Performance Analysis of an Inverse Notch Filter and Its Application to F 0 Estimation


 Abner Holland
 2 years ago
 Views:
Transcription
1 Cicuits and Systems, 013, 4, Published Online Januay 013 ( Pefomance Analysis of an Invese Notch Filte and Its Application to F 0 Estimation Yosuke Sugiua, Aata Kawamua, Youji Iiguni Gaduate School of Engineeing Science, Osaka Univesity, Osaka, Japan Received Novembe 1, 01; evised Decembe 1, 01; accepted Decembe 9, 01 ABSTRACT In this pape, we analyze an invese notch filte and pesent its application to F 0 (fundamental fequency) estimation. The invese notch filte is a naow band pass filte and it has an infinite impulse esponse. We deive the explicit foms fo the impulse esponse and the sum of squaed impulse esponse. Based on the analysis esult, we deive a nomalized invese notch filte whose pass band aea is identical to unit. As an application of the nomalized invese notch filte, we popose an F 0 estimation method fo a musical sound. The F 0 estimation method is achieved by connecting the nomalized invese notch filtes in paallel. Estimation esults show that the poposed F 0 estimation method effectively detects F 0 s fo piano sounds in a midange. Keywods: Band Pass Filte; Invese Notch Filte; Impulse Response Analysis 1. Intoduction In speech pocessing, image pocessing, biomedical signal pocessing, and many othe signal pocessing fields, it is impotant to eliminate the naowband signal. The examples of the naowband signal ae a hum noise fom the powe supply, an acoustic feedback, and an intefeeence noise, and so on. A notch filte is useful fo the elimination of the naowband signal [17], whee the notch filte passes all fequencies expect of a stop fequency band centeed on a cente fequency, called as the notch fequency. The notch filte has a simple stuctue, and its stop bandwidth and its notch fequency ae individually designed. The notch filte is used in many applications and it has been analyzed in many liteatues [1,47]. On the othe hand, an invese notch filte is a band pass filte which has the invese chaacteistics of the notch filte. In contast to the notch filte, thee ae few applications of the invese notch filte. As an example of the applications, an active noise contol system fo educing a sinusoidal noise has been poposed [8]. In this system, the invese notch filte is used to extact the sinusoidal noise. Unfotunately, the system is designed without espect to the impulse esponse of the invese notch filte. Hence, the invese notch filte cannot accuately extact the sinusoidal noise when the filte output is in the tansient state. To utilize the invese notch filte moe effectively fo not only the active noise contol system but also many othe applications, a moe detail analysis of the impulse esponse fo the invese notch filte needs to be equied. In this pape, we deive an explicit fom fo the infinite impulse esponse of the invese notch filte. Additionally, we deive an explicit fom fo the sum of the squaed impulse esponse. Then, we eveal the limit values of these two infinite sequences. Next, based on the analysis esults, we popose a nomalized notch filte whose pass band aea is adjusted to unit. The nomalized invese notch filte is efficient to estimate the output powe in the shot time such as the fame pocessing. Finally, as an application of the nomalized invese notch filte, we pesent an F 0 estimation method fo a musical sound. In the F 0 estimation method, we use multiple nomalized invese notch filtes whose pass fequencies ae identical to F 0 s fo each monophonic sound, espectively. These nomalized invese notch filtes ae connected in paallel. In the estimation pocedue, we detect F 0 fom the invese notch filte whose output powe is lagest among all the invese notch filte output powes. Fom the simulation esults, we see that the poposed F 0 estimation method can effectively detect the F 0 both of fo the monophonic sounds and the polyphonic sounds.. Pefomance Analysis of Invese Notch Filte In this section, we explain both of the notch filte and the invese notch filte, whee the latte filte has an invese chaacteistic of the notch filte. The notch filte passes all fequencies expect of the naow fequency band centeed on the notch fequency. The stop bandwidth and the Copyight 013 SciRes.
