EXPLORATIONS IN COMMUNICATION SYSTEMS USING A VIRTUAL TOOLKIT

Transcription

1 EXPLORATIONS IN COMMUNICATION SYSTEMS USING A VIRTUAL TOOLKIT Murat Tanyel Dordt College Session 2320 Abstrat A typial ommuniation systems ourse is rih with proesses that are best desribed by blok diagrams. While a typial textbook on the subjet may provide examples on the appliations of these proesses, students are motivated when these blok diagrams ome alive as they implement these proesses and are able to test signals at eah blok. Suh an endeavor requires hardware, spae and time alloations that not every institution is prepared to ommit. The next best teahing tools are omputer simulations in whih students an observe signals at eah stage of the proess. Preparation of suh simulations is simplified by software development tools tailored for digital signal proessing, suh as MATLAB, whih has beome the standard pakage most reent ommuniation systems books have adopted. Reent development of data-driven graphial programming languages has provided an improvement over textual languages suh as MATLAB by enhaning the oneptual link from the blok diagrams of these proesses to their omputer simulations. This paper is a follow-up on last years presentation 1, whih disussed the development of a virtual toolkit in LabVIEW. It will report on the use of the toolkit in a three-redit Communiation Systems ourse, with examples of how this toolkit was used as an exploratory tool to probe further into the simulated systems. I. Introdution This paper is a follow-up on a reent paper that desribes a simulation toolkit for ommuniation systems and its development with a freshman as the programmer 1. In that paper we stated that in the absene of hardware that would reinfore the theoretial presentation, omputer simulations of the systems desribed in lass are the next available tools to bring these onepts alive. We also desribed the partiular lass environment and the proess in whih the software development tool, namely LabVIEW, was hosen. Although MATLAB is the standard software tool employed in the areas of signals and systems, as evidened by the proliferation of books 2-4 devoted to MATLAB based exerises in those subjets, the hoie of the software tool is justified in 1, 5, 6. In a separate paper, Adams and I disuss this hoie from an engineering design aesthetis point of view 7. This paper will report on the first-time use of the toolkit in EGR 363, Communiation Systems ourse offered at Dordt College in Spring Setion II will provide an overview of the inlass presentations that made use of the toolkit while Setion III will review some examples that reveal the exploratory faet of the toolkit. Setion IV will disuss the student projets and will

2 offer a sample. I will then onlude with a disussion on the present state of the toolkit and on possible future developments. II. Presentations with the Toolkit Communiation Systems lasses and other upper level eletrial engineering lasses with low enrollments are held in small lassrooms that do not have built-in omputer and projetion systems. For suh lassrooms, the engineering department has a COW (omputer on wheels, a very appropriate aronym for a ollege in a rural setting), a personal omputer with a projetion system on a art that may be wheeled around. This mobile PC has a network ard and may be onneted to the ollege-wide network through network onnetors that are loated in every lassroom. The LabVIEW software development system is installed on the engineering COW. So any virtual instrument (or VI, a term used for LabVIEW programs) that I develop and save on the network drive may be easily run in any lassroom. I use the COW in most Communiation Systems lasses to demonstrate the onepts overed on that days topi. Figure 1: Demonstration of Amplitude Modulation (AM) using the toolkit.

3 Fig. 1 depits the front panel of a VI that I use to demonstrate Amplitude Modulation (AM). The effetiveness of this VI is amplified when it is run in ontinuous mode, in whih the VI runs, monitoring it inputs and adjusting its outputs, repeatedly until the stop button is pressed. In this mode, it beomes very easy to hange parameters and see the results immediately. For this partiular demonstration, one an easily swith through the different kinds of periodi signals as the baseband signal (upper left sliding swith in Fig. 1) and an observe how the modulated signal looks both in time and frequeny domain. The frequeny of the arrier signal (lower left knob) may be varied and the students wath as the replia of the baseband spetrum moves up and down the frequeny band in the lower right graph. It is this ontinuous mode of operation that makes in-lass demonstrations attrative. The ability to hange parameters and obtain immediate results is a definite enhanement over standard and stati textbook examples. The above example is one of the many demos I use. Other demos in the same spirit, showing PAM, FM and PM and their spetra have been useful in lass. Figure 2: The VI to demonstrate AM demodulation in ation.

