IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
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Spectral Analysis of Auditory Evoked Potentials with Pseudorandom Noise Excitation S. NARASIMHA REDDY, MEMBER, IEEE, AND R. LYNN KIRLIN, MEMBER, IEEE
subjects by means of spectral analysis of auditory evoked potentials (AEP's), the basis for which appear to be the frequency-following responses (FFR's). Spectral analysis provides such system features as power spectral densities (PSD's) and transfer and coherence functions (CF's). A brief discussion of spectral analysis, the method of testing, and the results is given in the following sections. II. SPECTRAL ANALYSIS OF LINEAR SYSTEMS A simple linear system with one input x(t) and one output y(t) is shown in Fig. 1. Its analysis with periodic signals is accomplished by the well-known convolution integral in the time domain and via its Fourier transform in the frequency domain. However, with random signals such as noise or EEG, use is made of correlation functions in the time-domain and PSD's in the frequency domain. I. INTRODUCTION For the system shown in Fig. 1, the cross-correlation funcTRADITIONALLY, auditory and electroacoustic research tion RXY(i-) is given by has been carried out with sinusoidal stimuli. Most of the neurophysiological knowledge of the auditory system is based h (a) Rxx (,r a) da upon such testing. Even the conventional audiogram, the (1) Rxy(7-) threshold of a person's hearing level versus frequency, is found by means of pure-tone testing. However, sinusoidal inputs are where h (t) and RX)C(r) are the impulse response and the input quite different from the usual stimuli occurring in nature. The autocorrelation function of the system, respectively, with response obtained with pure tones is often unrelated to that their arguments altered to conform to the classic definition obtained with a complex signal. For example, a person with of the cross-correlation function. neural hearing loss may hear pure tones, but is unable to do If the system is excited by a unit impulse 6(t) whose PSD as well in comprehending speech. It is, therefore, reasonable is unity over a frequency range much wider than the system's to test with signals that more closely resemble the natural bandwidth, then h(t) is given by R,y(r) [1]. This follows sounds to which the ear is exposed. Pseudorandom noise from (PRN) is such a signal and has many of the same properties as true random noise. Additionally, PRN possesses many Rx(,r)=h (a) 6(r - a) da = h (T) (2) testing and processing advantages over random noise. Much auditory research has concentrated on stimulus versus response relationships in the time domain. Even though fre- or quency analysis of the response can reveal more features (3) F[R,y(r)] =F[h('r)] which are not evident in the time-domain signal, it has been avoided mainly because of processing difficulties. Recently, and however, special purpose computers and computation algoSxy(f) = H(f), (4) rithms have made it possible to easily accomplish by automation many difficult signal processing tasks. where F denotes the Fourier transform, and Sxy(f) and H(f) In this research, PRN has been employed in testing human are the cross-power spectral density and the system's transfer function, respectively. However, a signal with a flat PSD is difficult to realize in Manuscript received December 16, 1977; revised January 8, 1979. practice, in which situation the transfer function is obtained This paper is based on a Ph.D. dissertation by S. N. Reddy. S. N. Reddy was with the Auditory and Electroacoustic Research from
Abstract-Pseudorandom noise (PRN) of various bandwidths was used in testing both normal and hearing impaired subjects by means of auditory-evoked potentials (AEP's). The AEP's were studied in the frequency domain via spectral analysis rather than in the time domain as is often done. Spectral analysis provides such system features as power spectral densities (PSD's) and transfer and coherence functions. The results show that these AEP's are similar to the frequency following responses obtained with pure tones. The PSD's of the evoked responses tend to correlate slightly with those of the PRN simuli, as verified by the presence of coherence between the stimulus and the response. The average coherence over the bandwidth of the stimulus decreases with increased sensory-neural hearing loss and also as the stimulus bandwidth is increased. No unique transfer functions, with respect to the subjects or the intensities of stimuli, could be obtained. However, an attempt has been made to correlate subjects' audiograms with the spectral analysis results.
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Group, University of Wyoming, Laramie, WY 82071. He is now with the Bureau of Medical Devices, Ottawa, Ont., Canada. R. L. Kirlin is with the Department of Electrical Engineering, University of Wyoming, Laramie, WY 82071.
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
xt)
Fig.
1.
h(t)
Simple linear system
y
I
(t)
in the time domain.
T
where SX,(f ) is the auto-PSD of x (t). An important feature of spectral analysis is the coherence function (CF) '2y(f) defined as [1]
yX2Y (f_y )
I
S2yS(f)I
Sxc(f )SYY(f)
(a)
,
RXX(T)
(6)
where 0 6 2Y f)(f 1 . A zero CF implies that the input and the output are uncorrelated; while a unity CF between zero and unity would mean any one or any combination of the following: 1) nonlinearity, (b) 2) intrinsic variability, 3) noisy system, and 4) part of output PRN sequence Fig. 2. (a) Typical binary being due to some other input [1], [2]. function. A measure of the mean square value of y(t) not accounted for by x(t) at frequency f is given by the term (1 - ' (f Ear y while yx'y(f) denotes the fractional portion of the mean square value of y (t) contributed by x (t). This leads to the Respo nse definition of the signal-to-noise ratio (SNR) [2] SNR=
lY f Il- yx2y(f)
T
and (b) its autocorrelation
CN V
(7)
which is seen to be a function of frequency. The CF is also related to the information capacity of the system [3]. Other important features of spectral analysis include the phase spectrum 0,y(f ) obtained from H(f), time delay versus frequency, and time delay between input and output commonly estimated as that value of r which maximizes RXY(r)
[I].
Linear system analysis techniques and random test signals such as PRN can be applied to nonlinear systems over a limited range of applications. As shown in Fig. 2 PRN is a signal with an impulse-like autocorrelation function, hence a flat PSD. An impulse with sufficient area to produce an observable output can drive the system into nonlinearity and even severely affect it. However, PRN has the advantages of 1) constant instantaneous power levels, 2) determinable and adjustable frequency content, 3) periodicity, which means integration need be performed over only one period of the input, 4) Gaussian amplitudes if low-pass filtered, 5) repeatable generation, and 6) immunity from environmental conditions because of its digitial characteristics [4]. A more comprehensive discussion of spectral analysis using PRN is given in [5]. III. AUDITORY EVOKED BRAIN POTENTIALS A typical auditory evoked brain potential is shown in Fig. 3 [6]. A total of 15 components have been identified in it [7]. The waveform has been arbitrarily divided into 1) the early response consisting of a series of fast waves, 2) the late response consisting of clearly defined slow waves with relatively long latencies and large amplitudes, and 3) the contingent negative variation which is a very slow response that persists until the arrival of the next stimulus.