2 118 Y. SUGIURA ET AL. notch fequency can be individually designed [17]. The seveal stuctues of the notch filte have been poposed and all of them can be tansfomed to the invese notch filte. In this pape, we use the stuctue of the notch filte poposed in [35], since the invese notch filte can be simply obtained fom the notch filte s tansfe function. The tansfe function of the notch filte N z is given by 1 1 z z Nz 1 1, (1) 1 z z whee is a paamete to design the notch fequency and 1 1 is the stop bandwidth paamete. The notch fequency paamete is given by F 1 cosπ, () FS F Hz denotes the notch fequency and F Hz whee S denotes the sampling fequency. When we put the stop bandwidth as K Hz, the elational expession of and K is epesented as K FSsin πk FS K F sin πk F 1cos π. (3) 1 cos π S Fom (1), we can deive the invese notch filte epesented as 1 1z Iz1Nz, (4) 1 1 z z whee the I z is the tansfe function of the invese notch filte. We see fom (4) that the invese notch filte is vey easy to implement. Note that the pass bandwidth paamete is also given as (3), whee K denotes the pass bandwidth. Figue 1 shows the stuctue of the invese notch filte, whee xn is the input signal, y n is the output signal, and un is the signal obtained fom the IIR unit within the invese notch filte. We see fom this figue that the invese notch filte equies only thee multiplications and thee additions to calculate the output signal. Figue shows the fequency amplitude esponse of I z when 0F FS with = 0.8, 0.9, 0.99, whee the vetical axis denotes the amplitude and the hoizontal axis denotes the nomalized fequency. We see fom Figue that the amplitude at the notch fequency is 1 egadless of, and the pass bandwidth becomes naow with inceasing Figue 1. Stuctue of invese notch filte. Copyight 013 SciRes. S Figue. Powe spectum of the invese notch filte. towad to 1, i.e., we can accuately extact a single sinusoidal signal by setting extemely close to 1. When filteing an input signal, one of the most impotant factos is the impulse esponse of the filte. We fistly deive the impulse esponse of the invese notch filte as an explicit fomulation. We see fom () o Figue 1 that the signal y n and un ae given as 1 yn unun (5) with 1 u n x n u n u n. (6) To obtain the impulse esponse, we put the input signal as the impulse signal epesented as n x n n, (7) whee is the Konecke s delta. In this case, (6) can be epesented as the following equation u n u n1 u n 0, (8) whee n. Solving the above homogeneous equation with espect to un and intoducing the initial condition that u 0 1 and u 1, we obtain the solution expessed as n1 un sin n1, (9) p p 4, (10) p actan. (11) We assume that 4. Note that this assumption is satisfied when 1. By substituting (9) into (5), we obtain the impulse esponse of the invese notch filte h n n expessed as yn h n xn n n1 n n 1 sin sin. p (1) Fom (1), we see that the impulse esponse becomes n 1 close to 0 with inceasing n due to the tem. When 0, 0, we also have h 0 and h 1 un n
3 Y. SUGIURA ET AL. 119 epesented as h n n h , (13) 1 h 1. (14) Next, we fomulate the sum of squaed impulse esponse to evaluate its convegence popety. Taking squae of (1), the squaed impulse esponse is obtained as p n1 h n p Re p j 1 1 e n j n1 whee we use the following elation 1 e, (15) cos 1 p. (16) The above elation is deived fom (10) and (11). Using (13), (14), and (15), the sum of the squaed impulse esponse J n is epesented as whee 1 1 n J n h m 4 4 m n 1 1 qcn, p 1 q, (18) (17) c n 1 cos n cos n1. (19) Fom (17), we easily obtain the limit value of with n as J n 1 lim Jn. (0) n The sum of the squaed impulse esponse J n conveges to the constant which is depending on the pass bandwidth paamete. Fom Paseval s theoem, we see that (0) is identical to the sum of the squaed fequency esponse. Note that (0) also shows the pass band aea of the invese notch filte, since its fequency esponses ae almost zeo expect of the pass band. Figue 3 shows the actual convegence popeties fo the sum of the squaed impulse esponse with = 0.8, 0.9, 0.99, whee the solid line denotes the sum of the squaed impulse esponse and the dashed line denotes the theoetical limit calculated fom (0). The hoizontal axis denotes sample numbe. We see fom Figue 3 that the sum of the squaed impulse esponse conveged to each theo etical limit. Also we see that convegence speed becomes fast with deceasing. In the audio signal pocessing, the invese notch filte is often utilized fo measuing a naowband fequency powe which is coesponding to the invese notch filte s output powe. Howeve, the pass band aea of the invese notch filte depends on the paamete as shown in (0), and thus the output powe also depends on. Hence, it is difficult to evaluate the invese notch filte s output powe when thee exist multiple invese notch filtes which have diffeent s. To solve this poblem, we deive a nomalized invese notch filte whose output powe is faily available independently with. Since the output powe is actually calculated in a shot fame length, we have to establish the nomalized invese notch filte by taking into account the fame length. The sum of the squaed output signal is given by L1 V L y n n1 L1 n n n0 m0 l0 h m h l x nm x nl whee L is the fame length. Hee, we conside the case that the obseved signal xn is a white noise whose mean value and vaiance ae 0 and N, especttively. Taking the expectation value of (1), we have L1 n L1 n N N E V L h m J n n0 m0 n0 m0 Substituting (17) into () gives whee L1 EV L N p 1 L q L, dl, (1). () (3) d cos 4 cos L. (4) L The white noise has the same magnitude fo all fequencies. Thus, it is desiable that the sum of the squaed Figue 3. Convegence popety fo sum of squaed impulse esponse. Copyight 013 SciRes.
