IEEE TRANSACTIONS ON BIOMEDICAL
94
ENGINEERING, VOL. BME-25, NO. 1, JANUARY 1978
for improved instrumentation. In animal research, long term brain stimulation has also been employed (13). The instrument described in this paper should be useful in both chronic experiments in animals and clinical applications in man.
V0
RERERENCES
.5K
4
Veq~~~~~~Vqs (ful lie)Ztisvribe
Ftigurea.tols,tage V0earose h
0eitne of theusoato switchin gatbe asw
ered. This is specially important in line operated stimulators which have a control signal provided by a non-isolated point. APPLI CATIONS
In collaboration with Dr. Parreno, the described stimulator has been tested on more than 100 steel electrodes immersed in saline. The passage of current up to 2.5 mA (monophasic, 100 Hz, 0.5 ms pulse duration) for more than 3 h, did not produce breakage in any of them. In contrast, the same number of electrodes was tested with a standard constant current stimulator, and all of them broke down physically in less than 40 min (for full details, see Parrenjo and Delgado, 1977). The hybrid stimulator has also been tested with intracerebral electrodes in the cat. Chronic stimulations totaling more than 40 h did not produce detectable changes in the impedance of the preparation. DISCUSSION Intensive research, mainly with cardiac pacemakers, has tried to minimize electrode failure and tissue damage by using optimum waveforms. Theoretically, symmetrical waves would
leave the electrode-tissue interface electrically and chemically unchanged. For this reason, capacity coupling has been used in monophasic stimulation. Unfortunately, the idea that symmetry of the charge would compensate for chemical reactions was not correct. When stainless steel and other non-noble metals are used, the current-voltage curves are not symmetrical, due to differences in the chemical kinetics of both anodic and cathodic phse~.(Frdcrciiain,wihgnrt. ot cathodic phases (Faradic rectification), which generate a voltage component related to the remaining post-pulse charge (1). case,even In In thisthis even when monophasic, case, monophasic, cathodal stimulation with AC coupling is used, the cathode will become an anode and paradoxical anodal corrosion may occur (4). To prevent this problem, some cardiac pacemakers have a diode connected backwards across the output side (from the capacitance to the reference electrode). This diode will eliminate positive charges above the saturation voltage of the diode (4). In brain research, there is less concern about these technical problems because few investigators are using chronic stimulation comparable to cardiac pacemaking. Recent clnical applications of chronic stimulation of the CNS for the therapy of epilepsy (10) and of intractable pain (11), and also for the auditory and visual protheses (12), have illustrated the need
(1) A. M. Dymond, "Characteristics of the metal-tissue interface of stimulation electrodes," IEEE Trans. Biomed. Eng., Vol. BME23, pp. 274-280, July, 1976. (2) L. Mihailovic and J. M. R. Delgado, "Electrical Stimulation of monkey brain with various frequencies and pulse durations," J. Neurophysiol.,Vol. l9,pp. 21-36, 1956. (3) S. B. Brummer and M. J. Turner, "Electrical stimulation of the nervous system: the principle of safe charge injection with noble metal electrodes," Bioelectrochemistry & Bioenergetics, Vol. 2, pp. 13-25, 1975. (4) A. Kahn and W. Greatbatch, "Physiologic Electrodes," Biomedical Handbook, C. D. Ray (Ed.), Part IV: Electronics and Instrumentation, pp. 1073-1082, 1974. (5) J. T. Mortimer, C. N. Shealy, and C. Wheeler, "Experimental nondestructive electrical stimulation of the brain and spinal cord," J. Neurosurg., Vol. 32, pp. 55 3-559, 1970. (6) R. B. Loucks, H. Weinberg, and M. Smith, "The erosion of electrodes by small current," EEC clin. Neurophysiol., Vol. 11, pp. 823-826, 1956. (7) A. Parrefio and J. M. R. Delgado, in preparation. (8) F. Del Pozo, Monteagudo, J. L., Jimenez, J. M., Delgado, J. M. R., in preparation. (9) H. A. Wittlinger, "Applications of the CA3080 and CA3080A high-performance operational transconductance Amplifiers," RCA Application Note ICAN-6668. pp. 247-248 RCA-SSD-202 Data Book, 1972. (10) I. S. Cooper, E. Grighel, and Im Amin, "Clinical and physiological effects of stimulation of the paleocerebellum in humans," J. Amer. geriat. Soc., Vol. 21, pp. 40-43, 1973. (11) J. M. R. Delgado, S. Obrador, and J. G. Martin-Rodriguez, "Two way radio communication with the brain in psychosurgical patients," Surgical Approaches in Psychiatry, L. V. Laitinen and K. E. Livingston (Eds.), Lancaster, Eng.: Medical & Technical Publ. Co., pp. 215-223, 1973. (12) M. G. Mladejovsky, D. E. Eddington, J. J. Evans, and W. H. Dobelle, "A computer-based brain stimulation system to investigate sensory protheses for the blind and deaf," IEEE Trans. Biomed. Eng., Vol. BME-23, pp. 286-296, July, 1976. (13) J. M. R. Delgado, M. Rivera, and D. Mir, "Repeated stimulation of amygdala in awake monkeys," Brain Res., Vol. 27, pp. 111-121, 1971.