00 ms
Fig. 3. Typical averaged auditory evoked potential.
The early response depends on stimulus parameters and the site of recording. It is thought to be generated by different neural populations, with brain-stem auditory potentials probably reflected in it [8]. Moushegian et al. [91 showed that brain-stem potential could be recorded from the vertex. The potential so recorded shows a response that resembles the pure-tone stimulus responsible for it. It is, therefore, known as the FFR. The FFR is a stable and reliable response with a latency of about 6 ms. It shows an amplitude of approximately 0.25 ,V and is most evident at low frequencies, 500 Hz to 2000 kHz [8], [9]. A comprehensive discussion on AEP's and FFR's can be found in [6] - [ 10]. IV. MATERIALS AND METHODS The auditory system of human subjects can be tested by means of audio-stimuli with the response being their AEP's or FFR's. Thus, the system tested would consist of the auditory system from external ear to the cortex or the brain stem, depending on the nature of the evoked potentials. A block diagram of the human experimentation employing PRN is shown in Fig. 4. Subjects studied in this research included four normal (DI, JR, MS, and MR) and three hearing impaired (JV, NR, and FT) persons with an average age of 33 years [5]. Their hearing losses have been classified, qualitatively, as mild (JV), moderate (NR), and severe (FT). One of
REDDY AND KIRLIN: SPECTRAL ANALYSIS OF AUDITORY EVOKED POTENTIALS MONITORING MICROPHONE
481
TABLE I CHARACTERISTICS OF FB PRN STIMULUS
CONNECTING
Number of stages = n = 12, Number of bits/period = N' = 4095, Clock frequency = fc = 150 kHz, PSD is flat up to 48 kHz, Bit length = A t' = 6.67 ,us, Length of PRN period = T'= 27.5 ms, PSD frequency separation = 36.6 Hz.
AUDIO PRN x (t)
Electrodes Al and A2 were connected together. This connection and the C. electrode formed the differential input to a low-level preamplifier (PAR Model 113) which was set to provide a passband of 300 Hz to 10 kHz and cascaded to a similar preamplifier. The overall gain was 105. Records of the acoustic PRN waveforms presented to the subject were obtained as the output from a sound level meter (Bruiel and Kjaer Model 2204) used in conjunction with a condenser microphone (B & K Model 4134) which was placed directly above the subject's head. The microphone response is considered the reference input x (t) to the subject's auditory system, and as noted earlier, evoked potential the output y (t). These signals were then processed on a Hewlett-Packard Fourier analyzer (Model 541 SB). Fig. 4. Experimentation block diagram.
the hearing impaired subjects (NR) showed severe impairment in the right ear, while the other two had almost symmetrical losses. The audiograms for the hearing impaired subjects are given in the Appendix. The AEP's were recorded from an electrode affLxed to the vertex (Ce) and gold earclip electrodes -(Grass Type E34G) affixed to the left and right earlobes (Al and A2). A ground electrode (Grass Type E5G) was placed at the center of the forehead. The vertex electrode was a subdermal platinum needle (Grass Type E2B). Electrode cream (Grass Type EC2) was used with the surface electrodes. The subjects were sealed comfortably in a reclining chair within an electrically shielded, relatively soundproof chamber. The chair provided a firm support to the head and neck, thus minimizing myotic artifacts. The normal subjects were tested at 65 dB (SPL). The stimuli to all subjects were PRN, filtered and amplified so as to drive the speakers to provide 1) a narrow-band (NB) signal of about 100 Hz bandwidth, 2) a wide-band (WB) signal of 1.5-3.0 kHz, or 3) a full-band (FB) signal of 300 Hz to 8.5 kHz. The center frequency of the stimulus was kept within the range of the speech frequencies (300 Hz to 4 kHz) for the NB and WB cases. The stimuli were either continuous PRN or, in the majority of cases, periodic short bursts of PRN, with each burst consisting of one period. The bursts were generated conveniently by means of logic circuitry, because PRN before filtering is a digital process. The bursts were spaced at 100 ms with a fast rise time. Subjects tend to get bored with a continuous stimulation, thus affecting the nature of evoked potentials. The characteristics of FB PRN used are given in Table I.
V. SIGNAL PROCESSING CONSIDERATIONS The evoked response is usually very small, 0.1-0.25 ,uV, while the EEG within which it is buried is large in comparison. It thus becomes necessary to perform an averaging operation in synchrony with the stimulus. In this research 1000 responses were averaged usually with satisfactory time-domain results as observed from the oscilloscope display of the computer employed. Estimates of the various parameters noted below were extracted from the averaged time signals. If XT(t) is the time record available from the signal x(t) over the duration of time T, it can be digitized into N samples such that
(8) where n = 0, 1, 2, * * *, N - 1 and At is the sampling interval T/N. Some of the important features of processing the data xn are 1) the sampling rate, which is guided by the highest frequency present in the data and which avoids "aliasing," 2) record length, which gives rise to leakage of power in the frequency domain, and guides the frequency resolution of the Fourier transformed estimates, and 3) statistical considerations, which are factors in understanding how close an estimated parameter is to the actual parameter being estimated. These features are discussed comprehensively in literature Xn =--X T(nA t)
[111, [12].
The digital signal processing parameters are given in Table II, while the flowchart of the computer program is shown in Fig. S. VI. AUDITORY EVOKED POTENTIAL RESULTS A. Results in Time Domain Some evoked responses are shown in Figs. 6-8. With the NB stimuli they resemble FFR's obtained with pure tones and show remarkable reproducibility. In one case an increase
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
482
TABLE II DIGITAL SIGNAL PROCESSING PARAMETERS
Sampling interval = A t = 50 ,us, Sampling frequency = fs 20 kHz Nyquist frequency = fN = 10 kHz Number of data samples = N = 512 Record length = T = 25.6 ms Frequency resolution before smoothing = Af= 39.06 Hz Cross-correlation function aligned (latency of evoked potentials): 5-7 ms Lag window used: Parzen Maximum lag = M = 64 points Frequency resolution after smoothing = 156.25 Hz
(a)
CSTART Input At, N, xn, y
(b) Fig. 6. (a) NB burst stimulus at 600 Hz and (b) its averaged AEP for subject MS.
