DOCSLIB.ORG

Spectral Analysis Oftremor

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Spectral Analysis Oftremor 976 Journal ofNeurology, Neurosurgery, and Psychiatry 1990;53:976-981 J Neurol Neurosurg Psychiatry: first published as 10.1136/jnnp.53.11.976 on 1 November 1990. Downloaded from Spectral analysis of tremor: understanding the results Michael Gresty, David Buckwell Abstract Nature of the tremor record: amplitude and Spectral analysis of a tremor record can frequency modulation sometimes produce a spectrum with Tremor is an approximately sinusoidal oscilla- multiple components of significant tion of a part of the body. The amplitude of amplitude. The problem is to determine the oscillation may fluctuate and this is whether the presence of several peaks termed amplitude modulation "AM". The represents the coexistence of separate frequency of the oscillation also varies. This is tremor mechanisms or be a consequence termed frequency jitter in physiology but here of fluctuations in the frequency or we will use the universal term frequency amplitude of a single tremor. The spec- modulation "FM". The tremor waveform trum of a tremor whose frequency or may be distorted, "harmonic distortion", amplitude vary and are independent has which arises, in part, because of mechanical the recognisable pattern of a central factors, and in part reflects the specific inten- carrier frequency with sidebands of sity and sequence in Wvhich various muscles equal amplitudes distributed sym- are activated during the tremor cycle. These metrically around the carrier. However, characteristics are illustrated in fig 1 showing if tremor amplitude and frequency the tremor in flexion/extension of the out- fluctuate and are not independent, stretched hand in a subject with essential (frequency proportional to amplitude or tremor. The AM, FM and harmonic distor- frequency inversely proportional to tion of tremor may vary in an unlimited num- amplitude), the spectrum has a pattern ber of ways; thus for example, the amplitude of sidebands which are asymmetrical may vary in a predictable way, waxing and in amplitudes and may resemble the waning at regular intervals ("spindling"); it spectrum of the combined signal from may maintain an almost constant level or different independent oscillators. The fluctuate randomly, or according to some investigation of sidebands in spectra has combination of these. been neglected in tremor studies and For some tremors, frequency and amplitude multiple irregular peaks on a tremor are related as in the example of essential spectrum have sometimes been used tremor given in fig 1. The superimposed wrongly as evidence for the coexistence cycles of tremor show that as the time length of multiple tremor mechanisms or of a cycle of the tremor decreases the frequency components assumed to be amplitude also decreases; thus for this tremor, http://jnnp.bmj.com/ concurrent. amplitude is inversely proportional to frequency within certain constraints. This Medical Research characteristic of tremor has not been studied Council Human As early as 1904 Gordon Holmes recognised Movement and that individual types of tremor, such as the Balance Unit, Institute rest tremor of Parkinson's disease ofNeurology, National or Hospital, Queen cerebellar action tremor, appear to be on October 3, 2021 by guest. Protected copyright. Square, London relatively fixed in frequency and speculated M Gresty that the frequency of a tremor is specific to its D Buckwell pathophysiological origin.' In contrast to This article is dedicated to Mr Edward Trinder, Chief frequency, the amplitude of tremor and the Research Officer of the shape of the tremor are subject to wide Medical Research Council Neuro-otology Unit who fluctuations. In recent times, precise 0-1 retired in the Autumn of measurement of the characteristics of tremor, 1989. His career was marked by great kindness to staff including frequency, has become widely under his care and available through spectral analysis which has Isb cf (2nd Hs) outstanding technical contributions to been used to quantify tremor in clinical trials understanding deafness and or as the bases of arguments concerning the ............... ........................ vertigo. nature of tremor mechanisms. Unfortunately, Correspondence to: 0 25 Halz Dr Gresty, Medical Research the results of spectral analysis can be as com- Council Human Movement plicated in themselves as the raw tremor Figure 1 Accelerometric recordings and averaged and Balance Unit, Institute spectrum ofpostural tremor of the hand in a 43 year old ofNeurology, National records. We draw attention to the problems of male with essential tremor. Individual cycles of tremor Hospital, Queen Square, interpreting spectral analyses of tremor are shown superimposed by triggeringfrom an London WCIN 3BG, United records and in particular to the circumstances oscilloscope. As amplitude increases, the period of the Kingdom tremor cycle elongates. The acceleration is scaled in units Received 12 January 1990. under which multiple peaks may appear in of "g" (earth gravitationalfield). lsb: lower sideband, Accepted 