An Electronc Circuit for Red/Infrared Oximeters EUGEN G. SCHIBLI, SINCLAIR S. YEE, AND VEDAVALLI M. KRISHNAN Abstract-An inexpensive electronic circuit is described for operation of a red/infrared oximeter that does not use fiberoptics. The cirlcuit provides low4evel amplitude modulation of the LED currents. NarrowLED band detectors separate the backscattered signal cnts into the Naro red and ifaecmoet.AlGIopromteiiinEE) infrared components. An AGC loop performs the division (E1/E7).
provideselow-leeluatudhemodulatte
INTRODUCTION Recently Yee et al. [1] have described a miniature reflectance type oximeter that is suitable for mounting on a catheter tip.
Manuscript received August 14, 1976; revised January 31, 1977. This work was supported in part by the National Institutes of Health
under Grants GM16436-04 and 16436-08. The authors are with the Microtechnology Laboratory, Center for Bioengineering and Department of Electrical Engineering, University of Washington, Seattle, WA 98195.
0018-9294/78/0100-0094$00.75 © 1978 IEEE
COMMUNICATIONS
95
Fig. 1. Block Diagram of the Oximeter Circuit.
'v +
Fig. 2. The Oximeter Circuit Diagram. The 1 kHz oscillator and switch are the same as those of the 1.7 kHz circuits, only the 1 k potentiometer is set differently. The supply voltages are V+ = +12 V, V - = -12 V. The resistances are in ohms, the capacitances in farads. The transistors are: Ql, Q2 2N5400; Q3 2N3823; Q4, Q5 2N5500; Q6 Spectronics SDC 410; Q7, Q8 2N2484; Q9, Q10, Qll TIS93. The OTAs and RCA CA3080.
The conversions between electrical and optical signals take place at the catheter tip. The oxygen saturation (O.S.) is obtained from O.S.=A-B (Et/Er) where El and Er are proportional to the backscattered infrared and red light intensities, respectively. The constants A and B were found to be hematocrit dependent. This note describes the electronic circuit that has been developed [2] to drive the red (R) and infrared (IR) light emitters (LEDs) and to process the reflected signals to yield (Et/Er). The circuit (Fig. 1) features continuous low-level operation of the LEDs, frequency multiplexing of the R and IR signals, low driving point impedance of the critical photodetector leads, synchronous AM demodulation of the backscattered signals, and automatic gain control (AGC) to obtain
the Eg/Er ratio over a 40 dB denominator range. The complete circuit diagram is shown in detail (Fig. 2).