Removal of means Preprocessing -Trend removal -Prefiltering -Data window
F.F.T.
"Raw" P.S.Ds.
(a)
Inverse F.F.T.
Correlation functions and
Realign R
(T)
Multiplication with Parzen or Bartlett Window
F.F. T. LSmoothed P.S.Ds . |
System' s parameters /-Time delay in sys tem /-P .S .Ds ./ -Transfer function/ -Phase spectrum/ -Time delay vs. frequency -Coherence function -Signal-to-noise ratio -Information Capacity
/ /
STOP
Fig. 5. Simplified flowchart of spectral analysis computer program.
in stimulus intensity was followed by an amplitude increase in the evoked response (Fig. 7). With hearing impaired sub-
Fig. 7. (a) NB continuous stimulus at 600 Hz, (b) its averaged AEP at 65 dB (SPL), and (c) at 75 dB (SPL) for subject JV.
peared to be uncorrelated to the stimulus. These results were more or less similar in all cases except with the severe hearing jects, the AEP's tended to be more distinct for stimulus at impaired subject FT in whose case the evoked responses were frequencies corresponding to the subject's best hearing than less distinct, much smaller in amplitude, and masked by exelsewhere. The distinctness of the evoked responses decreased cessive noise [5]. In all cases, the latencies varied from 5.0 to 7.0 ms as conas the bandwidth of the stimulus was increased. With FB PRN the response resembled noise, possibly electrode noise, and ap- firmed from the cross-correlation functions. These latencies
REDDY AND KIRLIN: SPECTRAL ANALYSIS OF AUDITORY EVOKED POTENTIALS
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functions obtained are very similar. Only in the case of FT they tend to resemble low-pass filter response characteristics. Curves marked "reciprocal threshold hearing level (RTHL)" were extracted from the audiograms by first adding the reference hearing levels at each frequency to the audiogram, and then negating the resulting decibel values to give an equivalent "filter" characteristic of hearing. This inverted curve was then superimposed on IH(f)l, shifting it vertically to a best visual fit of IH(f)l. The dimensions of IH(f)I and the RTHL curve are, of course, different; IH(f)l is in volts/SPL, and RTHL is in 1 /SPL. The RTHL curves tend to resemble the IH(f)I in some cases.
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the gain is found by determining the weakest signal at each frequency which after "amplification" is equal in power to the noise at the "output," or brain-stem level, which hopefully is monitored via the evoked potential. Thus, the sound pressure level decibel attenuation-to-threshold with respect to some arbitrary level is essentially reciprocal gain. To check the reliability of the evoked 'potentials, a dummy subject was created by attaching two electrodes with electrode cream through a 100 kQ2 resistor. The output PSD's and CF's have been found to show no resemblance to the input PSD's [5]. They have been found to be quite small (for example, CF was less than 0.1) and are probably due to estimation errors.
The rationale for putting the reciprocal of the audiogram corrected to SPL on the same plot as H(f) is as follows. If the hearing mechanism could be considered a linear amplifier VII. CONCLUSIONS with internally generated white noise (which appears at the "4amplifier output"), then the threshold SPL is a measure of Spectral analysis with PRN appears to be able to provide the amplification, but found differently. Rather than mea- useful information beyond that provided by traditional suring the "gain" at each frequency with constant input level, methods of testing. Moreover, the testing procedure can be
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entirely automatic. It should be possible to extend the spectral analysis techniques with PRN excitation to other areas of auditory and electroacoustic research. When dealing with AEP's, it is not always easy to draw conclusions because of numerous auditory nonlinearities. The number of subjects tested here was too small to assess with confidence the generalities of these results. With these factors in mind, some of the principal results and limitations of this research are discussed below. The time waveforms of the AEP's, especially those evoked by complex stimuli, tend to be too small, masked by excessive noise, and not comparable to the stimuli [5]. However, when transformed into the frequency domain, they provide information that is readily discernible. The output PSD's are characterized by only small peaks corresponding to the stimulus bandwidth (see Figs. 9-13). These correspondences tend to decrease as the bandwidth of the stimulus is increased [5], but as mentioned above it may be possible to obtain more information with- more averaging.
With FB PRN stimulus at the same audio power, no unique transfer function with respect to subject of intensity of stimulus was obtainable because of the dynamic nature of the auditory system. However, it is apparent that NB PRN signals can be used to test hearing up to the brain-stem level. Since both the literature on FFR (with pure tones) and this research (with complex signals) show results in speech frequencies, a specific number of complex, but NB signals could be chosen to cover the entire audiogram. Such signals might be designed to simulate speech properties in order to study perception of complex signals. The CF appears to be the most informative and important aspect of this research. When averaged over the bandwidth of the stimulus for various subjects, the coherence values tended to be a function of both the bandwidth of the stimulus and the sensory-neural hearing loss of the subject. The averaged CF's for the subjects discussed here, together with those from [51, are shown in Fig. 18. For lack of a clear-cut quantitative description of sensory-neural hearing loss, that axis
486
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
I.0 t
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Fig. 18. Averaged coherence versus bandwidth of stimulus as a function of sensory-neural impairment. The center frequency of the stimulus has been fixed, where possible, around the best frequency range of the subject. (Legend: X JR; o JV; NR; A FT.)
