.75.Cd @WJS# INTRODUCTION turn closely related to Helmholtz’8 ‘‘beat theory’’ of disso- nance in which the beating between higher harmonics causes The motion from consonance to dissonance and back a roughness that is perceived as dissonance. again is a standard feature of most Western music, and sev- Nonharmonic sounds can have dissonance curves that eral attempts have been made to explain, define, and quantify differ dramatically from Fig.
    [Show full text]
  • Harmonic Spectrum of Output Voltage for Space Vector Pulse Width Modulated Ultra Sparse Matrix Converter
    energies Article Harmonic Spectrum of Output Voltage for Space Vector Pulse Width Modulated Ultra Sparse Matrix Converter Tingna Shi * ID , Lingling Wu, Yan Yan and Changliang Xia ID School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China; [email protected] (L.W.); [email protected] (Y.Y.); [email protected] (C.X.) * Correspondence: [email protected]; Tel.: +86-22-27402325 Received: 19 January 2018; Accepted: 2 February 2018; Published: 8 February 2018 Abstract: In a matrix converter, the frequencies of output voltage harmonics are related to the frequencies of input, output, and carrier signals, which are independent of each other. This nature may cause an inaccurate harmonic spectrum when using conventional analytical methods, such as fast Fourier transform (FFT) and the double Fourier analysis. Based on triple Fourier series, this paper proposes a method to pinpoint harmonic components of output voltages of an ultra sparse matrix converter (USMC) under space vector pulse width modulation (SVPWM) strategy. Amplitudes and frequencies of harmonic components are determined precisely for the first time, and the distribution pattern of harmonics can be observed directly from the analytical results. The conclusions drawn in this paper may contribute to the analysis of harmonic characteristics and serve as a reference for the harmonic suppression of USMC. Besides, the proposed method is also applicable to other types of matrix converters. Keywords: ultra sparse matrix converter (USMC); space vector pulse width modulations (SVPWM); triple fourier series; harmonic analysis 1. Introduction The ultra-sparse matrix converter (USMC) evolved from the conventional matrix converter (CMC) and inherited many merits from CMC including compact structure without intermediate storage, sinusoidal input and output current, adjustable input power factor, etc.
    [Show full text]
  • Surprising Connections in Extended Just Intonation Investigations and Reflections on Tonal Change
    Universität der Künste Berlin Studio für Intonationsforschung und mikrotonale Komposition MA Komposition Wintersemester 2020–21 Masterarbeit Gutachter: Marc Sabat Zweitgutachterin: Ariane Jeßulat Surprising Connections in Extended Just Intonation Investigations and reflections on tonal change vorgelegt von Thomas Nicholson 369595 Zähringerstraße 29 10707 Berlin [email protected] www.thomasnicholson.ca 0172-9219-501 Berlin, den 24.1.2021 Surprising Connections in Extended Just Intonation Investigations and reflections on tonal change Thomas Nicholson Bachelor of Music in Composition and Theory, University of Victoria, 2017 A dissertation submitted in partial fulfilment of the requirements for the degree of MASTER OF MUSIC in the Department of Composition January 24, 2021 First Supervisor: Marc Sabat Second Supervisor: Prof Dr Ariane Jeßulat © 2021 Thomas Nicholson Universität der Künste Berlin 1 Abstract This essay documents some initial speculations regarding how harmonies (might) evolve in extended just intonation, connecting back to various practices from two perspectives that have been influential to my work. The first perspective, which is the primary investigation, concerns itself with an intervallic conception of just intonation, centring around Harry Partch’s technique of Otonalities and Utonalities interacting through Tonality Flux: close contrapuntal proximities bridging microtonal chordal structures. An analysis of Partch’s 1943 composition Dark Brother, one of his earliest compositions to use this technique extensively, is proposed, contextualised within his 43-tone “Monophonic” system and greater aesthetic interests. This is followed by further approaches to just intonation composition from the perspective of the extended harmonic series and spectral interaction in acoustic sounds. Recent works and practices from composers La Monte Young, Éliane Radigue, Ellen Fullman, and Catherine Lamb are considered, with a focus on the shifting modalities and neighbouring partials in Lamb’s string quartet divisio spiralis (2019).
    [Show full text]
  • Fundamental Frequency Estimation
    Fundamental frequency estimation summer 2006 lecture on analysis, modeling and transformation of audio signals Axel Robel¨ Institute of communication science TU-Berlin IRCAM Analysis/Synthesis Team 25th August 2006 KW - TU Berlin/IRCAM - Analysis/Synthesis Team AMT Part V: Fundamental frequency estimation 1/27 Contents 1 Pitch and fundamental frequency 1.1 Relation between pitch and fundamental frequency 1.2 Harmonic sound sources 2 Fundamental frequency estimation problem 3 Algorithms 3.1 direct evaluation of periodicity 3.2 frequency domain harmonic matching 3.3 spectral period evaluation 3.4 psycho acoustic approaches 3.5 Properties of the auditory processing model KW - TU Berlin/IRCAM - Analysis/Synthesis Team Contents AMT Part V: Fundamental frequency estimation 2/27 3.6 half wave rectification 3.7 Performance KW - TU Berlin/IRCAM - Analysis/Synthesis Team Contents AMT Part V: Fundamental frequency estimation 3/27 1 Pitch and fundamental frequency Pitch • perceived tone frequency of a sound in comparison with the perceptively best match with a pure sinusoid. fundamental frequency • inverse of the signal period of a periodic or quasi periodic signal, • spectrum contains energy mostly at integer multiples of the fundamental frequency. • the sinusoids above the fundamental are called the harmonics of the fundamental frequency. IRCAM - Analysis/Synthesis Team Contents AMT Part V: Fundamental frequency estimation 4/27 1.1 Relation between pitch and fundamental frequency • For many signals both terms are closely related, if the higher harmonics are strongly amplified due to formants the pitch may be located not at th first but a higher harmonic. • if a sound signal contains in-harmonically related sinusoids more then one pitch may be perceived while the signal is actually not periodic.