4 III. Exploratory Demonstrations Fig. 2 displays the front panel of the VI that I use to demonstrate the detetion of AM signals. With this VI, one an selet the type of the baseband signal with the seletor in the upper left (labeled Wave in Fig. 2) from a number of periodi waveforms and speify the number of yles to be generated. The fundamental frequeny of this waveform is 1 Hz. The baseband signal and its magnitude spetrum are displayed in the upper graphs of the VI. This signal is modulated by a arrier whose frequeny may be speified by the knob in the lower left orner of the VIs panel. The swith toward the middle of the left hand-side of the panel (labeled AM <- > DSBSC AM) hooses the type of modulation. If the swith is to the left, AM is employed, whih may be expressed by the equation: s( t) = A [1 + D m( t)]osω t (1) a where s(t) is the modulated signal, A is the amplitude of the arrier (assumed to be 1 in this VI), D a is the modulation index, m(t) is the baseband (message) signal and ω ( = 2πf ) is the arrier frequeny. If the same swith is to the right, the double-sideband suppressed arrier (DSB-SC) AM is employed, expressed by: s( t) = A m( t)osω t (2). Figure 3: Envelope detetor. AM signals may be demodulated by an envelope detetor omprised of a diode and a lowpass RC filter (Fig. 3) whereas DSB-SC AM signals require a produt detetor whih involves multiplying the signal with a replia of the arrier again: v int ( 0 t) = s( t) A0 os( ω t + θ 0 ) = Am( t)osωt A0 os( ωt + θ ) (3) This operation separates the signal into a low frequeny omponent, entered around DC, and a high frequeny omponent, entered around 2 ω :

5 v 1 1 t) = A A0 m( t) osθ 0 + A A0 m( t) os(2ω t + θ ) (4) 2 2 int ( 0 Low-pass filtering v int (t) of eq. 3 or 4 will reover a replia of the original baseband signal: 1 m ( t) = A A0 m( t) osθ 0 = Km( t) (5). 2 The lower two graphs of Fig. 2 display the reovered message signal and its magnitude spetrum. I should note that the low-pass filter used introdues some transients, whih may be observed in the time-domain representation of the demodulated signal and, due to the reord length, these transients ontribute a visible differene between the shapes of the magnitude spetrum of m(t) and m ( t). The intermediate signal (of eq. 4) of the produt detetor an be easily derived mathematially, either using trigonometri identities as I have done in going from eq. 3 to eq. 4 or using the property that multipliation in time domain results in a onvolution in frequeny domain. In either ase, the resulting spetrum is a replia of the message spetrum around DC and another translated to 2f. Fig. 4 is a snapshot from the front panel of the VI in Fig. 2 displaying the intermediate signal (before low-pass filtering) of the produt detetor. In this ase, a arrier signal of 10 Hz is used to modulate a sinusoidal message of 1Hz. We an see, in Fig. 4 (graph labeled Mag. Spet., Inter. Sig.), that the 1 Hz message is repliated around the origin as well as around 20 Hz. There is no spetral omponent at 20 Hz (or at DC) beause the method employed is double sideband suppressed arrier. Figure 4: The intermediate signal [v int (t) of eq. 4] from a produt detetor. The left graph displays the time domain signal and the right graph displays its magnitude spetrum.

6 Figure 5: The intermediate signal, that is, the signal that would be obtained without low-pass filtering from an envelope detetor. The mathematial development for the produt detetor is well understood and derivations like that of equations 3-5 may be found in most textbooks on ommuniation systems, inluding the textbook hosen for this ourse 8. The envelope detetor, on the other hand, involves a diode whih is a nonlinear devie. Sine most undergraduate students have been exposed to primarily linear system theory, the nonlinear devie in the envelope detetor presents a hallenge to the mathematial analysis of this method. A ursory san through introdutory textbooks on the subjets reveals a gap in the analysis of the envelope detetor. So, a display of the magnitude spetrum of the intermediate signal (the signal that would be obtained if the RC lowpass filter of Fig. 3 were absent) is an exploration for my students, the result of whih they ould not find in their textbook. Fig. 5 displays the time domain signal and its magnitude spetrum for the envelope detetor applied on an AM signal with the following parameters (of eq. 1): f = 10 Hz, D a = 1 and m(t) is a sinusoidal of 1 Hz. A omparison of the magnitude spetra of the intermediate signals of the produt detetor (Fig. 4) and the envelope detetor (Fig. 5) reveals that both signals ontain a replia of the message around DC, whih onstitutes the reeived message when low-pass filtered. The signal of Fig. 5 has a DC omponent beause the arrier is not suppressed in regular AM. The intermediate signal of the produt detetor has a replia around 2f as predited, but that of the envelope detetor has replias around f, 2f, 4f and 6f. Where do all these spetral omponents ome from? This is an exerise that an inquisitive student may be enouraged to probe further. Sine the simulation uses the model of an ideal diode in the envelope detetor, an explanation with linear system theory is possible. The ation of the diode may be modeled with the multipliation of the modulated signal with a pulse train of 50 % duty yle at the same frequeny (and phase) as the arrier signal. This is plotted in Fig. 6 for our example, where the arrier is a 10 Hz sinusoidal wave.