10 April 1990 tremor spectra. cf: carrierfrequency, Hs: harmonics.., Spectral analysis of tremor: understanding the results 977 J Neurol Neurosurg Psychiatry: first published as 10.1136/jnnp.53.11.976 on 1 November 1990. Downloaded from "baseband signal". The spectrum of an (i) F-A (i) F-1/A amplitude modulated signal consists of a peak usb at the carrier frequency equal amplitude FM o "sidebands" which are frequency components cf cf equally spaced above and below the carrier lsb frequency. If the amplitude of the tremor varies slowly over time (implying that the baseband signal is (AM * FM) low frequency) the sidebands merge with the a -I peak of the carrier frequency as shown in fig 3. If the tremor spindles, for example fluctuates in amplitude every 2s, there are two distinct + b I sidebands in the spectrum spaced 0-5 Hz above and below the carrier frequency. This is shown in graphs a, b, c of fig 2 which are AM spectra - 180° IIfc I I derived by amplitude modulation ofthe carrier frequency and of the upper sideband and the lower sideband of the FM signal. abc Frequency modulation and FM spectra: Tremor (AM * FM) varies in frequency about a typical centre frequency termed the "carrier frequency". The way in which the frequency varies can be Figure 2 A, B Graphical representation of the described by a waveform, which can be regular frequency components offrequency and amplitude or irregular, and is termed the "baseband modulated tremor signalsforfrequency proportional to amplitude F - A andfrequency inversely proportional to signal". The spectrum of this signal consists of amplitude F - 1/A. Each of the bar pictures is a a peak at the carrier frequency of the tremor spectrum. The horizontal axis in each case represents and equal amplitude "sidebands" which are frequency. The vertical bars represent the individual terms of the Sine series which makes up a signal (see frequency components equally spaced above appendix). Thefrequency of each Sine component is and below the carrier frequency. The greater shown by its location on thefrequency axis. The the variability in frequency ofa signal, the more coefficient of each term, that is, the size of each component, is shown by the length of the bars. The sidebands are produced. For example, the positive or negative sign of the coefficient is shown by the frequency of Parkinsonian postural or rest directions of the bars; 0°for + ve and - 180° for -ve. tremor varies within narrow limits of + /- The simplest case is shown ofsinusoidalfrequency and 0-5 Hz which amplitude modulation. Frequency modulation of a produces only two important sinusoidal signal produces thefrequency components sidebands. shown in the spectra labelled "FM" where "cf' is carrier If the frequency of a tremor signal varies frequency, "usb" is upper sideband and "lsb" is lower slowly over time (implying that the baseband sideband. Amplitude modulation takes place on each of the components of thefrequency modulated signal signal is low frequency) the sidebands merge producing thefrequency components shown in spectra with the peak ofthe carrier frequency as shown labelled "AM*FM a, b, c". Thus: "a" is the spectrum of in 3. amplitude modulation of the FM carrierfrequency, "b" fig If the tremor jitters, for example, is the spectrum ofamplitude modulation of the FM lower fluctuates in frequency in two second epochs sideband and "c" is the spectrum of amplitude modulation (05 Hz), then distinct sidebands appear on the of the FM upper sideband. Note that each of these spectrum spaced 0-5 Hz above and below the http://jnnp.bmj.com/ resulting spectra have a central carrier frequency with an upper and a lower sideband. Since all these components carrier frequency giving multiple peaks in coexist the resulting signal is their algebraic sum shown in spectrum. Important to the present argument the lowest traces labelled "Z;a,b,c (AM*FM)". Bars of is that the spectra ofboth the FM signal and the equal amplitude but in opposite directions cancel when AM signal are the same except that the FM added together. Thusfor FM - AM (fig 2A) the lower sidebands of spectra a and b cancel each other. For signal has a phase shift of 1800 in the lower FM 1/AM (fig 2B) the upper sidebands of spectra a sideband. This is shown by the downwards and c cancel each other. direction of the lower sideband of the FM on October 3, 2021 by guest. Protected copyright. spectra in fig 2 (see appendix). Combined FM and AM spectra: If the and yet is of crucial importance, for interac- frequency modulation and amplitude modula- tion between amplitude and frequency can tion of a signal are unrelated then the spectrum give rise to an ambiguous spectrum. typically has numerous upper and lower side- bands symmetrical in amplitude and evenly spaced in frequency about the carrier fre- Spectral analysis of combined FM and AM quency. For the special cases where amplitude waveforms and frequency are related (an example is shown The spectra of AM and FM waveforms are in the upper raw data traces of fig 1 where explained in the appendix and shown graph- cycles of tremor with higher amplitudes have ically in fig 2.