is scaled qualitatively, viz. normal sensory-neural function and mild, moderate, and severe sensory-neural hearing loss. The CF was assumed to be near unity in the case of FFR's evoked with pure tones because such reponses follow the stimuli linearly. Several observations based on Fig. 18 can be made. 1) As the bandwidth of stimulus is increased while holding audio power constant, the CF decreases. This is because the neural discharge becomes more complex and nonsynchronized, or the "signal" in the response is of lower magnitude. It has been found that by using the CF at FB stimulus as the reference, the calculated [via (7)] extrapolation of CF's at WB and NB were higher than those obtained experimentally. This is in accord with the behavior of a linear system with a fixed internal noise level. However, with the NB stimulus CF as the reference, the calculated CF's extrapolated to WB and FB were less than the experimental values. This is probable because estimation bias is greater at lower coherence levels [1], [12] and the experimental values will be greater than those calculated. 2) For a given bandwidth, the averaged coherence decreases as sensory-neural hearing loss increases. 3) Stein and French [3] describe information capacity of a system as a logarithmic function of its CF integrated over the frequency limits of the input spectrum. It then follows, that for a given bandwidth of signal, information capacity decreases as sensory-neural hearing loss is often accompanied by a decreased speech discrimination ability which depends on the information transmitted to the brain by the auditory system. 4) The averaged coherence relationship to the stimulus bandwidth and sensory-neural hearing loss has an exponential appearance and can perhaps be defined empirically by a mathematical equation. With FB PRN stimulus the CF for normal subjects is very small in midfrequencies as compared to that at low or high
frequencies [5]. This -seems to support Wever's principle of frequency coding [141 along the lines of arguments offered by [15]. The evoked potentials reported in this research appear to be of the same genesis as the FFR's. With an NB stimulus, the evoked potential was similar to FFR's, but so was the stimulus nearly sinusoidal. Both also show the same range of latencies of 5-7 ms. Therefore, those potentials might have neural generators at the brain stem or the collicular levels. Moller [16] had employed PRN in studying the dynamic properties of cochlear nucleus units in rats. However, the research reported here is the first known attempt to apply PRN testing to a more inclusive auditory system. Considerations for any future work include 1) the acoustics of EEG chamber, 2) the measurement accuracy of the true audio input to the test system, 3) understanding the effects of power with respect to its bandwidth, 4) information regarding phase spectra, and 5) more freedom in signal processing techniques despite large amounts of data. APPENDIX Audiograms of hearing impaired subjects are shown in Figs. 19-21. ACKNOWLEDGMENT The authors wish to thank Dr. D. Childers for his critical comments and helpful suggestions in the preparation of this manuscript.
REFERENCES [1] [2] [3]
[41
[5] [6]
J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurements Procedures. New York: Wiley, 1972. G. C. Carter, C. H. Knapp, and A. H. Nuttall, "Estimation of the magnitude-squared coherence function via overlapped FFT processing," IEEE Trans. Audio Electroacoust., vol. AU-21,- pp. 3 37-344, Aug. 1973. R. B. Stein and A. S. French, "The frequency response, coherence, and information capacity of two neuronal models," Biophys. J., vol. 12, pp. 295-322, 1972. R. L. Hampton, "Experiments using pseudorandom noise," Simulation, vol. 4, pp. 246-295, 1965. S. N. Reddy, "Spectral analysis of auditory evoked potentials with pseudorandom noise excitation," Ph.D. dissertation, Dep. Elec. Eng., Univ. Wyoming, Laramie, WY, June 1977. R. F. Goldstein, "Electroencephalic audiometry," in Modern Developments in Audiology, J. Jerger, Ed. New York: Academic,
1973.
[71 T. W. Picton, S. A. Hillyard, R. Galambos, and H. I. Krausz, "Human auditory evoked potentials: I. Evaluation of components," Electroencephalogr. Clin. Neurophysiol., vol. 36, pp.
175-190, 1974. [81 D. L. Jewett and J. S. Williston, "Auditory evoked far fields averaged from scalp of humans," Brain, vol. 94, pp. 681-696, 1971. [9] G. Moushegian, A. L. Rupert, and R. D. Stillman, "Scalp recorded early responses to frequencies in the speech range," Electroencephalogr. Clin. Neurophysiol., vol. 35, pp. 665-667, 1973. [101 H. Davis and S. K. Hirsh, "The audiometric utility of brain stem responses to low-frequency sounds," Audiology, vol. 15, pp. 181-195, 1976. [111 A. P. Yoganathan, R. Gupta, and W. H. Corcoran, "FFT in the analysis of biomedical data," Med. Biol. Eng., vol. 14, pp. 239244, 1976. [12] R. K. Otnes and L. Otnes, Digital Time Series Analysis. New York: Wiley, 1972.
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S. Narasimiha Reddy (S'72-M'77) received the B.E. degree in electrical engineering from Osmania 7 University, Hyderabad, India, in _1970, the M.S. degree in electrical engineering with biomedical option from- North Dakota State University, Fargo, in 1973, and the Ph.D. degree in bioengineering from the University of Wyoming, Laramie, in 1977. During his graduate studies he was a Research and Teaching Assistant concentrating on signal processing in auditory and electroacoutics areas. During 1977-1978 he was a Post-Doctorate with the Auditory and Electroacoustic Research Group, University of Wyoming. Since 1978 he has been associated with the Bureau of Medical Devices, Ottawa, Ont., Canada, as a Research Fellow. His current research interests are in pattem recognition, system identification, and signal processing in auditory and biological systems. Dr. Reddy is a member of the Canadian Medical and Biological Engineering Society and the American Tinnitus Association.
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LEFT EAR Fig. 20. Audiograms for subject NR with moderate mixed hearing loss. (Speech Reception Threshold: 35 dB, Speech Discrimination Score: 65 percent.)
[13] S. N. Reddy and R. L. Kirlin, "Hearing aid testing using pseudorandom noise: Preliminary results," Biomed. Sci. Instrum., vol. 12, pp. 73-76, Apr. 1976. [14] E. C. Wever, Theory of Hearing. New York: Wiley, 1949. [15] J. T. Marsh, W. S. Brown, and J. C. Smith, "Far-field recorded FFR's correlates of low pitch auditory perception in humans," Electroencephalogr. Clin. Neurophysiol., vol. 38, pp. 113-119,
1975.
[16] A. R. Moller, "Statistical evaluation of the dynamic properties of the cochlear nuclear units using stimuli modulated with pseudorandom noise,"Brain Res., vol. 57, pp. 443-456, 1973.
R. Lynn Kirlin (S'66-M'68) received the B.S. and M.S. degrees from the University of Wyoming, Laramie, in 1962 and 1963, respectively, and the Ph.D. degree from Utah State University, Logan, in 1968, aUlin electrical engineering. His industrial experience includes Martin, Boeing, and Datel. Since 1969 he has been with the Department of Electrical Engineering, University of Wyoming, where he was promoted to Professor in 1978. His professional interests, publications, and research have dealt with the areas of control, communications, and signal processing. Related to these interests is his continuing academic study in the field of statistics.