4 10 Y. SUGIURA ET AL. output signal of the invese notch filte is always constant egadless of the values of,, L. Howeve, as shown in (3), the expectation value of V Lstongly depends on the espective values. To solve this poblem, we popose the following nomalized invese notch filte. I z I z EV L 1 1z. 1 EVL 1 z z (5) The above nomalized invese notch filte adjusts the total pass band aea in L samples to unit. Figue 4 shows the stuctue of the nomalized invese notch filte, whee y n denotes its output signal. Compaing Figue 4 with Figue 1, we see that the diffeence is only one multiplie s value. Hence, the computational complexities of those filtes ae the same. To confim the popety of the nomalized invese notch filte, we caied out a simulation. In this simulation, the capability of the nomalized invese notch filte was compaed with the geneal invese notch filte shown in (4). We pepaed fou filtes which designed by diffeent paametes. The paamete setting is summaized in Table 1. We used white noise as the obseved signal, whee its mean and vaiance ae 0 and N 1. Figue 5 shows EV L fo fame length L, whee denotes the aveage value of V L in 1000 simulations and the solid line denotes the theoetical value calculated by (3). In this figue, the hoizontal axis de Figue 4. Stuctue of nomalized invese notch filte. notes fame length. We see that the each invese notch filte I gave diffeent cuves of m EV L due to the diffeent paamete setting. In this case, it is not easy to evaluate the elation between filte output powes. Figue 6 shows the esult of the nomalized invese notch filte I m. We see that all the obtained EV L ae unit fo evey fame length. Hence, we can evaluate the elation between the output powe egadless of the values of,, L. 3. Application to F 0 Estimation In this section, as an application of the nomalized invese notch filte, we pesent an F 0 estimation method fo musical signal. Hee, we assume that the music signal consists of the F 0 fequency and its hamonics, and the amplitude of F 0 fequency is geate than othe fequency amplitudes. We epesent the F 0 of the music signal such as P, whee i denotes an octave numbe and j denotes a pitch name numbe, e.g., the pitch 440 Hz is epesented as P 4,10. The estimating pitch ange is set to P3,9 P5,3, whee a piano sound in this fequency ange has the maximum amplitude at its F 0 fequency. We set the notch fequency of the nomalized invese notch filte to coespond to the pitch P. Then, the i, jth nomalized invese notch filte is epesented as 1 1 z I z, (6) 1 EVL 1 z z 1 cosπp F, (7) S and whee ae the notch fequency paamete and the pass bandwidth paamete fo I z, espectively. To eliminate ovelap with the neighbohood pass bandwidth of I z, we design the pass bandwidth paamete as K FS K FS K FS K FS 1cos π sin π 1 cos π sin π K P Pi 1,1, j 1 Pi, j Pi, j1,othewise, (8) Figue 5. Sum of squaed output signal of invese notch filte output. Table 1. Paametes fo nomalized invese notch filte. Filtes I, I 1 1 I, I I, I 3 3 I, I 4 4 Paametes Figue 6. Sum of squaed output signal of nomalized invese notch filte. Copyight 013 SciRes.
5 Y. SUGIURA ET AL. 11 Hee, we designed the pass bandwidth as the ange fom its notch fequency to one of the lowe neighboing notch fequency. The poposed F 0 estimato is achieved by connecting the designed nomalized invese notch filtes I z in paallel. The F 0 estimato is shown in Figue 7, whee y n denotes the output signal of I z. The estimation pocedue is the follows: Fist, we calculate V L defined in (1) fo each I z. We then detect the nomalized invese notch filte whose V L is lagest among all of filtes. Its filte numbe i and j diectly gives the fist F 0 estimate as P. Next, we emove the nomalized invese notch filte fo Pki, j k which is coesponding to hamonics of P. Repeating the above estimation pocedue gives the second and latte F 0 estimates. The epetition of the estimation pocess is finished when all the esidual V L s ae smalle than the theshold. We caied out simulations to confim the capability of the poposed F 0 estimato. In the simulations, we set the sampling fequency FS 10 khz, and the fame length L = 100 (=10 [ms]). We empiically set the theshold T to As the fist simulation, we caied out the F 0 estimation fo the monophonic sound which was played with a electonic piano. Figue 8 shows the wavefom of the input signal and the estimation esult, whee the tue octave numbe i and pitch numbe j ae displayed on the wavefom as i, j. We plotted the estimated F 0 as the thick black line. Fom the esult, we see that the F 0 estimation method can accuately estimate the F 0 of the obseved signal, although some eos occued in the keystoke. Additionally, we caied out the simulation fo the same monophonic signal with a white noise. The estimation esult shows in Figue 9. We see fom the figue that the F 0 estimation method can obustly estimate the F 0 unde the noisy envionment as accuately as unde the envionment without noise. As the second simulation, we caied out the F 0 estimation fo the polyphonic sound. The polyphonic sound P P P4.3, P5,3 contains the octave note 4.1, 5,1 and which ae known as a difficult combination to sepaately detect. Figue 10 shows the estimation esult. We see fom the figue that the F 0 estimation method can estimate the F 0 although thee also exist some eos at the keystoke. Especially, the poposed method can detect F 0 fo the octave note. Fom these esults, we confimed the nomalized invese notch filte is efficiently fo F 0 estimation. Figue 7. Stuctue of F 0 estimation method. Figue 9. Simulation esult fo noisy monophonic sound. Figue 8. Simulation esult fo monophonic sound. Figue 10. Simulation esult fo polyphonic sound. Copyight 013 SciRes.