Load more

Recommended publications
  • ETR 132 TECHNICAL August 1994 REPORT
    ETSI ETR 132 TECHNICAL August 1994 REPORT Source: EBU/ETSI JTC Reference: DTR/JTC-00011 ICS: 33.060 Key words: Broadcasting, FM, radio, transmitter, VHF European Broadcasting Union Union Européenne de Radio-Télévision EBU UER Radio broadcasting systems; Code of practice for site engineering Very High Frequency (VHF), frequency modulated, sound broadcasting transmitters ETSI European Telecommunications Standards Institute ETSI Secretariat Postal address: F-06921 Sophia Antipolis CEDEX - FRANCE Office address: 650 Route des Lucioles - Sophia Antipolis - Valbonne - FRANCE X.400: c=fr, a=atlas, p=etsi, s=secretariat - Internet: [email protected] Tel.: +33 92 94 42 00 - Fax: +33 93 65 47 16 Copyright Notification: No part may be reproduced except as authorized by written permission. The copyright and the foregoing restriction extend to reproduction in all media. © European Telecommunications Standards Institute 1994. All rights reserved. New presentation - see History box © European Broadcasting Union 1994. All rights reserved. Page 2 ETR 132: August 1994 Whilst every care has been taken in the preparation and publication of this document, errors in content, typographical or otherwise, may occur. If you have comments concerning its accuracy, please write to "ETSI Editing and Committee Support Dept." at the address shown on the title page. Page 3 ETR 132: August 1994 Contents Foreword .......................................................................................................................................................7 1 Scope
    [Show full text]
  • Maintenance of Remote Communication Facility (Rcf)
    ORDER rlll,, J MAINTENANCE OF REMOTE commucf~TIoN FACILITY (RCF) EQUIPMENTS OCTOBER 16, 1989 U.S. DEPARTMENT OF TRANSPORTATION FEDERAL AVIATION AbMINISTRATION Distribution: Selected Airway Facilities Field Initiated By: ASM- 156 and Regional Offices, ZAF-600 10/16/89 6580.5 FOREWORD 1. PURPOSE. direction authorized by the Systems Maintenance Service. This handbook provides guidance and prescribes techni- Referenceslocated in the chapters of this handbook entitled cal standardsand tolerances,and proceduresapplicable to the Standardsand Tolerances,Periodic Maintenance, and Main- maintenance and inspection of remote communication tenance Procedures shall indicate to the user whether this facility (RCF) equipment. It also provides information on handbook and/or the equipment instruction books shall be special methodsand techniquesthat will enablemaintenance consulted for a particular standard,key inspection element or personnel to achieve optimum performancefrom the equip- performance parameter, performance check, maintenance ment. This information augmentsinformation available in in- task, or maintenanceprocedure. struction books and other handbooks, and complements b. Order 6032.1A, Modifications to Ground Facilities, Order 6000.15A, General Maintenance Handbook for Air- Systems,and Equipment in the National Airspace System, way Facilities. contains comprehensivepolicy and direction concerning the development, authorization, implementation, and recording 2. DISTRIBUTION. of modifications to facilities, systems,andequipment in com- This directive is distributed to selectedoffices and services missioned status. It supersedesall instructions published in within Washington headquarters,the FAA Technical Center, earlier editions of maintenance technical handbooksand re- the Mike Monroney Aeronautical Center, regional Airway lated directives . Facilities divisions, and Airway Facilities field offices having the following facilities/equipment: AFSS, ARTCC, ATCT, 6. FORMS LISTING. EARTS, FSS, MAPS, RAPCO, TRACO, IFST, RCAG, RCO, RTR, and SSO.
