frequency-domain analysis of the human electroretinogram

Frequency-domain analysis of the human electroretinogramMoshe Gur and Yehoshua Zeevi

Department ofBiomedical Engineering and Department of Electrical Engineering, Technion, Haifa, Israel(Received 13 November 1978; revised 28 March 1979)

Normal corneal electroretinograms (ERG) are analyzed in the frequency domain using the fastFourier transform (FFT) and linear prediction (LP) methods. Four dominant frequencies at 18, 79,126, and 159 Hz are found in the dark-adapted state. Light adaptation shifts the low frequency tohigher frequency and the mid- and the two high-frequency components to lower frequencies. Therelative amplitude of the high-frequency component resulting from the oscillatory potentials is quan-tified. It is shown that frequency-domain features are of a smaller variability than time-domaincomponents, and can be extracted even from a noisy surface ERG.

INTRODUCTION

The ERG is an important tool for studying normal andpathological retinal mechanisms.1-2 It is usually studied bymeasuring a few selected features; the b-wave amplitude andthe a- and b-wave implicit times are most commonly used.The inherent variability of these parameters3 -4 within anormal population, however, limits the utility of the signal.

It seems reasonable therefore to apply signal analysistechniques so that the ERG signal can be considered as awhole in a quantitative, automatic way. Indeed, the ERG isa signal ideally suited for study by quantitative techniques.It is an evoked response, and as such there is no synchroni-zation problem. It is of a short duration and has a relativelysimple waveform, and, finally, the signal components are timelocked to the light flash, i.e., under the same set of conditions,two signals can be accurately superimposed. Little has beendone though, in applying methods of signal analysis to elec-troretinographic research5-11 and in utilizing these methodsin the regular clinical application of the ERG. In contrast,one encounters extensive application of signal analysis tomuch more complicated physiological signals such as theEEG.12 For example, a recent special issue of the proceedingsof the IEEE on biological signal processing and analysis (May1977) contains reports on signal analysis of the EEG, ECG,EMG, and nerve action potentials, but none on the ERG.

Considering the importance of the ERG,1 2 one is thereforetempted to apply to its analysis some of the methods suc-cessfully used on other physiological signals. We chose tostart by applying frequency domain techniques since they arewell developed, are relatively easy to implement with a digitalcomputer, and have been successfully employed in analysisof other physiological signals. Furthermore, the ERG con-tains an oscillatory component that by its very nature lendsitself well to frequency analysis. There have been severalattempts made to characterize this oscillatory potential (OP)in the time domain 5'1 3-' 5 but not a single one has been gen-erally applied. Finally, under certain recording conditionssuch as that of the noncorneal surface ERG,16 time-domainfeatures are masked by wide band noise and cannot be iden-tified, while certain frequency-domain techniques might beless sensitive to that kind of noise.

Thus, in order to extract quantitatively a set of featuressuitable for the characterization of the normal ERG, twofrequency-domain techniques were used: the fast Fouriertransform (FFT) and the linear prediction (LP). The resultsshow that a set of features characterizing the ERG and having

a very small variability can be extracted even under noisyconditions.

METHODS

SubjectsThirteen normal subjects were tested; ten were between the

ages of 23-32 and three were older (65-75 years old). Nosignificant differences were found between the two age groupsas well as between the two eyes of the same subject. Thusresults were pooled from all 26 eyes. All subjects were thor-oughly checked by a resident ophthalmologist to assure thatno pathologies were present.

Stimulating and recording techniquesThe subject lies in a light-shielded room. Flash lamp, ERG

electrodes and interface box are in the room. Other equip-ment is in the adjoining control room. Verbal communicationwith the subject is maintained via an intercom system.

Flash stimulatorThe stimulator used is Grass PS22; its flash lamp is placed

at 25 cm from the subject's eye. Maximum flash intensity of1500000 candlepower (setting No. 16) is used in all proce-dures. A red LED is used as fixation point.