6 1 Y. SUGIURA ET AL. 4. Conclusion In this pape, we analyzed the invese notch filte and deived the explicit foms fo the impulse esponse and the sum of squaed impulse esponse. Based on the analysis esult, we deived a nomalized invese notch filte whose pass band aea is identical to unit to evaluate the output powes between the multiple invese notch filtes which have diffeent paametes. Moeove, we established an F 0 estimato by connecting the nomalized invese notch filtes in paallel. Estimation esults showed that the poposed F 0 estimato effectively detects F 0 s fo electonic piano sound in a midange. REFERENCES [1] A. Nehoai, A Minimal Paamete Adaptive Notch Filte with Constained Poles and Zeos, IEEE Tansactions on Acoustics, Speech and Signal Pocessing, Vol. 33, No. 4, 1985, pp doi: /tassp [] H. C. Chong and U. L. Sang, Adaptive Line Enhancement by Using an IIR Lattice Notch Filte, IEEE Tansactions on Acoustics, Speech and Signal Pocessing, Vol. 37, No. 4, 1989, pp doi: / [3] C. C. Tseng and S. C. Pei, IIR Multiple Notch Filte Design Base on Allpass Filte, IEEE Tansactions on Cicuits and Systems II: Analog and Digital Signal Pocessing, Vol. 44, No., 1997, pp [4] S. C. Pei, W. S. Lu and C. C. Tseng, Analytical Two Dimensional IIR Notch Filte Design Using Oute Poduct Expansion, IEEE Tansactions on Cicuits and Systems II: Analog and Digital Signal Pocessing, Vol. 44, No. 9, 1997, pp [5] Y. V. Joshi and S. C. D. Roy, Design of IIR Multiple Notch Filtes Based on AllPass Filtes, IEEE Tansactions on Cicuits and Systems II: Analog and Digital Signal Pocessing, Vol. 46, No., 1999, pp [6] M. Goto, A RealTime MusicSceneDesciption System: PedominantF 0 Estimation fo Detecting Melody and Bass Lines in RealWold Audio Signals, Speech Communication, Vol. 43, No. 4, 004, pp doi: /j.specom [7] V. DeBunne, An Adaptive, HighOde, Notch Filte Using All Pass Sections, IEEE Intenational Confeence on Acoustics, Speech and Signal Pocessing, Vol. 3, Seattle, 115 May 1998, pp [8] Y. Xiao, A New Efficient Naowband Active Noise Contol System and Its Pefomance Analysis, IEEE Tansactions on Audio, Speech, and Language Pocessing, Vol. 19, No. 7, 011, pp doi: /tasl Copyight 013 SciRes.
Lesson 2 Power Factor Improvement, Harmonic Reduction, Filter
Lesson 2 Powe Facto Impovement, Hamonic Reduction, Filte 1. Powe Facto Impovement Fo phasecontolled opeation in both single phase full wave half and full contolled bidge convetes, the displacement facto
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationInfinitedimensional Bäcklund transformations between isotropic and anisotropic plasma equilibria.