CIRCUIT DESIGN The R and IR LED brightnesses are modulated by sinusoidal currents at 1.7 kHz and 1 kHz, respectively. These frequencies are low enough to minimize parasitic effects in the long catheter wires, and they are much greater than, and not harmonically related to, 60 Hz. Hence the 60 Hz interference could be better eliminated. The oscillators have a stable amplitude as the sinewaves are obtained from frequency determining active filters whose inputs are driven by square waves of well controlled amplitude. Analysis of the oscillator circuit indicates a third harmonic distortion of approximately -40 dB. The oscillator signals are further amplified in the LED current drivers. The amplitudes
96
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 1, JANUARY 1978
of the modulating currents were adjusted for a signal of 100 mVpp (peak-to-peak) at the photoamplifier output when the reflections from blood with 100% O.S. were measured. Typically the IR LED modulation current was then about 3 mApp, while the R LED current amplitude was larger by an order of magnitude. Different current booster circuits were needed for the R and IR LEDs, since the R LED chip is p-on-n, while the IR LED chip is n-on-p, and both substrates should be connected to ground in order to minimize the number of catheter lead wires. The backscattered light is sensed by the phototransistor Q6 that forms one half of a differential pair. Negative feedback linearizes and stabilizes the operation. The 1 M2 feedback resistor chip RB is mounted on the hybrid tip to eliminate pick-up by the sensitive phototransistor base lead. The signal at the photoamplifier output is 200 mVpp, i.e., 100 mVpp each for the R and IR signal. It is attenuated and ac coupled to the signal processor. The attenuation brings the signal amplitude within the 25 mV input voltage range of the subsequent amplifier. The signal processor consists of an AGC stage, synchronous demodulators, filters, and a feedback amplifier. Demodulation is achieved by the product detector circuits that multiply the composite signal by 1.7 kHz and 1 kHz square waves derived from the R and IR oscillators, respectively. In effect, each product detector alternately connects an inverting and a noninverting amplifier during the negative and positive half cycles of the multiplying square wave, respectively. The two output signals are summed and averaged over about 100 cycles by a single-pole low-pass filter. The averaged red signal VR is maintained constant at -2 V by AGC action. The error signal amplifier controls the bias current of the variable gain operational transconductance amplifier (OTA) stage, and thus the gain. The dynamic response of the AGC loop is, of course, dependent on the red signal amplitude, i.e., on the gain of the system. Typically steady-state was reached within 0.5 s when the input varied between 2 mV and 10 mV, the full scale input range being 25 mV. The averaged signal VIR is proportional to the ratio VIR/VR = Ei/Er, since both signals are amplified equally, with the denominator maintained constant. DISCUSSION Pulsed operation of the LEDs in a fiberoptic oximeter has been reported by Johnson et al. [3] . They used LED current pulses of 3 A amplitude with 0.166% duty cycle, which results in average LED currents comparable to those reported here. For the hybrid-circuit catheter tip oximeter, however, continuous low-level operation of the LEDs is thought to be preferrable for the same reasons that have led to the choice of rather low modulation frequencies. The synchronous detectors act as high Q filters whose passfrequency follows the oscillator frequency, but they also pass the odd harmonics that may be contained in the phototransistor output. As harmonic distortion is likely to depend on amplitude, it could affect the instrument reading. In our experiments, this has not been observed. Also a simple low pass filter prior to the demodulator could eliminate the harmonics. Experimental in vitro results that were obtained with a non-invasive tip using the circuit described here have been reported elsewhere [ 1] . REFERENCES [1] S. S. Yee, E. G. Schibli, and Vedavalli M. Krishnan, "A Proposed Miniature Red/Infrared Oximeter Suitable for Mounting on a Catheter Tip" IEEE Trans. Biomed. Eng., vol. 24, pp. 195-197, 1977. [21 Vedavalli M. Krishnan, "Development of a Hybrid-Tip Oximeter
and in vitro Calibration," master's thesis, Dept. of Elec. Eng., Univ. of Washington, Seattle, 1973. C. C. Johnson, R. D. Palm, D. C. Stewart, and W. E. Martin, "A Solid-State Fiberoptics Oximeter," J. Assn. Advan. Med. Instrum., vol. 5, pp. 77-83, 1971.
[31
Statistical Deconvolution of Electrocardiograms BRUCE A. EISENSTEIN AND LOUIS R. CERRATO Abstract-Distortion caused by the passage of an electrocardiogram (ECG) through a linear, time-invariant system can be removed by deconvolving the impulse response of the distorting system from the observation. By modeling the ECG as a cyclostationary signal, the deconvolution can be done without a priori knowledge of the impulse response of the distorting system.