RecordingThe pupil is dilated (Ruch medriaticun). The cornea is

anesthetized (Pantocain), methyl cellulose is added to preventcorneal drying and erosion, and the ERG is recorded via aBurian-Allen bipolar electrode. The signal is fed to an am-plifier with a band-pass filter of 0.1-3000 Hz. The ERG isdisplayed on a memory oscilloscope and sampled by a PDP11/55 computer. Both oscilloscope and computer samplingare triggered by the photostimulator.

Stimulating proceduresTwo procedures are employed; one for recording the dark-

adapted ERG and the other for recording the progressivelylight adapted ERG.

In the first procedure the subject is dark adapted for 15 minand about ten flashes are then given every 15 s. This methodwas chosen because it greatly enhances the oscillatory po-tentials while the slow components are practically identicalto those of the completely dark adapted ERG.5"13 To reducethe effect of random noise, four ERGs are averaged.

53 J. Opt. Soc. Am., Vol. 70, No. 1, January 1980 0030-3941/80/010053-07$00.50 (0 1980 Optical Society of America

1501VL20 ms

FIG. 1. Two superimposed dark adapted ERGs, recorded at 15-s interval.Note that the signals are time locked only for the first 55-60 ms.

In the second procedure a conditioning flash is given after15 min of dark adaptation; then a train of four flashes at aconstant interflash interval is given and the restulting fourERGs are averaged. The conditioning flash is identical to thefour stimuli flashes (maximum intensity, set # 16). The in-terval between flashes is different for each series and is variedfrom 60 to 0.5 s. Three minutes in the dark elapse betweeneach series, to allow the retina to return to the dark adaptedcondition. This is checked by superimposing the darkadapted ERG resulting from the conditioning flash ERG atthe beginning of each series. The signals thus compared arepractically identical. This procedure is adopted from otherinvestigators5' 1 3 to enable direct comparison of results.

Data acquisitionThe laboratory is interfaced with a PDP 11/55 computer.

The ERG is sampled for 200 ms at 1 KHz, then the sampledsignal is displayed on a second memory oscilloscope func-tioning in an X- Y mode and stored on the computer's disk.

AnalysisData analysis is done off-line. Any number of points or

segments can be displayed and analyzed. Graphical andnumerical results of the computations are documented onhard copy.

1. High-pass filtering: The normalized signal is convolvedwith a 5-ms window. The resultant smoothed signal is sub-tracted from the normalized signal to pre-emphasize thehigh-frequency components of the original normalizedERG.

2. Fourier transform: The fast Fourier transform (FFT)algorithms is used to obtain the power spectrum of the signal.The signal segment is multiplied by a smoothing window toprevent high-frequency "ringing" and then zeros are added(in the time domain) to obtain a 2-Hz resolution, regardlessof the signal length. The normalized power spectrum of thesignal is then displayed and the first 50 coefficients are printedout.

When the whole ERG (ca. 100 ins) is analyzed in the fre-quency domain, the decaying part of the b-wave, which ismuch slower than the rest of the ERG, dominates, since it hasa large amplitude, and other ERG components are not seen.Also, after approximately 60-70 ms, there is often an addi-tional component due to eye movements-the myoclonic re-flex' 8 (Fig. 1), which is not completely time-locked to thestimulus. We therefore analyze a short (55 rns) segment,during which the signal is completely timed-locked [withoutthe randomness introduced by the eye movement (see Fig. 1)].It should be pointed out that for the maximum-intensity flashused, the a wave, oscillatory potentials and most of the b-wave

54 J. Opt. Soc. Am., Vol. 70, No. 1, January 1980

are already present within the 55-ms segment and there is nomasking by slow components.

3. Spectral estimation (linear prediction): Here we usean autoregressive (all-pole) model of the signal in order toquantify the analysis of the signal in the frequency do-main.19' 20 The choice of the number of poles is conditionedby the spectrum obtained via the FFT method. Whereas inthe FFT routine the frequency components are equaly spacedwithout any bias, in the LP routine they are determined op-timally at the dominant frequencies, thus enabling both datacompresssion and automatic detection of changes offrequencies with changes in, say, stimulus conditions, or ret-inal pathologies. It was empirically found that 16 poles is anappropriate number for obtaining the three dominantfrequencies.