Infinitedimensional äcklund tansfomations between isotopic and anisotopic plasma equilibia. Infinite symmeties of anisotopic plasma equilibia. Alexei F. Cheviakov Queen s Univesity at Kingston, 00. Reseach
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationSTABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION
Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationAn Epidemic Model of Mobile Phone Virus
An Epidemic Model of Mobile Phone Vius Hui Zheng, Dong Li, Zhuo Gao 3 Netwok Reseach Cente, Tsinghua Univesity, P. R. China zh@tsinghua.edu.cn School of Compute Science and Technology, Huazhong Univesity
More informationLINES AND TANGENTS IN POLAR COORDINATES
LINES AND TANGENTS IN POLAR COORDINATES ROGER ALEXANDER DEPARTMENT OF MATHEMATICS 1. Polacoodinate equations fo lines A pola coodinate system in the plane is detemined by a point P, called the pole, and
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationCIRCUITS LABORATORY EXPERIMENT 7
CIRCUITS LABORATORY EXPERIMENT 7 Design of a Single Tansisto Amplifie 7. OBJECTIVES The objectives of this laboatoy ae to: (a) Gain expeience in the analysis and design of an elementay, single tansisto
More informationChapter 6. GraduallyVaried Flow in Open Channels
Chapte 6 GaduallyVaied Flow in Open Channels 6.. Intoduction A stea nonunifom flow in a pismatic channel with gadual changes in its watesuface elevation is named as gaduallyvaied flow (GVF). The backwate
More informationRain Attenuation Impact on Performance of Satellite Ground Stations for Low Earth Orbiting (LEO) Satellites in Europe
Int. J. Communications, Netwok and System Sciences, 2009, 6, 480485 doi:10.4236/ijcns.2009.26052 Published Online Septembe 2009 (http://www.scirp.og/jounal/ijcns/). Rain Attenuation Impact on Pefomance
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationIntroduction to Electric Potential
Univesiti Teknologi MARA Fakulti Sains Gunaan Intoduction to Electic Potential : A Physical Science Activity Name: HP: Lab # 3: The goal of today s activity is fo you to exploe and descibe the electic
More informationSolutions to Homework Set #5 Phys2414 Fall 2005
Solution Set #5 1 Solutions to Homewok Set #5 Phys414 Fall 005 Note: The numbes in the boxes coespond to those that ae geneated by WebAssign. The numbes on you individual assignment will vay. Any calculated
More informationA Study on the Conducted Interference of Capacitor Charging Power Supply
Enegy and Powe Engineeing, 13, 5, 11341138 doi:1.436/epe.13.54b16 Published Online July 13 (http://www.scip.og/jounal/epe) A Study on the Conducted Inteeence o Capacito Chaging Powe Supply Xiao Han 1,
More informationTracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors
Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg
More informationSimple Harmonic Motion
Simple Hamonic Motion Intoduction Simple hamonic motion occus when the net foce acting on an object is popotional to the object s displacement fom an equilibium position. When the object is at an equilibium
More information9. Mathematics Practice Paper for Class XII (CBSE) Available Online Tutoring for students of classes 4 to 12 in Physics, Chemistry, Mathematics
Available Online Tutoing fo students of classes 4 to 1 in Physics, 9. Mathematics Class 1 Pactice Pape 1 3 1. Wite the pincipal value of cos.. Wite the ange of the pincipal banch of sec 1 defined on the
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationSmart Antenna Array Calibration Procedure Including Amplitude and Phase Mismatch and Mutual Coupling Effects
Smat Antenna Aay alibation Pocedue Including Amplitude and Phase Mismatch and Mutual oupling Effects Kapil R. Dandeka, Hao Ling, and Guanghan Xu Univesity of Texas at Austin, Dept. of Elec. And omp. Eng.
More informationEXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN ROOF OF A CAR
EXPERIENCE OF USING A CFD CODE FOR ESTIMATING THE NOISE GENERATED BY GUSTS ALONG THE SUN ROOF OF A CAR Liang S. Lai* 1, Geogi S. Djambazov 1, Choi H. Lai 1, Koulis A. Peicleous 1, and Fédéic Magoulès
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495499, 2013 ISSN 18184952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationUSB True Emulation for KVM Switches. Transparent and reliable USB KVM switching technology.
Tanspaent and eliable KVM switching technology. 0118 7247465500 965 6000 www.blackbox.co.uk blackbox.com Table of Contents Intoduction... 3 Enumeated Switching... 4 Emulated Switching... 5 Tue Emulation...
More informationData Center Demand Response: Avoiding the Coincident Peak via Workload Shifting and Local Generation
(213) 1 28 Data Cente Demand Response: Avoiding the Coincident Peak via Wokload Shifting and Local Geneation Zhenhua Liu 1, Adam Wieman 1, Yuan Chen 2, Benjamin Razon 1, Niangjun Chen 1 1 Califonia Institute
More informationMultiband Microstrip Patch Antenna for Microwave Applications
IOSR Jounal of Electonics and Communication Engineeing (IOSRJECE) ISSN: 22782834, ISBN: 22788735. Volume 3, Issue 5 (Sep.  Oct. 2012), PP 4348 Multiband Micostip Patch Antenna fo Micowave Applications
More informationLecture 16: Color and Intensity. and he made him a coat of many colours. Genesis 37:3
Lectue 16: Colo and Intensity and he made him a coat of many colous. Genesis 37:3 1. Intoduction To display a pictue using Compute Gaphics, we need to compute the colo and intensity of the light at each
More informationPower and Sample Size Calculations for the 2Sample ZStatistic
Powe and Sample Size Calculations fo the Sample ZStatistic James H. Steige ovembe 4, 004 Topics fo this Module. Reviewing Results fo the Sample Z (a) Powe and Sample Size in Tems of a oncentality Paamete.