INTRODUCTION A technique is reported for removal of distortion from signals of the form of an electrocardiogram (ECG). This distortion arises from transmission of the ECG through any linear system and such distortion could conceivably distort the diagnosis. The novel feature of the present technique is that the distorting system may be unknown and yet allow for the removal of distortion and hence diagnostic improvement. The algorithm used to remove the distortion will be referred to as the Statistical Deconvolution Algorithm (SDA). Distortion, in the sense used here, comes from the convolution of the ECG with the impulse response of a linear time-invariant system (LTIS), hence distortion removal is deconvolution. One assumption which is required is that the ECG can be modeled as a sample function from a cyclostationary (CS) random process with known statistics [ 1, 21 . It is not the intent of this note to establish the validity of the CS model but instead to illustrate the applicability of the technique to an ECG-like signal. A random signal s(t) is CS with period T if
E{s (t + T)} = E{s (t)}
(1)
and
E{s(t1 + T)s(t2 + T)} =E{s(t1)s(t2)J.
(2) Many important signals, including ECG's, can be modeled as CS including those signals which are pulse modulated and time and frequency division multiplexed [ 2] . To show how the algorithm applies, assume that a distorted ECG x (t) was formed by passing s(t), an undistorted ECG, through an LTIS with unknown impulse response h (t), as illustrated in Figure 1. The LTIS may represent, for example, a communication channel over which the ECG has been transmitted, or the preamplifier of a chart recorder. The undistorted ECG and the properties of the distorting system are not available for direct observation but the effects of the distorting system on a test signal may be employed. If we wish to remove the effect of the distortion, that is, restore the ECG, we must do so by operating on the observed signal and the "learned" parameters only. Manuscript received December 8, 1975; revised August 2, 1976 and October 29,1976. This work was supported in part by the Pennsylvania Science and Engineering Foundation under Grant ME-928-(340). B. A. Eisenstein is with the Department of Electrical Engineering, Drexel University, Philadelphia, PA 19104. L. R. Cerrato is with the Frankford Arsenal, Philadelphia, PA.
0018-9294/78/0100-0096$00.75 i 1978 IEEE
94
ENGINEERING, VOL. BME-25, NO. 1, JANUARY 1978
for improved instrumentation. In animal research, long term brain stimulation has also been employed (13). The instrument described in this paper should be useful in both chronic experiments in animals and clinical applications in man.
V0
RERERENCES
.5K
4
Veq~~~~~~Vqs (ful lie)Ztisvribe
Ftigurea.tols,tage V0earose h
0eitne of theusoato switchin gatbe asw
ered. This is specially important in line operated stimulators which have a control signal provided by a non-isolated point. APPLI CATIONS
In collaboration with Dr. Parreno, the described stimulator has been tested on more than 100 steel electrodes immersed in saline. The passage of current up to 2.5 mA (monophasic, 100 Hz, 0.5 ms pulse duration) for more than 3 h, did not produce breakage in any of them. In contrast, the same number of electrodes was tested with a standard constant current stimulator, and all of them broke down physically in less than 40 min (for full details, see Parrenjo and Delgado, 1977). The hybrid stimulator has also been tested with intracerebral electrodes in the cat. Chronic stimulations totaling more than 40 h did not produce detectable changes in the impedance of the preparation. DISCUSSION Intensive research, mainly with cardiac pacemakers, has tried to minimize electrode failure and tissue damage by using optimum waveforms. Theoretically, symmetrical waves would
leave the electrode-tissue interface electrically and chemically unchanged. For this reason, capacity coupling has been used in monophasic stimulation. Unfortunately, the idea that symmetry of the charge would compensate for chemical reactions was not correct. When stainless steel and other non-noble metals are used, the current-voltage curves are not symmetrical, due to differences in the chemical kinetics of both anodic and cathodic phse~.