Although no preconditioning is required in order to extractthe dominant frequencies in this way, here too we apply thehigh-pass filtering algorithm as in the case of FFT, so thatresults of both analyses could be compared.

The estimated power spectrum is displayed and a list of thedominant poles and their absolute value is printed. An em-pirically determined threshold of absolute value greater than0.8 is used in selection of dominant frequencies. 2 0

RESULTS

Characteristic frequenciesA typical power spectrum, calculated by the FFT method

for the first 55 ms of the ERG [Fig. 2(b), continuous line]shows a large amplitude peak at ca. 18 Hz, a low amplitudewide peak in the range of 120-150 Hz, and some power at themidfrequency band. The peaks are not well defined due tothe small number of sample points (55) analyzed. Using the

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FIG. 2. (a) A normal dark adapted ERG. (b) Power spectrum of the ERG

shown in (a) as calculated by the FFT (continuous line), and estimated bythe LP (broken line). The relative energy is given on linear scale to facilitate

comparison with previous work.5

Moshe Gur and Yehoshua Zeevi 54

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FIG. 3. (a) Enhancement of the OP obtained by conditioning the ERG witha high-pass filter. (b) FFT spectrum (continuous line) and LP spectrum(broken line) of part (a). The midrange frequency lobe is clearly seen inthe FFT analysis and the high frequency FFT lobe splits into two maximain the LP spectrum.

LP method [Fig. 2(b), broken line] the low and highfrequencies are better defined and it appears as though thehigh-frequency range is characterized by two maxima.

Since the low frequencies have much more power than thehigh frequencies [Fig. 2(b)], the signal was preconditioned soas to enhance the high frequencies [Fig. 3(a)]. The powerspectrum of the preconditioned signal [FFT method; Fig. 3(b),continuous line] clearly shows now three dominant peaks atlow-, mid-, and high-frequency range, whereas when the LPmethod is used [Fig. 3(b), broken line] the wide, high-fre-quency peak is described by two peaks at 126 and 162 Hz.

It seems thus that when both LP and FFT methods areused, the normal dark adapted ERG can be characterized byfour dominant frequencies. A major one at the low-frequencyrange and three minor ones; one at the midfrequency and twoat the high-frequency range. The mean and standard de-viation of these frequencies, obtained from the ERG of 26normal eyes, are given in Table I. Time-domain parameters

extracted from the same signals are generally of a much highervariability (Table I). The dominant frequencies determinedby the LP method are also characterized by the absolute valueof the corresponding poles, which is a measure of the qualityfactor. The dominant ERG components are thus charac-terized by two indices, the frequencies and the absolute valueof the signal-model poles. Another result of the frequencyanalysis, given in Table I, is the oscillatory potentials indexdefined as the ratio of the low-frequency power spectrum peakto the high-frequency power spectrum peak-as calculatedfrom the FFT method. Since the power spectrum is calcu-lated in relative terms, the oscillatory potentials of the varioussubjects can be compared, whereas only intrasubject com-parison was possible when other methods were used,5,13-15since the OP amplitude was not normalized.

Light adaptationIn the light adapted state the a- and b-wave implicit times

are shorter than in the dark adapted state. These changes,we assumed, might affect the low- and midfrequency ERGcomponents. As for the high frequencies, Algyere andWestbeck5 have shown that the dominant frequency of theoscillatory potentials, as determined by the FFT method, isshifted from 140-160 Hz towards 110-120 Hz as the retinabecomes more light adapted. Since the LP method charac-terized the oscillatory potentials by two maxima, we wantedto see whether light adaptation will affect these maximaequally or not. The retina was progressively light adaptedas the interval between the light stimuli was progressivelyshortened (see methods). Figure 4 illustrates changes in theERG as a result of light adaptation. The frequency domainresults are given in Table II. As the retina becomes more lightadapted, the low-frequency component shifts toward higherfrequencies while the midfrequency component shifts at firsttoward lower frequencies and then, at photopic levels, dropsout. Most of the apparent time-domain changes occur at 1-and 0.5-s interflash intervals (Fig. 4). No such sudden changeis paralleled in the frequency domain.