More informationProblems on Force Exerted by a Magnetic Fields from Ch 26 T&M
Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuentcaying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More information(a) The centripetal acceleration of a point on the equator of the Earth is given by v2. The velocity of the earth can be found by taking the ratio of
Homewok VI Ch. 7  Poblems 15, 19, 22, 25, 35, 43, 51. Poblem 15 (a) The centipetal acceleation of a point on the equato of the Eath is given by v2. The velocity of the eath can be found by taking the
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationModal Characteristics study of CEM1 SingleLayer Printed Circuit Board Using Experimental Modal Analysis
Available online at www.sciencediect.com Pocedia Engineeing 41 (2012 ) 1360 1366 Intenational Symposium on Robotics and Intelligent Sensos 2012 (IRIS 2012) Modal Chaacteistics study of CEM1 SingleLaye
More information12.1. FÖRSTER RESONANCE ENERGY TRANSFER
ndei Tokmakoff, MIT epatment of Chemisty, 3/5/8 11 1.1. FÖRSTER RESONNCE ENERGY TRNSFER Föste esonance enegy tansfe (FR) efes to the nonadiative tansfe of an electonic excitation fom a dono molecule to
More informationTheory and practise of the gindex
Theoy and pactise of the gindex by L. Egghe (*), Univesiteit Hasselt (UHasselt), Campus Diepenbeek, Agoalaan, B3590 Diepenbeek, Belgium Univesiteit Antwepen (UA), Campus Die Eiken, Univesiteitsplein,
More informationTiming Synchronization in High Mobility OFDM Systems
Timing Synchonization in High Mobility OFDM Systems Yasamin Mostofi Depatment of Electical Engineeing Stanfod Univesity Stanfod, CA 94305, USA Email: yasi@wieless.stanfod.edu Donald C. Cox Depatment of
More informationSamples of conceptual and analytical/numerical questions from chap 21, C&J, 7E
CHAPTER 1 Magnetism CONCEPTUAL QUESTIONS Cutnell & Johnson 7E 3. ssm A chaged paticle, passing though a cetain egion of space, has a velocity whose magnitude and diection emain constant, (a) If it is known
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationRisk Sensitive Portfolio Management With CoxIngersollRoss Interest Rates: the HJB Equation
Risk Sensitive Potfolio Management With CoxIngesollRoss Inteest Rates: the HJB Equation Tomasz R. Bielecki Depatment of Mathematics, The Notheasten Illinois Univesity 55 Noth St. Louis Avenue, Chicago,
More informationDesign and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor
Euopean Symposium on Compute Aded Aided Pocess Engineeing 15 L. Puigjane and A. Espuña (Editos) 25 Elsevie Science B.V. All ights eseved. Design and Analysis of a Classical Contolle to the Residual Oil
More informationReduced Pattern Training Based on Task Decomposition Using Pattern Distributor
> PNN05P762 < Reduced Patten Taining Based on Task Decomposition Using Patten Distibuto ShengUei Guan, Chunyu Bao, and TseNgee Neo Abstact Task Decomposition with Patten Distibuto (PD) is a new task
More informationCHAPTER 10 Aggregate Demand I
CHAPTR 10 Aggegate Demand I Questions fo Review 1. The Keynesian coss tells us that fiscal policy has a multiplied effect on income. The eason is that accoding to the consumption function, highe income
More informationResearch on Risk Assessment of the Transformer Based on Life Cycle Cost
ntenational Jounal of Smat Gid and lean Enegy eseach on isk Assessment of the Tansfome Based on Life ycle ost Hui Zhou a, Guowei Wu a, Weiwei Pan a, Yunhe Hou b, hong Wang b * a Zhejiang Electic Powe opoation,
More informationOPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS
OPERATIONAL CHARACTERISTICS OF BRUSHLESS DC MOTORS Ronald De Fou Depatment of Electical & Compute Engineeing, The Univesity of the West Indies St. Augustine, Tinidad defou@eng.uwi.tt Emily Ramouta Univesity
More informationFinancing Terms in the EOQ Model
Financing Tems in the EOQ Model Habone W. Stuat, J. Columbia Business School New Yok, NY 1007 hws7@columbia.edu August 6, 004 1 Intoduction This note discusses two tems that ae often omitted fom the standad
More informationExcitation energies for molecules by TimeDependent. based on Effective Exact Exchange KohnSham potential
Excitation enegies fo molecules by TimeDependent DensityFunctional Theoy based on Effective Exact Exchange KohnSham potential Fabio Della Sala National Nanotechnology Laboatoies Lecce Italy A. Göling
More information2.2. Trigonometric Ratios of Any Angle. Investigate Trigonometric Ratios for Angles Greater Than 90
. Tigonometic Ratios of An Angle Focus on... detemining the distance fom the oigin to a point (, ) on the teminal am of an angle detemining the value of sin, cos, o tan given an point (, ) on the teminal
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationSIMULATION OF GAS TURBINES OPERATING IN OFFDESIGN CONDITION
SIMULAION OF GAS URBINES OPERAING IN OFFDESIGN CONDIION Analdo Walte: awalte@fem.unicamp.b Univesity of Campinas Dept. of Enegy DE/FEM/Unicamp P.O. Box 6122  ZIP code 13083970  Bazil Abstact. In many
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationModelling and Simulation of Four Quadrant Operation of Three Phase Brushless DC Motor With Hysteresis Current Controller
ISSN (Pint) : 30 375 Vol., Issue, June 03 Modelling and Simulation of Fou Quadant Opeation of Thee Phase Bushless DC Moto With Hysteesis Cuent Contolle Sanita C S, J T Kuncheia PG Student [IDAC], Dept.