7 Figure 6: A pulse train of 50 % duty yle at 10 Hz. Sine the model involves multipliation in time domain, the spetrum of the resulting signal will be the spetrum of the modulated signal onvolved with the spetrum of the pulse train. In the Signals and Spetra hapter of the textbook 8, the spetrum of a pulse train with 50 % duty yle is found to be: nπ sin A W 2 ) ( f ) = δ ( f nf 0 n= 2 nπ 2 (6) where W(f) is the spetrum of the pulse train, A is its amplitude, f 0 is its frequeny and () is the Dira delta (impulse) funtion. The spetrum of a 10 Hz pulse train of amplitude 1 is plotted in Fig. 7. The dashed lines in Fig. 7 trae the envelope (whih is a sin pattern) and the solid lines represent the impulses that make up the magnitude spetrum. The spetrum is made up of impulses at DC, at ± f 0, and at odd harmonis, following an envelope [E(f)] of πf sin 1 20 E( f ) = (7). 2 πf 20 To obtain the intermediate signal spetrum, one would onvolve the spetrum of Fig. 7 with that of the spetrum of the modulated signal depited in Fig. 8. A summary of the onvolution of the two spetra is as follows: The DC omponent of W(f) (Fig. 7) onvolved with S(f) (Fig. 8) gives rise to the spetral omponents around ± 10 Hz of the spetrum in Fig. 5. The onvolution of the ± 10 Hz omponents of W(f) with S(f) will give rise to the spetral omponents around DC and ontribute to the spetral omponents around ± 20 Hz in Fig. 5. The onvolution of the ± 30 Hz omponents of W(f) with S(f) will ontribute to the spetral omponents around ± 40 Hz and to those around ± 20 Hz while the onvolution of the ± 50 Hz omponents of W(f) with S(f) will ontribute to the spetral omponents around ± 60 Hz and to those around ± 40 Hz. This

8 explanation is enough to explain the predominant peaks around DC, ±f, ±2f, ±4f and ±6f of Fig. 5. The omponents beyond these frequenies an be aounted for by taking into onsideration the aliasing that also ours due to the disrete nature of the simulation. Figure 7: Magnitude spetrum of a 10 Hz, 50% duty yle pulse train. Figure 8: Spetrum of a 1 Hz sinusoid amplitude modulated by a 10 Hz arrier wave. IV. Student Projets This year, students in the ommuniations lass were asked to develop some new simulations in addition to the ones they had worked with in lass. There were six students in lass and they formed teams of two, eah working on a topi they were interested in. One group worked on ompanding, another worked on pulse oded modulation (PCM) while the third worked on M-

9 ary Phase-Shift Keying (MPSK). MPSK is a method of transmitting digital information over analog lines. The binary information is first onverted into a multilevel signal (of M levels) and this multilevel signal determines the disrete phase angles of the omplex envelope of the MPSK signal. A plot of the permitted values of the omplex envelope is alled a signal onstellation. Fig. 9 is a snapshot from the front panel of the MPSK Demonstration VI 9. In this example M = 16, so the signal onstellation displays the 16 permitted values of the omplex envelope (upper left graph in Fig. 9). Fig. 10 displays the onstellation in the presene of added noise, a feature whih the students have inorporated into the VI. In this simulation, M = 8. Figure 9: The front panel of the MPSK Demonstration VI. Figure 10: The signal onstellation with additive noise. In this simulation M = 8.