As shown in Table II, there is a shift in the OP frequencyobtained by the FFT, as a result of light adaptation. The twomaxima described by the LP method are, however, not equallyshifted by light adaptation. While the lower-frequencymaximum is shifted by 22 Hz (15.7% change), the high-fre-quency maximum is shifted by only 13 Hz (8.3% change). Thedifference appears to be significant when compared to thegenerally low S.D.

TABLE I. Frequency and time-domain ERG features averaged over 13 normal subjects (26 eyes).

Frequency domain Time domainFFT LP

Dominant freq. Coef. of Dominant Coef. of Abs. value Coef. of Coefficient(Hz) variation freq. (Hz) variation of poles variation of variation

(mean ± S.D.) (c-2/u) (mean + S.D.) (62/y) (mean + S.D.) (a2/g) Mean ± S.D. (tr2/M)

18.4 ± 1.4 0.1 23.1 ± 2.7 0.30 0.96 ± 0.006 0.006 a to b (trough to peak)amplitude (Volts)

79.1 ± 9.8 1.16 126.2 + 8.3 0.52 0.94 ± 0.02 0.02 500 + 73.9 10.2146.6 ± 9.1 0.56 159 ± 10.4 0.65 0.93 ± 0.015 0.015 a-wave implicit time (msec)Low freq. energy 15.3 ± 2.4 0.47High freq. energy b-wave implicit time (msec)

11 ± 4.1 1.4 44 ± 8.3 1.56

55 J. Opt. Soc. Am., Vol. 70, No. 1, January 1980 Moshe Gur and Yehoshua Zeevi

TABLE II. Dominant frequencies shift as a function of light adaptation as specified by intra-flash intervals (averaged from 10 eves).

Intervalbetweenflashes(s)

Dominantfrequenies\(Hz)

mean ± S.D. 60 30 15 5 2 1 0.5

Low frequencyFFT 17.1 + 1.0 18.4 + 0.5 19 ± 0.9 19.5 ± 0.9 20.4 ± 1.3 21.8 + 2.2 22.7 ± 1.5LP 22.3 + 2.0 23.9 ± 2.5 25.5 + 0.9 27 + 1.0 27.8 ± 1.8 28.9 + 1.1 29.2 + 0.5

Mid frequencyFFT 87 ± 1.3 86 + 1.2 84.6 + 1.5 82 + 1.2 - - -

High frequencyFFT 145 + 12.7 142 ± 12.6 140 ± 11.1 136 + 10 129.1 + 10.2 130 + 7.2 129 ± 8.3LP 127.2 + 13.9 122.6 + 9.4 122.7 + 9.4 117.3 + 7.6 108.1 + 3.3 107.2 + 3.9

155 + 13.3 151.4 + 7.9 154 ± 10.5 148.1 + 7.1 143.4 + 4.4 143.1 + 4.4

Sensitivity to noiseDetermination of the ERG time-domain parameters, such

as peak-to-peak amplitude and a- and b-wave implicit times,is very sensitive to noise. Indeed, when the signal-to-noiseratio is very low, as is the case in certain pathologies 1-22 orwhen a noncorneal ERG is recorded,16 the signal has to beaveraged many times before the relevant parameters can bereliably determined.

Figure 5(a) shows an ERG recorded from the lower eye lid.No averaging was used and the signal is very noisy, since thesignal amplitude (ca. 30 AV) is within the range of physio-logical and system noise. When the signal is analyzed by theFFT method, however, [Figs. 5(b) and 5(c), continuous line],one can clearly see the dominant low and high frequencies (at19 and 142 Hz), in addition to the maxima contributed by thenoise.