479
Spectral Analysis of Auditory Evoked Potentials with Pseudorandom Noise Excitation S. NARASIMHA REDDY, MEMBER, IEEE, AND R. LYNN KIRLIN, MEMBER, IEEE
subjects by means of spectral analysis of auditory evoked potentials (AEP's), the basis for which appear to be the frequency-following responses (FFR's). Spectral analysis provides such system features as power spectral densities (PSD's) and transfer and coherence functions (CF's). A brief discussion of spectral analysis, the method of testing, and the results is given in the following sections. II. SPECTRAL ANALYSIS OF LINEAR SYSTEMS A simple linear system with one input x(t) and one output y(t) is shown in Fig. 1. Its analysis with periodic signals is accomplished by the well-known convolution integral in the time domain and via its Fourier transform in the frequency domain. However, with random signals such as noise or EEG, use is made of correlation functions in the time-domain and PSD's in the frequency domain. I. INTRODUCTION For the system shown in Fig. 1, the cross-correlation funcTRADITIONALLY, auditory and electroacoustic research tion RXY(i-) is given by has been carried out with sinusoidal stimuli. Most of the neurophysiological knowledge of the auditory system is based h (a) Rxx (,r a) da upon such testing. Even the conventional audiogram, the (1) Rxy(7-) threshold of a person's hearing level versus frequency, is found by means of pure-tone testing. However, sinusoidal inputs are where h (t) and RX)C(r) are the impulse response and the input quite different from the usual stimuli occurring in nature. The autocorrelation function of the system, respectively, with response obtained with pure tones is often unrelated to that their arguments altered to conform to the classic definition obtained with a complex signal. For example, a person with of the cross-correlation function. neural hearing loss may hear pure tones, but is unable to do If the system is excited by a unit impulse 6(t) whose PSD as well in comprehending speech. It is, therefore, reasonable is unity over a frequency range much wider than the system's to test with signals that more closely resemble the natural bandwidth, then h(t) is given by R,y(r) [1]. This follows sounds to which the ear is exposed. Pseudorandom noise from (PRN) is such a signal and has many of the same properties as true random noise. Additionally, PRN possesses many Rx(,r)=h (a) 6(r - a) da = h (T) (2) testing and processing advantages over random noise. Much auditory research has concentrated on stimulus versus response relationships in the time domain. Even though fre- or quency analysis of the response can reveal more features (3) F[R,y(r)] =F[h('r)] which are not evident in the time-domain signal, it has been avoided mainly because of processing difficulties. Recently, and however, special purpose computers and computation algoSxy(f) = H(f), (4) rithms have made it possible to easily accomplish by automation many difficult signal processing tasks. where F denotes the Fourier transform, and Sxy(f) and H(f) In this research, PRN has been employed in testing human are the cross-power spectral density and the system's transfer function, respectively. However, a signal with a flat PSD is difficult to realize in Manuscript received December 16, 1977; revised January 8, 1979. practice, in which situation the transfer function is obtained This paper is based on a Ph.D. dissertation by S. N. Reddy. S. N. Reddy was with the Auditory and Electroacoustic Research from
Abstract-Pseudorandom noise (PRN) of various bandwidths was used in testing both normal and hearing impaired subjects by means of auditory-evoked potentials (AEP's). The AEP's were studied in the frequency domain via spectral analysis rather than in the time domain as is often done. Spectral analysis provides such system features as power spectral densities (PSD's) and transfer and coherence functions. The results show that these AEP's are similar to the frequency following responses obtained with pure tones. The PSD's of the evoked responses tend to correlate slightly with those of the PRN simuli, as verified by the presence of coherence between the stimulus and the response. The average coherence over the bandwidth of the stimulus decreases with increased sensory-neural hearing loss and also as the stimulus bandwidth is increased. No unique transfer functions, with respect to the subjects or the intensities of stimuli, could be obtained. However, an attempt has been made to correlate subjects' audiograms with the spectral analysis results.
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Group, University of Wyoming, Laramie, WY 82071. He is now with the Bureau of Medical Devices, Ottawa, Ont., Canada. R. L. Kirlin is with the Department of Electrical Engineering, University of Wyoming, Laramie, WY 82071.
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IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
xt)
Fig.
1.
h(t)
Simple linear system
y
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(t)
in the time domain.
T
where SX,(f ) is the auto-PSD of x (t). An important feature of spectral analysis is the coherence function (CF) '2y(f) defined as [1]
yX2Y (f_y )
I
S2yS(f)I
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(a)
,
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where 0 6 2Y f)(f 1 . A zero CF implies that the input and the output are uncorrelated; while a unity CF between zero and unity would mean any one or any combination of the following: 1) nonlinearity, (b) 2) intrinsic variability, 3) noisy system, and 4) part of output PRN sequence Fig. 2. (a) Typical binary being due to some other input [1], [2]. function. A measure of the mean square value of y(t) not accounted for by x(t) at frequency f is given by the term (1 - ' (f Ear y while yx'y(f) denotes the fractional portion of the mean square value of y (t) contributed by x (t). This leads to the Respo nse definition of the signal-to-noise ratio (SNR) [2] SNR=
lY f Il- yx2y(f)
T
and (b) its autocorrelation
CN V
(7)
which is seen to be a function of frequency. The CF is also related to the information capacity of the system [3]. Other important features of spectral analysis include the phase spectrum 0,y(f ) obtained from H(f), time delay versus frequency, and time delay between input and output commonly estimated as that value of r which maximizes RXY(r)
[I].
Linear system analysis techniques and random test signals such as PRN can be applied to nonlinear systems over a limited range of applications. As shown in Fig. 2 PRN is a signal with an impulse-like autocorrelation function, hence a flat PSD. An impulse with sufficient area to produce an observable output can drive the system into nonlinearity and even severely affect it. However, PRN has the advantages of 1) constant instantaneous power levels, 2) determinable and adjustable frequency content, 3) periodicity, which means integration need be performed over only one period of the input, 4) Gaussian amplitudes if low-pass filtered, 5) repeatable generation, and 6) immunity from environmental conditions because of its digitial characteristics [4]. A more comprehensive discussion of spectral analysis using PRN is given in [5]. III. AUDITORY EVOKED BRAIN POTENTIALS A typical auditory evoked brain potential is shown in Fig. 3 [6]. A total of 15 components have been identified in it [7]. The waveform has been arbitrarily divided into 1) the early response consisting of a series of fast waves, 2) the late response consisting of clearly defined slow waves with relatively long latencies and large amplitudes, and 3) the contingent negative variation which is a very slow response that persists until the arrival of the next stimulus.