    [Show full text]
  • Reception Performance Improvement of AM/FM Tuner by Digital Signal Processing Technology
    Reception performance improvement of AM/FM tuner by digital signal processing technology Akira Hatakeyama Osamu Keishima Kiyotaka Nakagawa Yoshiaki Inoue Takehiro Sakai Hirokazu Matsunaga Abstract With developments in digital technology, CDs, MDs, DVDs, HDDs and digital media have become the mainstream of car AV products. In terms of broadcasting media, various types of digital broadcasting have begun in countries all over the world. Thus, there is a demand for smaller and thinner products, in order to enhance radio performance and to achieve consolidation with the above-mentioned digital media in limited space. Due to these circumstances, we are attaining such performance enhancement through digital signal processing for AM/FM IF and beyond, and both tuner miniaturization and lighter products have been realized. The digital signal processing tuner which we will introduce was developed with Freescale Semiconductor, Inc. for the 2005 line model. In this paper, we explain regarding the function outline, characteristics, and main tech- nology involved. 22 Reception performance improvement of AM/FM tuner by digital signal processing technology Introduction1. Introduction from IF signals, interference and noise prevention perfor- 1 mance have surpassed those of analog systems. In recent years, CDs, MDs, DVDs, and digital media have become the mainstream in the car AV market. 2.2 Goals of digitalization In terms of broadcast media, with terrestrial digital The following items were the goals in the develop- TV and audio broadcasting, and satellite broadcasting ment of this digital processing platform for radio: having begun in Japan, while overseas DAB (digital audio ①Improvements in performance (differentiation with broadcasting) is used mainly in Europe and SDARS (satel- other companies through software algorithms) lite digital audio radio service) and IBOC (in band on ・Reduction in noise (improvements in AM/FM noise channel) are used in the United States, digital broadcast- reduction performance, and FM multi-pass perfor- ing is expected to increase in the future.
    [Show full text]
  • Chapter 7 Amplitude Modulation
    page 7.1 CHAPTER 7 AMPLITUDE MODULATION Transmit information-b earing message or baseband signal voice-music through a Communications Channel Baseband = band of frequencies representing the original signal for music 20 Hz - 20,000 Hz, for voice 300 - 3,400 Hz write the baseband message signal mt $ M f Communications Channel Typical radio frequencies 10 KHz ! 300 GHz write ct= A cos2f ct c ct = Radio Frequency Carrier Wave A = Carrier Amplitude c fc = Carrier Frequency Amplitude Mo dulation AM ! Amplitude of carrier wavevaries a mean value in step with the baseband signal mt st= A [1 + k mt] cos 2f t c a c Mean value A . c 31 page 7.2 Recall a general signal st= at cos[2f t + t] c For AM at = A [1 + k mt] c a t = 0 or constant k = Amplitude Sensitivity a Note 1 jk mtj < 1or [1 + k mt] > 0 a a 2 f w = bandwidth of mt c 32 page 7.3 AM Signal In Time and Frequency Domain st = A [1 + k mt] cos 2f t c a c j 2f t j 2f t c c e + e st = A [1 + k mt] c a 2 A A c c j 2f t j 2f t c c e + e st = 2 2 A k c a j 2f t c + mte 2 A k c a j 2f t c + mte 2 To nd S f use: mt $ M f j 2f t c e $ f f c j 2f t c e $ f + f c expj 2f tmt $ M f f c c expj 2f tmt $ M f + f c c A c S f = [f f +f +f ] c c 2 A k c a + [M f fc+Mf +f ] c 2 33 page 7.4 st = A [1 + k mt] cos 2f t c a c A c = [1 + k mt][expj 2f t+ expj 2f t] a c c 2 If k mt > 1, then a ! Overmo dulation ! Envelop e Distortion see Text p.