The LP description of the noncorneal ERG in Figs. 5(b) and5(c) is practically the same as that of the relatively noise-freecorneal ERG (Figs. 2 and 3). Analysis of the backgroundnoise recorded with no stimulus indicates that it has a wide-band spectrum. The LP method is therefore suitable for thefrequency analysis of the ERG under noisy conditions, sincethe dominant frequencies are obtained by means of correlationalgorithms, thereby becoming relatively insensitive to wide-band noise.

DISCUSSION

The few published reports on frequency analysis of theERG 5'7-8'10 -1 1 deal only with a specific aspect of the ERG, such

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as the nonlinear character of the b-wave or changes in OPfrequency with light adaptation, but do not attempt to char-acterize the whole ERG in a normative way.

Wiener's G -functional or Voltera expansion,22 applied firstby Stark2 3 in the analysis of biological signals and systems, wasrecently used to characterize the human ERG,6' 9 and it wasfound that one can predict, approximately, the flash ERGaccording to the first-order kernel, and correlate some pho-topic and scotopic components with certain kernel compo-nents. This technique, however, necessitates a large numberof flashes and hence is usually limited to the photopic regime;it also requires an extensive computation facility.

Our aim was to use the conventionally recorded ERG andquantitatively characterize it by using signal analysis tech-niques in the frequency domain. These techniques can bereadily applied and a direct comparison with the vast amountof data on normal and pathological ERG is possible. Oncethe signal is characterized, changes resulting from eithermanipulation of recording parameters (intensity, wavelengths,retinal location, etc.) or retinal pathologies can be quantifiedand correlated with possible retinal mechanisms.

The conventional and widely used FFT technique yieldsthe total frequency content of the signal, thereby enabling theselection of the appropriate signal processing parameters suchas bandwidth and sampling rate. It also indicates the domi-nant frequency features as determined by the relative valuesof the power-spectrum maxima. Having determined thedominant frequency components, the LP method can be usedwith the appropriate number of poles, so that the abovecomponents are obtained. The LP method emphasizes the

FIG. 4. 55-ms segments of pro-gressively light adapted ERGs.The interflash interval (seconds) isindicated beside each segment.


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FIG. 5. (a) A noncorneal, single-flash, dark adapted ERG. (b) FFT and LPspectra of (a). The FFT spectrum contains the main maxima of the ERGat 19 and 136 Hz plus other maxima contributed by the background noise.The LP spectrum is not contaminated by the noise and the maxima obtainedare those of the ERG only. (c) FFT and LP spectra of the signal given in (a)after enhancement of the high-frequency portion. As in (b), the FFT givesthe ERG plus noise spectrum, while the LP filters out the noise.

important frequency component which may be buried in thewide lobe of the FFT spectrum (see results, Figs. 2, 3, and 5).Also, since the poles are obtained by correlation computation,the method is relatively insensitive to wideband noise, and,finally, the automatic selection of a small number of polesestimating the spectrum of the wave form can be used as asignal compression technique in building a large data base ofERG signals.

Our results show that is possible to characterize the normaldark-adapted ERG in the frequency domain in a normativeway since the frequency features are consistent for all normalsand are of a very low variability which is generally much lowerthan that of the time domain features.

The decrease in variability is due partly to the normaliza-tion of the signal amplitude in the frequency analysis proce-dure which eliminates the changes in amplitude from subjectto subject 4 and even intrasubject changes as a result of dailyvariations.2 4 Also, the fact that b-wave peak is not always welldefined increases the b-wave implicit time variability. Sincein the frequency domain a whole slope contributes to the


characteristic feature and not just a single peak position, thisvariability is reduced.