00 ms
Fig. 3. Typical averaged auditory evoked potential.
The early response depends on stimulus parameters and the site of recording. It is thought to be generated by different neural populations, with brain-stem auditory potentials probably reflected in it [8]. Moushegian et al. [91 showed that brain-stem potential could be recorded from the vertex. The potential so recorded shows a response that resembles the pure-tone stimulus responsible for it. It is, therefore, known as the FFR. The FFR is a stable and reliable response with a latency of about 6 ms. It shows an amplitude of approximately 0.25 ,V and is most evident at low frequencies, 500 Hz to 2000 kHz [8], [9]. A comprehensive discussion on AEP's and FFR's can be found in [6] - [ 10]. IV. MATERIALS AND METHODS The auditory system of human subjects can be tested by means of audio-stimuli with the response being their AEP's or FFR's. Thus, the system tested would consist of the auditory system from external ear to the cortex or the brain stem, depending on the nature of the evoked potentials. A block diagram of the human experimentation employing PRN is shown in Fig. 4. Subjects studied in this research included four normal (DI, JR, MS, and MR) and three hearing impaired (JV, NR, and FT) persons with an average age of 33 years [5]. Their hearing losses have been classified, qualitatively, as mild (JV), moderate (NR), and severe (FT). One of
REDDY AND KIRLIN: SPECTRAL ANALYSIS OF AUDITORY EVOKED POTENTIALS MONITORING MICROPHONE
481
TABLE I CHARACTERISTICS OF FB PRN STIMULUS
CONNECTING
Number of stages = n = 12, Number of bits/period = N' = 4095, Clock frequency = fc = 150 kHz, PSD is flat up to 48 kHz, Bit length = A t' = 6.67 ,us, Length of PRN period = T'= 27.5 ms, PSD frequency separation = 36.6 Hz.
AUDIO PRN x (t)
Electrodes Al and A2 were connected together. This connection and the C. electrode formed the differential input to a low-level preamplifier (PAR Model 113) which was set to provide a passband of 300 Hz to 10 kHz and cascaded to a similar preamplifier. The overall gain was 105. Records of the acoustic PRN waveforms presented to the subject were obtained as the output from a sound level meter (Bruiel and Kjaer Model 2204) used in conjunction with a condenser microphone (B & K Model 4134) which was placed directly above the subject's head. The microphone response is considered the reference input x (t) to the subject's auditory system, and as noted earlier, evoked potential the output y (t). These signals were then processed on a Hewlett-Packard Fourier analyzer (Model 541 SB). Fig. 4. Experimentation block diagram.
the hearing impaired subjects (NR) showed severe impairment in the right ear, while the other two had almost symmetrical losses. The audiograms for the hearing impaired subjects are given in the Appendix. The AEP's were recorded from an electrode affLxed to the vertex (Ce) and gold earclip electrodes -(Grass Type E34G) affixed to the left and right earlobes (Al and A2). A ground electrode (Grass Type E5G) was placed at the center of the forehead. The vertex electrode was a subdermal platinum needle (Grass Type E2B). Electrode cream (Grass Type EC2) was used with the surface electrodes. The subjects were sealed comfortably in a reclining chair within an electrically shielded, relatively soundproof chamber. The chair provided a firm support to the head and neck, thus minimizing myotic artifacts. The normal subjects were tested at 65 dB (SPL). The stimuli to all subjects were PRN, filtered and amplified so as to drive the speakers to provide 1) a narrow-band (NB) signal of about 100 Hz bandwidth, 2) a wide-band (WB) signal of 1.5-3.0 kHz, or 3) a full-band (FB) signal of 300 Hz to 8.5 kHz. The center frequency of the stimulus was kept within the range of the speech frequencies (300 Hz to 4 kHz) for the NB and WB cases. The stimuli were either continuous PRN or, in the majority of cases, periodic short bursts of PRN, with each burst consisting of one period. The bursts were generated conveniently by means of logic circuitry, because PRN before filtering is a digital process. The bursts were spaced at 100 ms with a fast rise time. Subjects tend to get bored with a continuous stimulation, thus affecting the nature of evoked potentials. The characteristics of FB PRN used are given in Table I.
V. SIGNAL PROCESSING CONSIDERATIONS The evoked response is usually very small, 0.1-0.25 ,uV, while the EEG within which it is buried is large in comparison. It thus becomes necessary to perform an averaging operation in synchrony with the stimulus. In this research 1000 responses were averaged usually with satisfactory time-domain results as observed from the oscilloscope display of the computer employed. Estimates of the various parameters noted below were extracted from the averaged time signals. If XT(t) is the time record available from the signal x(t) over the duration of time T, it can be digitized into N samples such that
(8) where n = 0, 1, 2, * * *, N - 1 and At is the sampling interval T/N. Some of the important features of processing the data xn are 1) the sampling rate, which is guided by the highest frequency present in the data and which avoids "aliasing," 2) record length, which gives rise to leakage of power in the frequency domain, and guides the frequency resolution of the Fourier transformed estimates, and 3) statistical considerations, which are factors in understanding how close an estimated parameter is to the actual parameter being estimated. These features are discussed comprehensively in literature Xn =--X T(nA t)
[111, [12].
The digital signal processing parameters are given in Table II, while the flowchart of the computer program is shown in Fig. S. VI. AUDITORY EVOKED POTENTIAL RESULTS A. Results in Time Domain Some evoked responses are shown in Figs. 6-8. With the NB stimuli they resemble FFR's obtained with pure tones and show remarkable reproducibility. In one case an increase
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
482
TABLE II DIGITAL SIGNAL PROCESSING PARAMETERS
Sampling interval = A t = 50 ,us, Sampling frequency = fs 20 kHz Nyquist frequency = fN = 10 kHz Number of data samples = N = 512 Record length = T = 25.6 ms Frequency resolution before smoothing = Af= 39.06 Hz Cross-correlation function aligned (latency of evoked potentials): 5-7 ms Lag window used: Parzen Maximum lag = M = 64 points Frequency resolution after smoothing = 156.25 Hz
(a)
CSTART Input At, N, xn, y
(b) Fig. 6. (a) NB burst stimulus at 600 Hz and (b) its averaged AEP for subject MS.