    [Show full text]
  • United States Patent [19] [11] Patent Number: 5,410,735 Borchardt Et Al
    U SOO54l0735A United States Patent [19] [11] Patent Number: 5,410,735 Borchardt et al. - [45] Date of Patent: Apr. 25, 1995 [54] WIRELESS SIGNAL TRANSMISSION 4,739,413 4/1983 Meyer - SYSTEMS, METHODS AND APPARATUS 4,771,344 9/1988 Fallacaro e141- - 4,847,903 7/1989 Schotz ................................... .. 381/3 [76] Inventors: Robert L. Borchardt, 120 E. End '. ' . ' ' Ave" New York, NY. 10028; _(L1st contlnued on next page.) _ William T. McGreevy, 43 Thompson FOREIGN PATENT DOCUMENTS Ave., Babylon, NY. 11702; Ashok _ Naw ge’ 3L7‘) 34th St.’ Apt.#3F, 0040481 2/1988 Japan .............................. .. 358/194.l Astoria, NY. 11105; Efrain L. OTHER PUBLICATIONS §°d"lf1“ez’§6; Y" “New 902-928 MHZ Band Now Open!”, Spec-Com mo yn’ ' ' Journal, Sep/Oct. 1985, cover page and p. 9. __ [21] Appl. No.: 259,339 Federal Register, vol. 50, Aug. 22, 1985, Final Rulemak . ing re addition of 902-928 MHz band to Amateur Radio [22] E169 J‘m' 13,1994 Service Rules, pp. 33937 through 33940. Related Us. Application Data (List continued on next page.) . - _ Primary Examiner—Reinhard J. Eisenzopf [63] ggéietanuation of Ser. No. 822,598, Jan. 17, 1992, aban Assistant Examiner_Andrew Faile [51] In G 6 H04B 1/00 Attorney, Agent, or Firm-Levisohn, Lerner & Berger t. > ............................................. .. [52] US. Cl. .................................... .. 455/42; 455/110; [571 ABSTRACT 455/205; 455/ 344; 455/ 351 ; 381/3 Systems, methods and apparatus are provided for con [58] Field of Search .................................. .. 455/42-43, ‘ducting local wireless audio signal transmissions from a 455/66, 95, 110-113, 120-125, 205, 208, 214, 'local audio signal source to a person within a local 344, 351, 352, 127, 343; 348/725, 731, 738; signal transmission area.
    [Show full text]
  • ELEC3027 Radio Communications Background Information on Amplitude Modulation
    ELEC3027 Radio Communications Background Information on Amplitude Modulation 1 Analogue Modulation 1.1 Amplitude Modulation When a Radio Frequency (RF) signal is placed onto the antenna of a transmitter, it will propagate through free space and can be detected on the antenna of a receiver. The higher the frequency of this signal, the smaller the antennas that are required. However, we are often interested in communicating relatively low frequency message signals, such as audio. Hence, we must modulate our low frequency message signal onto a high frequency carrier, in order to transmit it. This has the added benefit of allowing us to modulate different message signals onto different carrier frequencies, in order to transmit them without interfering with each other. Figure 1 shows the schematic of a transmission scheme that uses Amplitude Modulation (AM) to transmit a time-varying input signal x(t), as well as demodulation to obtain a received signal xˆ(t). Modulator Demodulator A cos(2πfct) x(t) y(t) u(t) xˆ(t) + LPF × Figure 1: AM modulation and demodulation. 1.1.1 Operation The AM modulator of Figure 1 uses the message signal x(t) to vary the amplitude of the carrier sinusoid cos(2πfct), where the carrier frequency fc is usually much higher than the highest frequency in the message signal. As shown in Figure 1 y(t) = [A + x(t)] cos(2πfct), (1) 1 where A is a constant DC offset. In the AM demodulator of Figure 1, the diode symbol represents a rectifier which gives y(t) if y(t) > 0 u(t)= .
    [Show full text]
  • Modulation, Overmodulation, and Occupied Bandwidth: Recommendations for the AM Broadcast Industry
    Modulation, Overmodulation, and Occupied Bandwidth: Recommendations for the AM Broadcast Industry An AM Improvement Report from the National Association of Broadcasters September 11, 1986 Harrison J. Klein, P.E. Hammett & Edison, Inc. Consulting Engineers San Francisco on behalf of the AM Improvement Committee Michael C. Rau, Staff Liaison National Association of Broadcasters National Association of Broadcasters 1771 N Street, N.W. Washington, D.C. Washington, DC 20036 - Modulation, Overrnodulation, and Occupied Bandwidth: Recommendations for the AM Broadcast Industry HARRISON J. KLEIN, P.E. TABLE OF CONTENTS I. EXECUTIVE SUMMARy .1 II. INTRODUCTION .1 III. DEFINITIONS OF MODULATION AND OVERMODULATION 2 IV. THE AMPLITUDE MODULATION SPECTRUM .2 V. AM DEMODULATION 4 VI. THEORETICAL AMPLITUDE MODULATION ANALySIS 4 A. Fast Fourier Transform Techniques .4 B. FFT Modulation Analysis , 4 VII. TRANSMITTER MODULATION MEASUREMENTS 8 A. Sine Wave Measurements 8 B. Noise Measurements 12 C. Band-Limited Noise .15 D. Occupied Bandwidth Analysis of Noise Modulation .15 E. DC Level Shift. .18 F. Minimizing Occupied Bandwidth .18 VIII. AMPLITUDE AND PHASE ERRORS .18 A. Envelope Distortion .18 B. Modulation Nonlinearities 20 C. Previous Papers .20 D. Evaluating Station Antenna Performance 20 IX. MONITORING OF MODULATION AND OCCUPIED BANDWIDTH .22 A. Transmitter Monitoring 22 B. Need for Field Monitoring Improvements .22 C. Accurate Occupied Bandwidth Measurements .22 D. Modulation Percentage Measurement Limitations .23 X. CONCLUSIONS AND RECOMMENDATIONS 23 ACKNOWLEDGEMENTS 24 APPENDIX A DERIVATION OF SYNCHRONOUS DETECTION CHARACTERISTICS.. .24 APPENDIX B FAST FOURIER TRANSFORM PARAMETERS .25 APPENDICES C, D, E Attached papers FIGURES 1. Waveforms of AM Carriers for Various Modulation Indices 3 2. Overmodulation in a Typical AM Transmitter.