Our analysis confirms the results of Algvere and Westbeck14who, by means of the FFT method, found a low-frequencypeak around 25 Hz and a high-freqency peak around 150 Hz.Since they used only one subject, no quantitative comparisonis possible. They concentrated on the high frequency bandof the spectrum since they found the low-frequency band tobe too variable and complicated to allow clear interpretation.We find that such variability may result from selection of anERG segment longer than 55-65 ms where extraretinal arti-facts are introduced (cf. Fig. 1). If, however, a 55-ms segmentis used, the low-frequency lobe is well defined and is of a verylow variability (Table I). Also, by using 55-ms segments,combined with high-pass filtering, a midfrequency band lobe,which was not identified by Algvere and Westbeck, was foundhaving a maximum at 79 Hz. The maximum is not always asclear as the first two since it is situated between two higher-power maxima and may be masked by them, but when boththe unfiltered and filtered signals are considered this lobe canalways be identified. The LP method defines the low- andhigh-frequency main maxima in a sharper way. Also, thesingle high-frequency maximum described by the FFT isconsistently resolved into two maxima by the LP method.However, any conclusion as to its physiological significancehas to be supported by additional investigation. Regardlessof such a conclusion, these features, characterizing a reducedmodel of the signal, may be useful in classification of patho-logies and in detection of stimulus parameter effects on refinalresponse via ERG analysis.

Light adaptationHaving extracted frequency domain features, it is inter-

esting to find out to which component of the ERG signal eachof them corresponds. At this stage we can say only that thelow- and midfrequency peaks are contributed by the a and bwaves, while the high-frequency peak is contributed by theOP. A more detailed analysis relating time to frequencycomponents is inherently limited, since both the LP and FFTmethods will be inaccurate for the short ERG segments (10-20ms) necessary for such an analysis. A better understandingof the correspondence between the ERG signal and frequencycomponents can be gained by manipulating the recordingconditions and observing the resulting changes in both timeand frequency domains.

Since some effects of light adaptation on the high frequencywas demonstrated, 5 we chose to test our analyses and observethe changes in the extracted set of frequency features withlight adaptation.

A gradual shift of the low frequency toward higherfrequencies and the midfrequency toward lower frequency isseen as the retina becomes progressively light adapted. Theshift in the low-frequency component is consistent with thedecrease in the a- and b-wave implicit times under theseconditions. The fact that the shift in frequency is gradual andis noticed already at a long interflash interval, while timedomain changes (particular amplitude changes) are ratherabrupt and are observed mostly at a very short interflash in-terval (Fig. 5, Table II), indicates that frequency analysis maybe a convenient tool for detecting effects of light adaptation


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at an earlier phase and over a wider range of adaptionlevels.

We are as yet unclear about the exact origin of the midfre-quency, but the direction of its shift with light adaptation andits disappearance under photopic conditions indicate that itmay reflect the splitting between the photopic and scotopica waves. This hypothesis is supported by analysis of an ERGrecord taken from a diabetic retinophothy patient that lackedany OP but had a very prominent split of the a-wave. Thefrequency spectrum showed no high-frequency componentsbut a very clear 72-Hz peak in addition to the low-frequencypeak.

The oscilliatory potentials are a curious component. Theyare of clinical value in diagnosis of circulatory changes in theretina25 and appear in various animal species.2 6' 27 It is knownthat the OP is a phenomenon separate from the a- and b-wave,but unlike the major components of the ERG, the OP's originis not clear, even though most researchers attribute it to theinner nuclear layer.26' 27

Algvere and Westbeck 5 showed that the dominant fre-quency of the OP is shifted from 160 to 120 Hz as the retinais progressively light adapted. Our results confirm such ashift with adaptation, but in addition, since in using the LPmethod the high-dominant frequency splits into two com-ponents, we were in a position to refine the analysis of theeffect of adaptation. Indeed, we found that the lower of thetwo maxima is shifted more by light adaptation than thehigher one. The OP is probably not a homogeneous phe-nomenon since the effect of light adaptation on the first peakis different from its effect on the other peaks.'5 It is con-ceivable that the two LP peaks represent the two OP phe-nomena. We can further speculate that since the first OPpeak changes less with light adaptation than the other peak,it might correspond to the high-frequency LP peak which alsochanges very little by light adaptation.