Removal of means Preprocessing -Trend removal -Prefiltering -Data window
F.F.T.
"Raw" P.S.Ds.
(a)
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Correlation functions and
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(T)
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F.F. T. LSmoothed P.S.Ds . |
System' s parameters /-Time delay in sys tem /-P .S .Ds ./ -Transfer function/ -Phase spectrum/ -Time delay vs. frequency -Coherence function -Signal-to-noise ratio -Information Capacity
/ /
STOP
Fig. 5. Simplified flowchart of spectral analysis computer program.
in stimulus intensity was followed by an amplitude increase in the evoked response (Fig. 7). With hearing impaired sub-
Fig. 7. (a) NB continuous stimulus at 600 Hz, (b) its averaged AEP at 65 dB (SPL), and (c) at 75 dB (SPL) for subject JV.
peared to be uncorrelated to the stimulus. These results were more or less similar in all cases except with the severe hearing jects, the AEP's tended to be more distinct for stimulus at impaired subject FT in whose case the evoked responses were frequencies corresponding to the subject's best hearing than less distinct, much smaller in amplitude, and masked by exelsewhere. The distinctness of the evoked responses decreased cessive noise [5]. In all cases, the latencies varied from 5.0 to 7.0 ms as conas the bandwidth of the stimulus was increased. With FB PRN the response resembled noise, possibly electrode noise, and ap- firmed from the cross-correlation functions. These latencies
REDDY AND KIRLIN: SPECTRAL ANALYSIS OF AUDITORY EVOKED POTENTIALS
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functions obtained are very similar. Only in the case of FT they tend to resemble low-pass filter response characteristics. Curves marked "reciprocal threshold hearing level (RTHL)" were extracted from the audiograms by first adding the reference hearing levels at each frequency to the audiogram, and then negating the resulting decibel values to give an equivalent "filter" characteristic of hearing. This inverted curve was then superimposed on IH(f)l, shifting it vertically to a best visual fit of IH(f)l. The dimensions of IH(f)I and the RTHL curve are, of course, different; IH(f)l is in volts/SPL, and RTHL is in 1 /SPL. The RTHL curves tend to resemble the IH(f)I in some cases.
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the gain is found by determining the weakest signal at each frequency which after "amplification" is equal in power to the noise at the "output," or brain-stem level, which hopefully is monitored via the evoked potential. Thus, the sound pressure level decibel attenuation-to-threshold with respect to some arbitrary level is essentially reciprocal gain. To check the reliability of the evoked 'potentials, a dummy subject was created by attaching two electrodes with electrode cream through a 100 kQ2 resistor. The output PSD's and CF's have been found to show no resemblance to the input PSD's [5]. They have been found to be quite small (for example, CF was less than 0.1) and are probably due to estimation errors.
The rationale for putting the reciprocal of the audiogram corrected to SPL on the same plot as H(f) is as follows. If the hearing mechanism could be considered a linear amplifier VII. CONCLUSIONS with internally generated white noise (which appears at the "4amplifier output"), then the threshold SPL is a measure of Spectral analysis with PRN appears to be able to provide the amplification, but found differently. Rather than mea- useful information beyond that provided by traditional suring the "gain" at each frequency with constant input level, methods of testing. Moreover, the testing procedure can be
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entirely automatic. It should be possible to extend the spectral analysis techniques with PRN excitation to other areas of auditory and electroacoustic research. When dealing with AEP's, it is not always easy to draw conclusions because of numerous auditory nonlinearities. The number of subjects tested here was too small to assess with confidence the generalities of these results. With these factors in mind, some of the principal results and limitations of this research are discussed below. The time waveforms of the AEP's, especially those evoked by complex stimuli, tend to be too small, masked by excessive noise, and not comparable to the stimuli [5]. However, when transformed into the frequency domain, they provide information that is readily discernible. The output PSD's are characterized by only small peaks corresponding to the stimulus bandwidth (see Figs. 9-13). These correspondences tend to decrease as the bandwidth of the stimulus is increased [5], but as mentioned above it may be possible to obtain more information with- more averaging.
With FB PRN stimulus at the same audio power, no unique transfer function with respect to subject of intensity of stimulus was obtainable because of the dynamic nature of the auditory system. However, it is apparent that NB PRN signals can be used to test hearing up to the brain-stem level. Since both the literature on FFR (with pure tones) and this research (with complex signals) show results in speech frequencies, a specific number of complex, but NB signals could be chosen to cover the entire audiogram. Such signals might be designed to simulate speech properties in order to study perception of complex signals. The CF appears to be the most informative and important aspect of this research. When averaged over the bandwidth of the stimulus for various subjects, the coherence values tended to be a function of both the bandwidth of the stimulus and the sensory-neural hearing loss of the subject. The averaged CF's for the subjects discussed here, together with those from [51, are shown in Fig. 18. For lack of a clear-cut quantitative description of sensory-neural hearing loss, that axis
486
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 8, AUGUST 1979
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STIMULUS BANDWIDTH IN Hz (LOG SCALE)
Fig. 18. Averaged coherence versus bandwidth of stimulus as a function of sensory-neural impairment. The center frequency of the stimulus has been fixed, where possible, around the best frequency range of the subject. (Legend: X JR; o JV; NR; A FT.)