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationAlternative Formulas for Rating Prediction Using Collaborative Filtering
Altenative Fomulas fo Rating Pediction Using Collaboative Filteing Ama Saic, Misad Hadziadic, David Wilson College of Computing and Infomatics The Univesity of Noth Caolina at Chalotte, 901 Univesity City
More information1.4 Phase Line and Bifurcation Diag
Dynamical Systems: Pat 2 2 Bifucation Theoy In pactical applications that involve diffeential equations it vey often happens that the diffeential equation contains paametes and the value of these paametes
More informationSUPPORT VECTOR MACHINE FOR BANDWIDTH ANALYSIS OF SLOTTED MICROSTRIP ANTENNA
Intenational Jounal of Compute Science, Systems Engineeing and Infomation Technology, 4(), 20, pp. 677 SUPPORT VECTOR MACHIE FOR BADWIDTH AALYSIS OF SLOTTED MICROSTRIP ATEA Venmathi A.R. & Vanitha L.
More informationmv2. Equating the two gives 4! 2. The angular velocity is the angle swept per GM (2! )2 4! 2 " 2 = GM . Combining the results we get !
Chapte. he net foce on the satellite is F = G Mm and this plays the ole of the centipetal foce on the satellite i.e. mv mv. Equating the two gives = G Mm i.e. v = G M. Fo cicula motion we have that v =!
More informationExponentially Weighted Moving Average Charts for Monitoring the Process Generalized Variance
Geogia Southen Univesity Digital Commons@Geogia Southen Electonic Theses & Dissetations Jack N Aveitt College of Gaduate Studies COGS Summe 014 Exponentially Weighted Moving Aveage Chats fo Monitoing the
More informationExperiment MF Magnetic Force
Expeiment MF Magnetic Foce Intoduction The magnetic foce on a cuentcaying conducto is basic to evey electic moto  tuning the hands of electic watches and clocks, tanspoting tape in Walkmans, stating
More informationArithmetics with Fuzzy Numbers: a Comparative Overview
Aithmetics with Fuzzy Numbes: a Compaative Oveview János Fodo John von Neumann Faculty of Infomatics, Budapest Tech Bécsi út 96/B, H34 Budapest, Hungay email: fodo@bmf.hu Banabás Bede Depatment of Mechanical
More informationComplex Envelope Vectorization for the solution of midhigh frequency acoustic problems. A. Sestieri
Complex Envelope Vectoization fo the solution of midhigh fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout  Low fequency
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationSkills Needed for Success in Calculus 1
Skills Needed fo Success in Calculus Thee is much appehension fom students taking Calculus. It seems that fo man people, "Calculus" is snonmous with "difficult." Howeve, an teache of Calculus will tell
More informationA LineStructurePreserving Approach to Image Resizing
A LineStuctuePeseving Appoach to Image Resizing CheHan Chang YungYu Chuang National Taiwan Univesity Email:fank@cmlab.csie.ntu.edu.tw, cyy@csie.ntu.edu.tw Abstact This pape poposes a contentawae image
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More informationEAS Groundwater Hydrology Lecture 13: Well Hydraulics 2 Dr. Pengfei Zhang
EAS 44600 Goundwate Hydology Lectue 3: Well Hydaulics D. Pengfei Zhang Detemining Aquife Paametes fom TimeDawdown Data In the past lectue we discussed how to calculate dawdown if we know the hydologic
More informationThe Detection of Obstacles Using Features by the Horizon View Camera
The Detection of Obstacles Using Featues b the Hoizon View Camea Aami Iwata, Kunihito Kato, Kazuhiko Yamamoto Depatment of Infomation Science, Facult of Engineeing, Gifu Univesit aa@am.info.gifuu.ac.jp
More informationNontrivial lower bounds for the least common multiple of some finite sequences of integers
J. Numbe Theoy, 15 (007), p. 393411. Nontivial lowe bounds fo the least common multiple of some finite sequences of integes Bai FARHI bai.fahi@gmail.com Abstact We pesent hee a method which allows to
More informationUNIVERSIDAD DE CANTABRIA TESIS DOCTORAL
UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de
More informationThe Critical Angle and Percent Efficiency of Parabolic Solar Cookers
The Citical Angle and Pecent Eiciency o Paabolic Sola Cookes Aiel Chen Abstact: The paabola is commonly used as the cuve o sola cookes because o its ability to elect incoming light with an incoming angle
More information81 Newton s Law of Universal Gravitation
81 Newton s Law of Univesal Gavitation One of the most famous stoies of all time is the stoy of Isaac Newton sitting unde an apple tee and being hit on the head by a falling apple. It was this event,