Effects of stimulus intensityIt would be instructive to apply our analyses to ERGs re-

sulting from stimuli of various intensities since with low-in-tensity stimuli, implicit times, particularly that of the scotopicb-wave, are longer and thus one would expect to find largechanges in the low-frequency component. Also, in certainretinal pathologies such as tapeto-retinal degeneration2 ' anincrease in implicit times is observed even under high-inten-sity stimulus and it would be of interest to compare the re-sulting frequency changes to those occurring with reducedintensities.

We found, in preliminary experiments, using various levelsof stimulus intensity, that when the scotopic b-wave is justabove threshold, the low-frequency peak is located around 6Hz and when the a-wave threshold is reached, the frequencypeaks shifts to 10-12 Hz. For these low intensities, however,one must analyze a longer segment (about 80-100 ms) butwhen such a length is analyzed at higher intensities, the low-scotopic-frequency component dominates and masks thephotopic, higher-frequency components. Also, eye movementartifacts appear after 55-60 ms. Thus one has either to es-tablish a standard of intensity-dependent segment length or,more elegantly, eliminate the high-intensity eye movementartifacts 2 8 and then use a long segment for all intensities and


analyze it piecewise. This way, changes in both scotopic andphotopic components could be followed, (e.g., 0-55-ms seg-ment would show changes around 20-Hz component reflectingmostly the photopic a- and b-waves while 35-90 ms segmentwould reflect changes in the scotopic b-wave).

Improvement of signal-to-noise ratio

Recording the ERG with a corneal electrode results in arelatively low noise signal. While this procedure is simple touse with the cooperating adult, a general anesthesia is usuallyapplied when children are examined.'6 Alternatively, theERG can be recorded by placing an electrode on the upper orlower lid. This way no discomfort is experienced and ERGcan easily be recorded from the awake child. Such a surfaceERG has however a very low amplitude (ca. 30-50 ,uv), as inFig. 5(a), and many times it is completely buried in the base-line noise. Thus, in order to improve the signal to noise ratio,the signal is averaged usually 64 to 128 times. The averagingprocedure greatly limits the utility of the surface ERG, since,if a dark adapted ERG is to be recorded, the interval betweenflashes has to be at least 10 s, and if a minimal number of 64ERGs are averaged it takes almost 11 min to get one mea-surable dark adapted ERG.

When frequency-domain methods are employed, however,meaningful information can be obtained even from a singlesurface-ERG response (Fig. 5). The low- and high-frequencymaxima of both the FFT and LP spectra are very similar tothose obtained when the corneal ERG is analysed. The LPspectrum is less affected by the noise and therefore a singleresponse is sufficient, but even the noisier FFT spectrum canbe smoothed out when a smaller number of signals is averaged(about 16).

It seems thus that frequency-domain technique can makepossible the usage of surface ERG without the need for a greatdeal of averaging. This should allow a wider application ofthis simple technique. Furthermore, it is conceivable thatin certain pathological conditions such as retinitis pigmen-tosa2' where the ERG amplitude is greatly diminished and thesignal must be averaged, frequency analysis might also obviateextensive averaging and thus simplify the recording proce-dure.

In conclusion, by applying frequency domain analyses tothe ERG we were able to characterize it by several features:four dominant frequencies, the relative energy of the OP, andthe signal-model features extracted via the LP method.These features are of very low variability and thus define theERG within a range narrower than is possible in the timedomain.

How useful this definition of the ERG is can be answeredonly empirically, using both normal and pathological ERGs.In the normal ERG, the frequency components should becorrelated with a wide range of stimulus conditions so thatthese components could be related to retinal mechanisms.This may increase the ERG sensitivity to various input pa-rameters, e.g., the possible dependent of OP on wavelength2 9

that has not been detected in the time domain 30 may be re-solved by means of frequency-domain analysis. Also, certainpathologies might be better diagnosed when the ERG is lookedat in the frequency domain. Finally, we would like to stress

Moshe Gur and Yehoshua Zeevi

that we do not consider the extracted set of frequency featuresa substitute for time-domain features but rather as a sup-plementary set that may be used to extend the ERG utilityin both scientific and clinical applications.