is scaled qualitatively, viz. normal sensory-neural function and mild, moderate, and severe sensory-neural hearing loss. The CF was assumed to be near unity in the case of FFR's evoked with pure tones because such reponses follow the stimuli linearly. Several observations based on Fig. 18 can be made. 1) As the bandwidth of stimulus is increased while holding audio power constant, the CF decreases. This is because the neural discharge becomes more complex and nonsynchronized, or the "signal" in the response is of lower magnitude. It has been found that by using the CF at FB stimulus as the reference, the calculated [via (7)] extrapolation of CF's at WB and NB were higher than those obtained experimentally. This is in accord with the behavior of a linear system with a fixed internal noise level. However, with the NB stimulus CF as the reference, the calculated CF's extrapolated to WB and FB were less than the experimental values. This is probable because estimation bias is greater at lower coherence levels [1], [12] and the experimental values will be greater than those calculated. 2) For a given bandwidth, the averaged coherence decreases as sensory-neural hearing loss increases. 3) Stein and French [3] describe information capacity of a system as a logarithmic function of its CF integrated over the frequency limits of the input spectrum. It then follows, that for a given bandwidth of signal, information capacity decreases as sensory-neural hearing loss is often accompanied by a decreased speech discrimination ability which depends on the information transmitted to the brain by the auditory system. 4) The averaged coherence relationship to the stimulus bandwidth and sensory-neural hearing loss has an exponential appearance and can perhaps be defined empirically by a mathematical equation. With FB PRN stimulus the CF for normal subjects is very small in midfrequencies as compared to that at low or high
frequencies [5]. This -seems to support Wever's principle of frequency coding [141 along the lines of arguments offered by [15]. The evoked potentials reported in this research appear to be of the same genesis as the FFR's. With an NB stimulus, the evoked potential was similar to FFR's, but so was the stimulus nearly sinusoidal. Both also show the same range of latencies of 5-7 ms. Therefore, those potentials might have neural generators at the brain stem or the collicular levels. Moller [16] had employed PRN in studying the dynamic properties of cochlear nucleus units in rats. However, the research reported here is the first known attempt to apply PRN testing to a more inclusive auditory system. Considerations for any future work include 1) the acoustics of EEG chamber, 2) the measurement accuracy of the true audio input to the test system, 3) understanding the effects of power with respect to its bandwidth, 4) information regarding phase spectra, and 5) more freedom in signal processing techniques despite large amounts of data. APPENDIX Audiograms of hearing impaired subjects are shown in Figs. 19-21. ACKNOWLEDGMENT The authors wish to thank Dr. D. Childers for his critical comments and helpful suggestions in the preparation of this manuscript.
REFERENCES [1] [2] [3]
[41
[5] [6]
J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurements Procedures. New York: Wiley, 1972. G. C. Carter, C. H. Knapp, and A. H. Nuttall, "Estimation of the magnitude-squared coherence function via overlapped FFT processing," IEEE Trans. Audio Electroacoust., vol. AU-21,- pp. 3 37-344, Aug. 1973. R. B. Stein and A. S. French, "The frequency response, coherence, and information capacity of two neuronal models," Biophys. J., vol. 12, pp. 295-322, 1972. R. L. Hampton, "Experiments using pseudorandom noise," Simulation, vol. 4, pp. 246-295, 1965. S. N. Reddy, "Spectral analysis of auditory evoked potentials with pseudorandom noise excitation," Ph.D. dissertation, Dep. Elec. Eng., Univ. Wyoming, Laramie, WY, June 1977. R. F. Goldstein, "Electroencephalic audiometry," in Modern Developments in Audiology, J. Jerger, Ed. New York: Academic,
1973.
[71 T. W. Picton, S. A. Hillyard, R. Galambos, and H. I. Krausz, "Human auditory evoked potentials: I. Evaluation of components," Electroencephalogr. Clin. Neurophysiol., vol. 36, pp.
175-190, 1974. [81 D. L. Jewett and J. S. Williston, "Auditory evoked far fields averaged from scalp of humans," Brain, vol. 94, pp. 681-696, 1971. [9] G. Moushegian, A. L. Rupert, and R. D. Stillman, "Scalp recorded early responses to frequencies in the speech range," Electroencephalogr. Clin. Neurophysiol., vol. 35, pp. 665-667, 1973. [101 H. Davis and S. K. Hirsh, "The audiometric utility of brain stem responses to low-frequency sounds," Audiology, vol. 15, pp. 181-195, 1976. [111 A. P. Yoganathan, R. Gupta, and W. H. Corcoran, "FFT in the analysis of biomedical data," Med. Biol. Eng., vol. 14, pp. 239244, 1976. [12] R. K. Otnes and L. Otnes, Digital Time Series Analysis. New York: Wiley, 1972.
REDDY AND KIRLIN: SPECTRAL ANALYSIS OF AUDITORY EVOKED POTENTIALS 0
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S. Narasimiha Reddy (S'72-M'77) received the B.E. degree in electrical engineering from Osmania 7 University, Hyderabad, India, in _1970, the M.S. degree in electrical engineering with biomedical option from- North Dakota State University, Fargo, in 1973, and the Ph.D. degree in bioengineering from the University of Wyoming, Laramie, in 1977. During his graduate studies he was a Research and Teaching Assistant concentrating on signal processing in auditory and electroacoutics areas. During 1977-1978 he was a Post-Doctorate with the Auditory and Electroacoustic Research Group, University of Wyoming. Since 1978 he has been associated with the Bureau of Medical Devices, Ottawa, Ont., Canada, as a Research Fellow. His current research interests are in pattem recognition, system identification, and signal processing in auditory and biological systems. Dr. Reddy is a member of the Canadian Medical and Biological Engineering Society and the American Tinnitus Association.
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LEFT EAR Fig. 20. Audiograms for subject NR with moderate mixed hearing loss. (Speech Reception Threshold: 35 dB, Speech Discrimination Score: 65 percent.)
[13] S. N. Reddy and R. L. Kirlin, "Hearing aid testing using pseudorandom noise: Preliminary results," Biomed. Sci. Instrum., vol. 12, pp. 73-76, Apr. 1976. [14] E. C. Wever, Theory of Hearing. New York: Wiley, 1949. [15] J. T. Marsh, W. S. Brown, and J. C. Smith, "Far-field recorded FFR's correlates of low pitch auditory perception in humans," Electroencephalogr. Clin. Neurophysiol., vol. 38, pp. 113-119,
1975.
[16] A. R. Moller, "Statistical evaluation of the dynamic properties of the cochlear nuclear units using stimuli modulated with pseudorandom noise,"Brain Res., vol. 57, pp. 443-456, 1973.
R. Lynn Kirlin (S'66-M'68) received the B.S. and M.S. degrees from the University of Wyoming, Laramie, in 1962 and 1963, respectively, and the Ph.D. degree from Utah State University, Logan, in 1968, aUlin electrical engineering. His industrial experience includes Martin, Boeing, and Datel. Since 1969 he has been with the Department of Electrical Engineering, University of Wyoming, where he was promoted to Professor in 1978. His professional interests, publications, and research have dealt with the areas of control, communications, and signal processing. Related to these interests is his continuing academic study in the field of statistics.
