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subsystem to function properly within the system and in writingproject reports that will eventually be combined into their final report.

Even the students whose robots were unsuccessful at the task saidthat they had leamed much from the course and commented that ifthey just had another week, their robot would have been successful.Therefore, the most important change that we m ay try with this courseis to offer it to students over two class quarterdsemesters.

Students rated this course very wellon the student course evalu-ation forms. Eighty-two percent of the students rated the course asvery goo d o r oneof the best courses that I have had. Only onestudent did not care for the course. All of the students felt that theyhave leamed at least as much in this course as they had in theirother cour ses 12 -average, 24 -more than other courses, and50 -an exceptional amoun t more than other courses).

When the students were asked if the course content was important,69% of the students felt that the material was very important,25felt that i t was important, and6 (one student) had mixed feelings.

The main drawbackof the course is that it requires a significantamount of time during a period when the student is interviewingand trying to complete a number of other technical electives. Twelvepercent of the students claimed that there wasan average amount ofwork in this course, 19% claim that the workload was heavy, and

56 felt that the work required for this course was the heaviestofall of their courses. The work load problem could be eliminated ifa class were held on a semester basis, or held over the duration of

quarters.

REFERENCES

R. D. Klafter, T. A . Chmielewski, and M. Megin, Rnhntic Engineering:An Integrated Approach.J. L. Jonra and A . M. Flynn, Mobile Rohors: Inspiration t Implemen-ta tion.P. Horowitz and W. Hill, The Art ofElectronic.s. Cambridge Univer-sity, 1980.

Prentice Hall, 1989.

Wellesley, MA: A . K. Peters, 1993.

A Simple Low Cost LaboratoryHardware for Noise Generation

Francisco DAlvano and RennyE. Badra

Ab s t r a c t A circuit hardware for custom noise generation is presenteddescribed and explained. Its very low circuit complexity along with thespectral and statistical features of the noise signal obtained make itspecially suitable for student use in laboratory sessions related to digitaland analog communications systems.

I. I N T R O D U C T I O N

Artificial noise generation for laboratory use has been addressed

by comm ercial equipmen t manufacturers [4]. Nevertheless, existingcommercial equipment tends to be too expensive for massive lab-oratory use. On the other hand, custom implementation of randomsignal generators has been avoided due to the circuit complexity of

Manuscript received March3 1994.The authors are with the Departainento de Electronica y Circuitos, Univer-

Publisher t em Identilier S 00 I8-9359(96)04408-s idad S im h Bo liva r, A part ad o89000. Caracah I086A Venezuela.

CKI1 MHz

- CK2 1.5 MHzI I I

8-bit Shift Register

I I I

8.2K

Fig. 1 Noise generator.

ircuitoutput

the existing schemes. This work presents a simple and inexpensivehardware conceived and implemented at Universidad Simdn Boldvar(USB Caracas, Venezuela) for random noise generation designedfor student use. Although the spectral and statistical features of thesignal obtained differ slightly from those usually desired (i.e., spectralflatness and Gaussianity), this signal is shown to be quite suitable forexperimental simulation of noisy environments in digital and analogcommunication systems within a reasonable degree of likenesstoreality.

This circuit hardware consists of two independent digital oscil-lators, an eight-tap shift-register, two XOR gates, an opamp-basedactive filter, and a resistive network. Digital chips may be eitherCMOS or TTL. Circuit power can be drawn from a dual-voltagepower source or from a single-voltage one( 5 volts or more). If thecircuit is to be mountedon a prototyping board, i t can be designedto produce low-pass noise signals with a reasonably flat frequencyspectrum up to 200 kHz or more. A band-pass noise signal can alsobe obtained by slightly changing the basic configuration of the circuit.

11. C IR C U IT E S C R IP T IO N

The circuit proposed, as many other noise generators, is based ona pseudo noise (PN) sequence generator[ I ] as shown in Fig. I Theeight-tap shift-register and its logic feedback (through X ORA only,XOR B should be ignored for the time being) configure a pseudo-random sequence generator with a cycle length of255. To achievethis maximum sequence length, inputs of XORA must be outputsnumber 8 and 5 (or 3) of the shift-register.

The periodicity in the sequence obtainedis clearly an undesirable

feature (since sequence length is only 255). To eliminate it, anadditional XOR gale (XOR B) is included in the feedback path.This XOR gate is fed with a clock signal (CK2) which is generatedindependently from the shift-register main clock(CKI) . Also, bothtiming signals have different nominal frequency values. The effectof this second XOR gate is to break the pseudo random patterneach time CK2 is high during a shift operation, which is orderedindependently by CK1 This will cause the sequence to be, if not

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completely nonperiodic, at least periodic with an extremely longperiod.