    [Show full text]
  • Appl. Note, Tech. Info, White Paper, Edu. Note
    Modulation and Signal Generation with R&S® Signal Generators Educational Note Products: ® ı R&S SMB100A ® ı R&S SMBV100A ® ı R&S SMC ı HM8134-3/HM8135 ı HMF2525 / HMF2550 Signal generators play a vital role in electrical test and measurement. They generate the test signals that are applied to components such as filters and amplifier, or even to entire modules, in order to ascertain and test their behavior and characteristics. The first part of this educational note presents the applications for and the most important types of signal generators. This is followed by a description of the construction and functioning of analog and vector signal generators. To permit a better understanding of the specifications found on data sheets, a closer look at the most important parameters for a signal generator is provided. Beyond the output of spectrally pure signals, a key function of RF signal generators is the generation of analog- and digitally modulated signals. The second part of this note therefore presents the fundamentals for the most significant analog and digital modulation methods. The third part of this educational note contains exercises on the topics of analog and digital modulation. All described measurements were performed using the R&S®SMBV100A vector signal generator and the R&S®FSV spectrum analyzer. Note: The most current version of this document is available on our homepage: http://www.rohde-schwarz.com/appnote/1MA225. e 2 - , M. Reil 1MA225 agner Educational Note R. W 8.2016 Contents Contents 1 What Is a Signal Generator? .............................................................. 4 1.1 Why Do We Need Signal Generators? ......................................................................
    [Show full text]
  • Double Sideband (DSB) and Amplitude Modulation (AM)
    Double Sideband (DSB) and Amplitude Modulation (AM) Modules: Audio Oscillator, Wideband True RMS Meter, Multiplier, Adder, Utilities, Phase Shifter, Tuneable LPF, Quadrature Utilities, Noise Generator, Speech, Headphones 0 Pre-Laboratory Reading Double sideband (DSB) is one of the easiest modulation techniques to understand, so it is a good starting point for the study of modulation. A type of DSB, called binary phase-shift keying, is used for digital telemetry. Amplitude modulation (AM) is similar to DSB but has the advantage of permitting a simpler demodulator, the envelope detector. AM is used for broadcast radio, aviation radio, citizens’ band (CB) radio, and short-wave broadcasting. 0.1 Double Sideband (DSB) Modulation A message signal 푥(푡) can be DSB modulated onto a carrier with a simple multiplication. The modulated carrier 푦(푡) can be represented by 푦(푡) = 푥(푡) ∙ cos⁡(2휋푓푐푡) (1) where 푓푐 is the carrier frequency. The Fourier transform 푌(푓) of the modulator output is related to the Fourier transform 푋(푓) of the message signal by 1 1 푌(푓) = 푋(푓 − 푓 ) + 푋(푓 + 푓 ) 2 푐 2 푐 (2) For a real 푥(푡), |푋(푓)| is symmetric about 푓 = 0 and |푋(푓 − 푓푐)| is symmetric about 푓 = 푓푐. For the present discussion, it is only necessary to consider that part of 푌(푓) that lies in the positive half of the frequency axis. The signal content that lies in the frequency domain below 푓푐 is the lower sideband. The signal content that lies in the frequency domain above 푓푐 is the upper sideband.