More informationProblems of the 2 nd International Physics Olympiads (Budapest, Hungary, 1968)
Poblems of the nd ntenational Physics Olympiads (Budapest Hungay 968) Péte Vankó nstitute of Physics Budapest Univesity of Technical Engineeing Budapest Hungay Abstact Afte a shot intoduction the poblems
More informationTrading Volume and Serial Correlation in Stock Returns in Pakistan. Abstract
Tading Volume and Seial Coelation in Stock Retuns in Pakistan Khalid Mustafa Assistant Pofesso Depatment of Economics, Univesity of Kaachi email: khalidku@yahoo.com and Mohammed Nishat Pofesso and Chaiman,
More informationTransformations in Homogeneous Coordinates
Tansfomations in Homogeneous Coodinates (Com S 4/ Notes) YanBin Jia Aug, 6 Homogeneous Tansfomations A pojective tansfomation of the pojective plane is a mapping L : P P defined as u a b c u au + bv +
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationUNIVERSITY OF CANTABRIA
Failue Assessment Diagam  Cack Diving Foce Diagam COMPATIBILITY UNIVERSITY OF CANTABRIA Novembe 1997 J. Ruiz Ocejo F. GutiéezSolana M.A. GonzálezPosada I. Goochategui Depatamento de Ciencia e Ingenieía
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationRadio frequency dielectric properties of limestone and sandstone from Ewekoro, Eastern Dahomey Basin
Available online at www.pelagiaeseachlibay.com Pelagia Reseach Libay Advances in Applied Science Reseach, 213, 4(6):15158 ISSN: 976861 CODEN (USA): AASRFC Radio fequency dielectic popeties of limestone
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationContinuous Compounding and Annualization
Continuous Compounding and Annualization Philip A. Viton Januay 11, 2006 Contents 1 Intoduction 1 2 Continuous Compounding 2 3 Pesent Value with Continuous Compounding 4 4 Annualization 5 5 A Special Poblem
More informationSupplementary Material for EpiDiff
Supplementay Mateial fo EpiDiff Supplementay Text S1. Pocessing of aw chomatin modification data In ode to obtain the chomatin modification levels in each of the egions submitted by the use QDCMR module
More informationON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION
ON NEW CHALLENGES FOR CFD SIMULATION IN FILTRATION Michael Dedeing, Wolfgang Stausbeg, IBS Filtan, Industiestasse 19 D51597 MosbachLichtenbeg, Gemany. Oleg Iliev(*), Zaha Lakdawala, Faunhofe Institut
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationLearning Objectives. Decreasing size. ~10 3 m. ~10 6 m. ~10 10 m 1/22/2013. Describe ionic, covalent, and metallic, hydrogen, and van der Waals bonds.
Lectue #0 Chapte Atomic Bonding Leaning Objectives Descibe ionic, covalent, and metallic, hydogen, and van de Waals bonds. Which mateials exhibit each of these bonding types? What is coulombic foce of
More informationAutomatic Closed Caption Detection and Filtering in MPEG Videos for Video Structuring
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, 1145116 (006) Automatic Closed Caption Detection and Filteing in MPEG Videos fo Video Stuctuing Depatment of Compute Science and Infomation Engineeing National
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationManual ultrasonic inspection of thin metal welds
Manual ultasonic inspection of thin metal welds Capucine Capentie and John Rudlin TWI Cambidge CB1 6AL, UK Telephone 01223 899000 Fax 01223 890689 Email capucine.capentie@twi.co.uk Abstact BS EN ISO 17640
More informationPredictive Control of Permanent Magnet Synchronous Motor Based on Optimization Model Algorithmic Control
Pedictive Contol of Pemanent Magnet Synchonous Moto Based on Optimization Model Algoithmic Contol 1 Chen Junshuo, 2 Liu Jinglin, 3 Zhang Ying *1, Chen Junshuo School of Automation, Nothwesten Ploytechnical
More information867 Product Transfer and Resale Report
867 Poduct Tansfe and Resale Repot Functional Goup ID=PT Intoduction: This X12 Tansaction Set contains the fomat and establishes the data contents of the Poduct Tansfe and Resale Repot Tansaction Set (867)
More informationChapter 13 Gravitation. Problems: 1, 4, 5, 7, 18, 19, 25, 29, 31, 33, 43
Chapte 13 Gavitation Poblems: 1, 4, 5, 7, 18, 19, 5, 9, 31, 33, 43 Evey object in the univese attacts evey othe object. This is called gavitation. We e use to dealing with falling bodies nea the Eath.
More informationProblem Set # 9 Solutions
Poblem Set # 9 Solutions Chapte 12 #2 a. The invention of the new highspeed chip inceases investment demand, which shifts the cuve out. That is, at evey inteest ate, fims want to invest moe. The incease
More information