ACKNOWLEDGMENTS

This research was supported in part by the Julius SilverInstitute for Biomedical Engineering Sciences, Technion. Wewish to thank Dr. M. Bialik and Ms. Z. Portnoy for valuabletechnical and clinical assistance.

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I4S. E. Simonson, "ERG in diabetics," in The Clinical Value ofElectroretinography, edited by J. Francois (ISCERG Symposium,Ghent, 1966). (Karger, New York, 1968), pp. 403-412.

5E. Usami, "Studies on the method of measurement of oscillatorypotential on ERG," Acta Soc. Ophthalmol. Jpn. 70, 84-91 (1965).

'6A. Harden, "Non-corneal electroretinogram," Brit. J. Ophthalmol.58, 811-816 (1974).

17J. W. Cooley, P. A. W. Lewis and P. D. Welch, "The fast Fouriertransform," IEEE Trans. Audio Electroacoust. 17, 77-85 (1969).

18 R. G. Bickford, P. T. White, C. W. Sem-Jacobson, and E. A. Rodin,"Components of the photomyoclonic response in man," Fed. Proc.12, 15 (1953).

19J. Makhoul, "Linear prediction: A tutoral review," Proc. IEEE 63,561-580 (1975).

20We denote the sampled normalized signal by S(n) and assume thatit can be estimated by a linear combination of its past values:

S(n) = - £ ah S(n - h).k~I

Using the z transform we get the following all-pole model:

H(z) = 1/1 + E ah z-h.h=1

In order to find the required model of the signal one has to deter-mine the set of p coef., Iak . The estimated spectrum is accordinglyequal to:

P(w) = 1/| + A ak e-ku, 2k=1

The signal is thus characterized by the set of p poles and thedominant frequencies are selected with respect to their absolutevalue which is a measure of the quality factor.

21 J. C. Armington, P. Gouras, D. I. Tepas, and R. Gunkel, "Detectionof the electroretinogram in retinitis pigmentosa," Exp. Eye Res.1, 74-80 (1961).

2 2Y. M. Lee, Statistical Theory of Communication (Wiley, New York,1961).

23L. Stark, Neurological Control Systems -Studies in Bioengineering(Plenum, New York, 1968).

24 L. Ronchi, "Some questions concerning electroretinographic re-

sponse and its variability," Med. Res. Eng. 12, 20-24 (1978).25 D. Yonemura, T. Aoki and K. Tsuzuki, "Electroretinogram in di-

abetic retinopathy," Arch. Ophthalmol. 68, 14-24 (1962).2 6

p. Algvere, "Studies on the oscillatory potentials of the clinicalelectroretinogram," Acta Ophthalmol. Suppl. 96, 11 (1968).

27 L. Wachtmeister and J. Dowling, "The oscillatory potentials of themudpuppy retina," Invest. Ophthalmol. Visual Sci. 12, 1177-1188(1978).

28Since eye movements are conjugate, one could record from both eyeswhile simulating only one eye. Since the record from the stimu-lated eye would contain ERG plus artifacts while the record fromthe other, covered eye would contain only artifacts, one couldeliminate the common element either by simple subtraction or bymore sophisticated methods such as cross correlation or adaptivefiltering.

29J. H. Jacobson, T. Suzuki, and G. Stephens, "The electroretinogramobtained by computer techniques in color-deficient humans," Arch.Ophthalmol. 69, 424-435 (1963).

30K. Y. Fujimara, I Tsuchida, and J. H. Jacobson, "Oscillatory po-tential of the human electroretinogram evoked by monochromaticlight," Invest. Ophthalmol. 4, 683-693 (1972).

59 J. Opt. Soc. Am., Vol. 70, No. 1, January 1980 Moshe Gur and Yehoshua Zeevi

frequency-domain analysis of the human electroretinogram

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