    [Show full text]
  • April 27, 2017 * This Document Is Being Released As Part of a "Permit-But-Disclose" Proceeding. Any Presentations Or V
    April 27, 2017 FCC FACT SHEET* Part 95 Personal Radio Service Reform Report and Order - WT Docket No. 10-119 Background: The Commission’s Part 95 Personal Radio Services (PRS) rules address a wide variety of wireless devices that are used by the general public to satisfy personal communications needs. These devices generally use low-power transmitters, communicate over shared radio frequencies, and (with a few exceptions) do not require an individual FCC license for each user. Some common examples of PRS devices include walkie-talkies; radio control toy cars, boats, and planes; hearing assistance devices; CB radios; medical implant devices; and Personal Locator Beacons. This draft Report and Order completes a thorough review of the PRS rules in order to modernize them, remove outdated requirements, and reorganize them to make it easier to find information. As a result of this effort, the rules will become consistent, clear, and concise. What the Rules Would Do: GMRS/FRS Reform. General Mobile Radio Service (GMRS) and Family Radio Service (FRS) devices are both used for personal communications over several miles. The public may be most familiar with FRS walkie-talkies. While GMRS and FRS share spectrum, GMRS provides for greater communications range and requires an FCC license, while FRS does not require a license. The rules will increase the number of communications channels for both GMRS and FRS, expand digital capabilities to GMRS (currently allowed for FRS), and increase the power/range for certain FRS channels to meet consumer demands for longer range communications (while maintaining higher power capabilities for licensed GMRS).
    [Show full text]
  • Analog Communications
    Analog Communications Student Workbook 91578-00 Ê>{YpèRÆ3*Ë Edition 4 3091578000503 FOURTH EDITION Second Printing, March 2005 Copyright March, 2003 Lab-Volt Systems, Inc. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopied, recorded, or otherwise, without prior written permission from Lab-Volt Systems, Inc. Information in this document is subject to change without notice and does not represent a commitment on the part of Lab-Volt Systems, Inc. The Lab-Volt F.A.C.E.T.® software and other materials described in this document are furnished under a license agreement or a nondisclosure agreement. The software may be used or copied only in accordance with the terms of the agreement. ISBN 0-86657-224-4 Lab-Volt and F.A.C.E.T.® logos are trademarks of Lab-Volt Systems, Inc. All other trademarks are the property of their respective owners. Other trademarks and trade names may be used in this document to refer to either the entity claiming the marks and names or their products. Lab-Volt System, Inc. disclaims any proprietary interest in trademarks and trade names other than its own. Lab-Volt License Agreement By using the software in this package, you are agreeing to 6. Registration. Lab-Volt may from time to time update the become bound by the terms of this License Agreement, CD-ROM. Updates can be made available to you only if a Limited Warranty, and Disclaimer. properly signed registration card is filed with Lab-Volt or an authorized registration card recipient.
    [Show full text]
  • Recommendation Itu-R Bs.412-9*
    Recommendation ITU-R BS.412-9 (12/1998) Planning standards for terrestrial FM sound broadcasting at VHF BS Series Broadcasting service (sound) ii Rec. ITU-R BS.412-9 Foreword The role of the Radiocommunication Sector is to ensure the rational, equitable, efficient and economical use of the radio-frequency spectrum by all radiocommunication services, including satellite services, and carry out studies without limit of frequency range on the basis of which Recommendations are adopted. The regulatory and policy functions of the Radiocommunication Sector are performed by World and Regional Radiocommunication Conferences and Radiocommunication Assemblies supported by Study Groups. Policy on Intellectual Property Right (IPR) ITU-R policy on IPR is described in the Common Patent Policy for ITU-T/ITU-R/ISO/IEC referenced in Annex 1 of Resolution ITU-R 1. Forms to be used for the submission of patent statements and licensing declarations by patent holders are available from http://www.itu.int/ITU-R/go/patents/en where the Guidelines for Implementation of the Common Patent Policy for ITU-T/ITU-R/ISO/IEC and the ITU-R patent information database can also be found. Series of ITU-R Recommendations (Also available online at http://www.itu.int/publ/R-REC/en) Series Title BO Satellite delivery BR Recording for production, archival and play-out; film for television BS Broadcasting service (sound) BT Broadcasting service (television) F Fixed service M Mobile, radiodetermination, amateur and related satellite services P Radiowave propagation RA Radio astronomy RS Remote sensing systems S Fixed-satellite service SA Space applications and meteorology SF Frequency sharing and coordination between fixed-satellite and fixed service systems SM Spectrum management SNG Satellite news gathering TF Time signals and frequency standards emissions V Vocabulary and related subjects Note: This ITU-R Recommendation was approved in English under the procedure detailed in Resolution ITU-R 1.
    [Show full text]