Electromagnetic impulse noise which is harmful to signal measurement or transmission of information, is smoothed by the orthogonal transform processor. The idealized impulse noise with infinitesimal duration and Gaussianly-distributed amplitude shows the same spectral characteristics as white Gaussian noise. Optimal correlation detector against such noise is easily realized by the orthogonal transform processor. Photoelectric pulse signals disturbed by the impulse noise from the power supply can be well detected through the Walsh waveform analyzer. Also, orthogonally-synthesized signals can be demodulated with firmly-suppressed impulse noise, where both the statistical and instantaneous SNRs are superior to those in the usual PCM transmission system

Sano, Hiroya

Tanada, Yoshihiro

Okayama University Scientific Achievement Repository

Memoirs of the School of Engineering, Okayama University, Vol. 15·2, March 1981Smoothing of Impulse Noise by Orthogonal TransformYoshihiro TANADA* and Hiroya SANO*(Received February 4, 1981)SynopsisElectromagnetic impulse noise which is harmful tosignal measurement or transmission of information, issmoothed by the orthogonal transform processor. Theidealized impulse noise with infinitesimal duration andGaussianly-distributed amplitude shows the same spectralcharacteristics as white Gaussian noise. Optimal corre-lation detector against such noise is easily realizedby the orthogonal transform processor. Photoelectricpulse signals disturbed by the impulse noise from thepower supply can be well detected through the Walshwaveform analyzer. Also, orthogonally-synthesized signalscan be demodulated with firmly-suppressed impulse noise,where both the statistical and instantaneous SNRs aresuperior to those in the usual PCM transmission system.1. IntroductionElectromagnetic impulse noise generally originates from the sparkdischarge on an electric contact or gap, or from the transient phenom-enon in sWitching~) This noise with its high peak power and wide spec-trum causes signal processing systems to make errors during operation.Many physical methods to control the generation and propagationof the noise are adopted. This paper deals with the systematic methodto smooth impulse noise for signal detection.* Department of Electronics6970 Yoshihiro TANADA and Hiroya SANOReal electromagnetic impulse noise may be quite complex~) But,here it is treated as the idealized one in order to give a fundamentalconsideration to filtering. Namely, it is represented by random pulseswith infinitesimal duration and Gaussianly-distributed amplitude, andtherefore its spectrum is the same as white Gaussian noise's~) ,4)For the signal detection in the presence of such impulse noise,the synchronous matched filter is utilized~),4) This works as noisesmoother. The filter can be constructed by an orthogonal transformprocessor. As examples, the method of measuring photoelectric pulsesignal by using the Walsh waveform analyzer, and the method of datatransmission by the orthogonal transform are discussed.2. Correlation DetectorCorrelation detector is useful for the signal detection under thebad SNR environment. Figure I shows a model 'of correlation detector,and Figure 2 shows typical waveforms of an input signal f(t), inputimpulse noise g (t), weighting function h (t) and trigger pulse', whereinput signal, weighting function and trigger pulse are synchronous.g (t)f(t) Input I JII OutputTrigger Function-----------,-......;;lIIGeneratorFig.l A model of correlation detector.The value of detector output is given bySmoothing of Impulse Noise by Orthogonal Transform~ JOT { f ( t ) + g ( t) } h * (t) d t71(1)where T is time base and the asterisk denotes complex conjugate forconvenience of the spectrum representation later on.Signal f(t)WeightingImpulse noise g(t) ~k_--,......., ...1_--.-_-I t=tkfunctionh(~Trigger -~'------~Time base T~~Time tFig.2 Typical waveforms on the detector.Now, let an impulse noise consist of numerable square pulses withthe infinitesimal duration E and the pulse height gk' as shown inFigure 2. This is represented by(2)where u(t) is unit step function, and the impulse noise is zero-meanGaussian and ergodic. 3 ) ,4) White Gaussian noise can be considered tobe denumerable sets of such pulses. Therefore, this impulse noise canbe treated similarly to white Gaussian noise, and the design of corre-lation detector becomes easy.3. Spectrum Expression of Matched FilterCorrelation detector becomes the matched filter under a certainmatching condition. Here, the matched filter is explained using theorthogonal transform. S)Using the first N orthonormal functions {~(i,t)}, the signal, theimpulse noise, and the weighting function are respectively expanded ina series as72 Yoshihi ro T ANADA and Hi roya SANON-lf(t) " L a.¢(i,t)i=O '1-N-lg(t) " L b.¢(i,t)i=O '1-N-lh(t) " L c.¢(i,t)i=O '1-( 3)(4 )(5)where a., b. and c. are the amplitude spectra and the impulse noise'1- '1- '1-spectrum b i holds zero-mean Gaussian. Then the spectrum expression ofthe detector output becomesN-lL (a.+b.)c~i=O '1- '1- '1-(6)Figure 3 shows the correlation detector using a waveform analyzer,such as a Walsh or Fourier transform processor. Here the summing am-plifier follows the analyzer and gives the output according to Equation(6) •Inputf(t)+g(t)Triggeral+b 1Wave f orm I---I--';;~Analyzer IIaN-l+bN-lOutputFig.3 Correlation detector using waveform analyzer.This method without generating the weighting function is conven-ient for construction of the matched filter as below.The matched filter in this case satisfies the matching conditionthat the weighting function should present the same waveform as theinput signal ( h(t)=Kf(t), c.