10 V. Disussion In this paper, I have given an aount of how a virtual toolkit, the preparation of whih was doumented in 1, was used for the first time in my ommuniation systems lass. Setion II gave an example of how a virtual instrument an enhane the presentation in lass. Setion III demonstrated how the availability of simulated signals and other tools an turn one demo into an exploration and prepare the ground for interesting further disussion. Setion IV reported on student work along the same lines with one example. The utilization of the tools in this toolkit is understood better with a rudimentary understanding of disrete signals. Sine these are omputer simulations, one would need to remember that simulations of analog proesses are valid when the results of the proesses all fall within the Nyquist rate determined by the original hosen sampling frequeny. The disussion development in setion III gave an example of a proess that would result in frequenies beyond the Nyquist rate. The onept of sampling frequeny gets interesting and potentially onfusing when we simulate the sampling of analog signals where we an talk about two sampling frequenies: the sampling frequeny of the entire simulation and the sampling frequeny at whih we retain samples from the simulated signal. I refer to the former as simulation lok frequeny and the latter as simply sampling frequeny. Sine my students take ommuniation systems after DSP, I have hosen to make the simulation lok frequeny as one of the inputs and expet the students to pay attention to the Nyquist rate as they implement these simulations and wath for aliasing in their simulations. Clearly, the list of VIs in the toolkit may be expanded. Spring 2002 offering of EGR 363 has added a few and the work will be ontinued. There is also the task of doumentation to be finished, whih always seems to lag in amateur programming projets. Students also appreiate the exposure to LabVIEW. I have noted that most senior design projets of 2002 have inorporated LabVIEW in one way or another this year. As a matter of fat, one of the senior design projet teams has ombined LabVIEW and MATLAB, using the LabVIEW interfae to all MATLAB sripts beause the LabVIEW interfae is aesthetially more pleasing. As I have noted elsewhere 7 : Part of the enthusiasm is due to the aesthetis of LabVIEW virtual instruments. I have seen many a student revisiting and perfeting the way the front panel looks long after his/her VI has ahieved its omputational goals and long after the lass period has ended. ACKNOWLEGEMENTS: The LabVIEW software used in this ourse was purhased through a grant from Johnson Controls in Holland, MI. I would like to thank Johnson Controls for the upgrade of the eletronis lab whih also benefited the ourse mentioned in this paper. I would also like to thank Kathrine Nguru, who programmed some of the subvis used in the VIs depited in this paper as well as Howard Gorter and Brian Matherly, whose projet is mentioned in this paper.

11 Bibliography 1. M. Tanyel, K. Nguru, Preparation of a Virtual Toolkit for Communiation Systems, 2002 ASEE Annual Conferene and Exposition Proeedings, Montréal, QC, June Proakis, J. G., Salehi, M., Contemporary Communiation Systems using MATLAB, Paifi Grove, CA: Brooks/Cole (2000). 3. Frederik, D., Chow, J., Feedbak Control Systems using MATLAB and the Control Systems Toolbox, Paifi Grove, CA: Brooks/Cole (2000). 4. Ingle, V. K., Proakis, J. G., Digital Signal Proessing using MATLAB, Paifi Grove, CA: Brooks/Cole (2000). 5. Viss, M. and Tanyel, M. From Blok Diagrams to Graphial Programs in DSP, 2001 ASEE Annual Conferene & Exposition Proeedings, Albuquerque, NM, June Tanyel, M., Enhaning the DSP Toolkit of LabVIEW, 2002 ASEE Annual Conferene and Exposition Proeedings, Montréal, QC, June Tanyel, M., Adams, C., On the Aesthetis of Computer Aided Tools for Signal Proessing, Proeedings of 64 th Annual ASEE North Midwest Setion Meeting, Madison, WI, Ot Couh II, L. W., Digital and Analog Communiation Systems, Sixth Edition, Upper Saddle River, NJ: Prentie Hall (2001). 9. Gorter, H., Matherly, B., MPSK Demo Projet Report, EGR 363 Projet Report, Dordt College, Sioux Center, IA, May MURAT TANYEL Murat Tanyel is a professor of engineering at Dordt College. He teahes upper level eletrial engineering ourses. Prior to teahing at Dordt College, Dr. Tanyel taught at Drexel University where he worked for the Enhaned Eduational Experiene for Engineering Students (E 4 ) projet, setting up and teahing laboratory and hands-on omputer experiments for engineering freshmen and sophomores. For one semester, he was also a visiting professor at the United Arab Emirates University in Al-Ain, UAE where he helped set up an innovative introdutory engineering urriulum. Dr. Tanyel reeived his B. S. degree in eletrial engineering from Boaziçi University, Istanbul, Turkey in 1981, his M. S. degree in eletrial engineering from Buknell University, Lewisburg, PA in 1985 and his Ph. D. in biomedial engineering from Drexel University, Philadelphia, PA in 1990.