    [Show full text]
  • The Suppression of Selected Acoustic Noise Frequencies In
    The Suppression of Selected Acoustic Noise Frequencies in MRI by XINGXIAN SHOU Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Dissertation Adviser: Robert W. Brown, Ph.D. Department of Physics CASE WESTERN RESERVE UNIVERSITY January, 2011 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of ______________________________________________________XINGXIAN SHOU candidate for the ________________________________degreePh.D. *. (signed)_______________________________________________Robert W. Brown (chair of the committee) ________________________________________________Jeffrey Duerk ________________________________________________David Farrell ________________________________________________Harsh Mathur ________________________________________________Shmaryu Shvartsman ________________________________________________ (date) _______________________July 26, 2010 *We also certify that written approval has been obtained for any proprietary material contained therein. To my parents Jun Shou, Huiqin Bian and my fiancée Shuofen Li ii Table of Contents Chapter 1 An Overview of Magnetic Resonance Imaging ....................................................... 1 1.1 What Is MRI? .................................................................................................................. 1 1.2 Principles of Magnetic Resonance Imaging .................................................................... 2 1.2.1 Spin Precession and Larmor Frequency ..................................................................
    [Show full text]
  • United States Patent (10) Patent N0.: US 6,319,203 B1 Averkiou (45) Date of Patent: Nov
    US006319203B1 (12) United States Patent (10) Patent N0.: US 6,319,203 B1 Averkiou (45) Date of Patent: Nov. 20, 2001 (54) ULTRASONIC NONLINEAR IMAGING AT 5,833,613 11/1998 Averkiou et al. FUNDAMENTAL FREQUENCIES 5,848,968 12/1998 Takellchi~ 5,873,829 2/1999 Kamiyama et al. (75) Inventor: Michalakis Averkiou, Kirkland, WA 5,879,303 3/1999 Averkiou et a1- - (Us) 6,048,316 4/2000 Zhao et al. 6,186,949 * 2/2001 Hat?led et al. .................... .. 600/443 (73) Assigneez ATL Ultrasound, Bothell, WA (Us) 6,251,074 * 6/2001 Averkiou et al. .................. .. 600/447 * . ( * ) Notice: Subject to any disclaimer, the term of this cued by exammer patent is extended or adjusted under 35 _ _ _ U S C 154(k)) by 0 days Prtmary Examtner—Marvm M. Lateef ' i i ' Assistant Examiner—Maulin Patel (21) Appl NO _ 09/627 918 (74) Attorney, Agent, or Firm—W. Brinton Yorks, Jr. .. , (22) Filed: Jul. 28, 2000 (57) ABSTRACT 7 Nonlinear tissue or contrast agent effects are detected by (2;) ............................................ .gbbyhlss?onos?g Combining echoes from multiple, differently modulated ( ) _' ' ' ’ transmit pulses beloW the second harmonic band. The Fleld Of Search ................................... .. received eChoes may even Overlap the fundamental transmit 600/445’ 437’ 447’ 448’ 128/416 frequency band. The modulation may be amplitude modu , lation or phase or polarity modulation, and is preferably both (56) References Clted amplitude and phase or modulation. The present invention U_S_ PATENT DOCUMENTS affords the ability to utiliZe a majority of the transducer _ passband for both transmission and reception, and to trans lg ELOCk'FISh‘ZI ‘lat a1‘ ' mit pulses Which are less destructive to microbubble contrast , , apman e a .
    [Show full text]
  • White Paper Harmonics
    2014 Six tough topics about harmonic distortion and Power Quality indices in electric power systems A white paper of the Schaffner Group Written by Alexander Kamenka All rights reserved. Copyright © 2014 by the Schaffner Group. No part of this publication may be changed in any form or by any means for any purpose without written permission from the Schaffner Group. This document may contain errors or inaccuracies, and it may be revised without advance notice. The Schaffner Group welcomes any recommendations or criticism regarding this paper. Customer feedback is always welcome as it helps us to continuously improve upon the quality of our products. If you have any comments or advice, please feel free to contact the Schaffner Group. Distribution of substantively modified versions of this document is prohibited without the explicit permission of the copyright holder. Distribution of the work or derivative of the work in any standard (paper) book form for commercial purposes are prohibited unless prior permission is obtained from the copyright holder. Copyright: Alexander Kamenka, The Schaffner Group Schaffner Group Nordstrasse 11 4542 Luterbach / Switzerland Phone +41 (0)32 681 66 26 • Fax +41 (0)32 681 66 41 Corporate website: http://www.schaffner.com Corporate email: [email protected] Six tough topics about harmonic distortion and power quality indices in electric power systems A white paper of the Schaffner Group Written by Alexander Kamenka Six tough topics about harmonic distortion and power quality indices in electric power systems
    [Show full text]