=Ka.). The output SNR of this matched'1- '1-filter becomesSmoothing of Impulse Noise by Orthogonal Transform 73N-lL I a. 1 2i=O 1.- (7)where the noise power is uniformly spread over the spectrum.Another matched filter that the weighting function is one of theorthogonal functions as h(t}=~(i,t), is to be called the orthogonalmatched filter and useful for data transmission. Its output SNR becomes( 8 )4. Pulse Signal Measurement by Walsh Waveform AnalyzerHere, the matched filter for pulse signal measurement is construc-ted by the Walsh waveform analyzer. 6 )The analyzer transforms a solitary waveform of 16 microsecondsinto parallel 16 amplitude spectra using {wal(i,t/T}} functions. Inthe application of this analyzer to the matched filter, input impulsenoise must not exceed its allowable input range of -1 to +1 volt.Therefore, a linear-time-invariant pre-filter as given by{u(t} - u(t-M) }/. (9 )should be followed by the analyzer, where ~t=l~s and .=constant.Figure 4 shows the block diagram of the system to measure thepulse laser-light signals. The input signal and the trigger are derivedfrom the light of the pulsed laser. The input noise consists of theadditive impulse noise leaking from the laser power supply and of thewhite Gaussian noise from the electronic circuits.The matched filter output is quantized by the analog to digitalconverter and transferred into the personal computer, which accumulatesthe output data for the better SNR.74 Yoshihiro TANADA and Hiroya SANONoiseTriggerLTIPre-filter Matched Filterby Walsh Analyzer AIDTo PersonalComputerFig.4 The system to measure the pulsed-laser light signals.5. Data Transmission by Orthogonal Matched FiltersThe orthogonal matched filters are effectively applied to thefollowing data transmission system.Figure 5 shows a typical model of the system. Here, the noise isassumed to be the impulse noise. The signal on the transmissionchannel is assumed to be the orthogonal synthesis signal, given byf(t)N-lL a.¢(i,t)i=O '1,.(10 )whose spectrum a i is analog or digital datum. At the receiver, thewaveform analyzer which forms the N synchronous matched filters, givesthe estimate of the transmitted data.WaveformAnalyzerReceiverWaveformSynthe-sizerNoise g(t),....-----, r----..,Fig.5 Data transmission system using orthogonal transform."Now, let us consider the SNR in the data transmission system usingthe block-pulse train, where the received signal is the PAM signalgiven bySmoothing of Impulse Noise by Orthogonal Transform 75N-lI IN a.[u(t-iM) - u{t-(i+l)M}]i=O 1.-TIN ( 11)whose power is equal to that of the orthogonal synthesis signal.The statistical SNR in receiving the i-th datum in both systemsbecomes(12)On the other hand, in case an impulse noise has the power g2 onlyat the i-th time slot, the short time SNRs become(SNR) orthNI a .1 21.- ( 13)for the orthogonal transmmission and(14)for the PAM transmission. If ¢(i,tl is a Walsh function, the SNR valuein the orthogonal transmission takes N times as much as in the PAMtransmission, since the noise power spreads over each spectrum.Figures 6(a) and 6(b) show respectively a Walsh-synthesis multi-level signal and a peM dipolar signal on the digital data transmissionchannel, where a l =a 4=a 7=-E and others = +E, and N=8, and ¢(i,t)=wal(i,tiT). Both signal powers are constant and the Walsh synthesis signalis easily amplified if aO=O.--8EflJ L- 00 T~t---8EFig.6 (a) Walsh synthesis multi-level signal.76 Yoshihiro TANADA and Hiroya SAND~tFig.6 (b) PCM dipolar signal.6. ConclusionElectromagnetic impulse noise is idealized to be a finite set ofrandom pulses with infinitesimal duration and Gaussianly-distributedamplitude. It is shown that the synchronous matched filter againstimpulse noise can be constructed by an orthogonal transform processor.As the first example, the matched filter using the Walsh waveform ana-lyzer is effectively applied to photo-electric pulse signals. As thesecond example, the orthogonal matched filter in data transmission iseffective in suppression of impulse noise. In each example, impulsenoise power is smoothed through matched filtering and spectrum decom-position.For strict processing of real impulse noise, the model of impulsenoise and the method of filtering might have to be modified to someextent.AcknowledgementWe would like to thank Miss Megumi Kosaka for her figure drawingand Miss Keiko Nakamura for her typewriting.References(1) T.Takagi: A review of electromagnetic compatibility by an inst-rument action and control engineering, Jour.SICE, Vol.18(1979),12, pp.1012-1018.Smoothing of Impulse Noise by Orthogonal Transform 77(2) D.Middleton: Canonical non-gaussian noise models, Their implicationsfor measurement and for prediction of receiver performance, IEEETrans.Electromagn.Comat., Vol.EMC-21(1979), 2, pp.209-220.(3) Y.Tanada and H.Sano: Suppression of Electromagnetic impulse noisesby synchronous matched filters, Proc.1980 IEEE International Sympo-sium on Electromagnetic Compatibility (1980), pp.354-359.(4) Y.Tanada and H.Sano: Suppression of impulse noises by synchronousmatched filters, Technical Report of IECE, EMCJ80-23 (1980), pp.31-36.(5) Y.Tanada and H.Sano: A Walsh waveform analyzer and its applicationsto filtering of pulse signals, Memoirs of the School of Engineering,Okayama University, Vol.13(1979), pp.163-180.(6) Y.Tanada and H.Sano: A hybrid Walsh waveform analyzer, Trans.IECE,Vol.J59-D(1976), ~, pp.10l-108.

Smoothing of Impulse Noise by Orthogonal Transform

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