To obtain an analog voltage from this eight-digit binary sequence,the shift-register outputs are linearly combined through a resistivenetwork, which also plays the role of the coefficient setof a discrete-time FIR filter [2]. In the specific implementation displayed in Fig.1, these weights provide a low-pass transfer function with a raised-

cosine impulse response.Despite this resistive network, onlya finite set of voltage levels is

obtained at its output. Additional low-pass filtering eliminates abruptpulse transitions and finally delivers an analog low-pass noise signal,which can be used to contamina te baseband analog messages as wellas digital ones. In the version displayed in Fig.1, a single-pole activeRC filter was selected, although a higher pole number will providea better frequency shape, if needed. Output level can be adjustedthrough the 1 KR trimmer.

The shift-register should provide polar voltage swing. Thus,CMOStechnology is recommended, although positive voltage range(TTLcompatible) can also be used along with a DC-block capacitor.

111. THE NOISESIGNAL

It seems reasonable to expect that the noise signal obtained willshow a low-pass spectral characteristic, given the nature of thefrequency response of both the discrete-time and continuous-timefilters included in the signal path (a band-pass spectral shape canalso be obtained, as shown in the Appendix).

On the other hand, the probability density function (pdf) of thenoise signal can be approximately predicted, given the random natureof the binary sequence generated at each of the shift-register paralleloutputs. Although time-related, these eight random binary variables,which are added to form the noise signal, are statistically independentfrom one another, and the central limit theorem [3] holds. Thus, aGaussian-like pdf is expected to be obtained.

Although it is desirable to extend the frequency range up to itsmaximum, this would require reducing or canceling the contributionsof some of the shift-register taps (by increasing their respectiveresistance values, or eventually eliminating them), which woulddeviate the noise from being Gaussian-like and would tend to produceundesirable peaks in its pdf. This trade-off situation can be solved byusing all of the shift-register outputs, along with convenient scalingof the frequency domain (achieved through the adjustment of thefrequency of the main oscillator CK1).

An implementation of this generator was simulated in a computer inorder to perform the spectral and statistical analysis. The weightingresistances were set to produce a raised-cosine impulse response,which provides a low-pass transfer function . Main oscillator (CK 1)was set to 1 MHz, while CK2 was set to1.5 MHz (to emulate toler-ances of the real circuit, simulation values included some inaccuracyin these frequency settings,as well as in the resistance values). Thelow-pass filter (one pole) cut-off frequency was set to 200 kHz.Fig. 2 shows the histogram of a1.6 mS segment of the noise signal obtained,while Fig. 3 displays its power spectrum, estimated by averagingeight 4096-points periodograms. Both results seem to confirm thearguments presented above.

As a part of the Digital Communications Laboratory experiences,the circuit (low-pass version) has been widely used by electronicengineering students at USB, Results have beenq u i t e s a t i s f ac to r y.

IV. CONCLUSION

A low-cost, simple, and efficient hardware for laboratory noisegeneration has been presented and described. The features of thenoise signal were discussed; simulation results confirmed that noise

-Vmax 0 VmaxFig. 2. Histogram from a sample noise sequence (simulation).

50 B

-100dB

-150 dB f

0 200kHz 6OOkHz

Fig. 3 . Noise power spectrum (simulation).

obtained through this circuit has a Gaussian-like probability densityfunction and a low-pass spectral shape, which can be arbitrarilyscaled. A band-pass version was also introduced. The study of thecircu it constitutes by itself an interesting ap plication of the timeand frequency domain signal analysis and digital signal processing.A11 these features strongly suggest that the circuit introduced canbe useful for student use in some laboratory experiences related todigital and analog communications.

APPENDIX:HE BAND-PASS ERSION

A band-pass version of the circuit presented can be easily imple-mented by inverting the logic outputs of registers2 4, 6, and 8 (or 13, 5 , and 7), using additional NOT gating. This will make the impulseresponse of the discrete time filter a band-pass one, centered at halfthe frequenc y of CK l First-null bandwidth of this noise signal is alsohalf of CK1. The analog filter must also be changed to band-pass,using the same center frequency. By adjusting the 3-dB bandwidthof the latter, noise spectrum can be made more frequency selective.The band-pass version described here has only been tested throughcomputer simulation.

ACKNOWLEDGMENT

The authors would liketo thank Prof. T. Adrian de PCrez, head ofthe BID-CONICIT ProjectE-18 (Digital Signal Processing Applied

to ISDN) USB, for facilitating the equipment used in the elaborationof this paper.

REFERENCES

S Haykin, Digital Communications.A Oppenheim and R. Schaffer, Digital Signal Processing.Cliffs, NJ: Prentice-Hall, 1974.A B. Carlson, Communication Systems.1986.Operating und Service Manual. H P 37 A Noise Generator.U.K.: Hewlett Packard, 1971.

New York: Wiley, 1988.Englewood

New York: McGraw-Hill,

Scotland,