(Frdcrciiain,wihgnrt. ot cathodic phases (Faradic rectification), which generate a voltage component related to the remaining post-pulse charge (1). case,even In In thisthis even when monophasic, case, monophasic, cathodal stimulation with AC coupling is used, the cathode will become an anode and paradoxical anodal corrosion may occur (4). To prevent this problem, some cardiac pacemakers have a diode connected backwards across the output side (from the capacitance to the reference electrode). This diode will eliminate positive charges above the saturation voltage of the diode (4). In brain research, there is less concern about these technical problems because few investigators are using chronic stimulation comparable to cardiac pacemaking. Recent clnical applications of chronic stimulation of the CNS for the therapy of epilepsy (10) and of intractable pain (11), and also for the auditory and visual protheses (12), have illustrated the need
(1) A. M. Dymond, "Characteristics of the metal-tissue interface of stimulation electrodes," IEEE Trans. Biomed. Eng., Vol. BME23, pp. 274-280, July, 1976. (2) L. Mihailovic and J. M. R. Delgado, "Electrical Stimulation of monkey brain with various frequencies and pulse durations," J. Neurophysiol.,Vol. l9,pp. 21-36, 1956. (3) S. B. Brummer and M. J. Turner, "Electrical stimulation of the nervous system: the principle of safe charge injection with noble metal electrodes," Bioelectrochemistry & Bioenergetics, Vol. 2, pp. 13-25, 1975. (4) A. Kahn and W. Greatbatch, "Physiologic Electrodes," Biomedical Handbook, C. D. Ray (Ed.), Part IV: Electronics and Instrumentation, pp. 1073-1082, 1974. (5) J. T. Mortimer, C. N. Shealy, and C. Wheeler, "Experimental nondestructive electrical stimulation of the brain and spinal cord," J. Neurosurg., Vol. 32, pp. 55 3-559, 1970. (6) R. B. Loucks, H. Weinberg, and M. Smith, "The erosion of electrodes by small current," EEC clin. Neurophysiol., Vol. 11, pp. 823-826, 1956. (7) A. Parrefio and J. M. R. Delgado, in preparation. (8) F. Del Pozo, Monteagudo, J. L., Jimenez, J. M., Delgado, J. M. R., in preparation. (9) H. A. Wittlinger, "Applications of the CA3080 and CA3080A high-performance operational transconductance Amplifiers," RCA Application Note ICAN-6668. pp. 247-248 RCA-SSD-202 Data Book, 1972. (10) I. S. Cooper, E. Grighel, and Im Amin, "Clinical and physiological effects of stimulation of the paleocerebellum in humans," J. Amer. geriat. Soc., Vol. 21, pp. 40-43, 1973. (11) J. M. R. Delgado, S. Obrador, and J. G. Martin-Rodriguez, "Two way radio communication with the brain in psychosurgical patients," Surgical Approaches in Psychiatry, L. V. Laitinen and K. E. Livingston (Eds.), Lancaster, Eng.: Medical & Technical Publ. Co., pp. 215-223, 1973. (12) M. G. Mladejovsky, D. E. Eddington, J. J. Evans, and W. H. Dobelle, "A computer-based brain stimulation system to investigate sensory protheses for the blind and deaf," IEEE Trans. Biomed. Eng., Vol. BME-23, pp. 286-296, July, 1976. (13) J. M. R. Delgado, M. Rivera, and D. Mir, "Repeated stimulation of amygdala in awake monkeys," Brain Res., Vol. 27, pp. 111-121, 1971.
An Electronc Circuit for Red/Infrared Oximeters EUGEN G. SCHIBLI, SINCLAIR S. YEE, AND VEDAVALLI M. KRISHNAN Abstract-An inexpensive electronic circuit is described for operation of a red/infrared oximeter that does not use fiberoptics. The cirlcuit provides low4evel amplitude modulation of the LED currents. NarrowLED band detectors separate the backscattered signal cnts into the Naro red and ifaecmoet.AlGIopromteiiinEE) infrared components. An AGC loop performs the division (E1/E7).
provideselow-leeluatudhemodulatte
INTRODUCTION Recently Yee et al. [1] have described a miniature reflectance type oximeter that is suitable for mounting on a catheter tip.
Manuscript received August 14, 1976; revised January 31, 1977. This work was supported in part by the National Institutes of Health
under Grants GM16436-04 and 16436-08. The authors are with the Microtechnology Laboratory, Center for Bioengineering and Department of Electrical Engineering, University of Washington, Seattle, WA 98195.
0018-9294/78/0100-0094$00.75 © 1978 IEEE
COMMUNICATIONS
95
Fig. 1. Block Diagram of the Oximeter Circuit.
'v +
Fig. 2. The Oximeter Circuit Diagram. The 1 kHz oscillator and switch are the same as those of the 1.7 kHz circuits, only the 1 k potentiometer is set differently. The supply voltages are V+ = +12 V, V - = -12 V. The resistances are in ohms, the capacitances in farads. The transistors are: Ql, Q2 2N5400; Q3 2N3823; Q4, Q5 2N5500; Q6 Spectronics SDC 410; Q7, Q8 2N2484; Q9, Q10, Qll TIS93. The OTAs and RCA CA3080.
The conversions between electrical and optical signals take place at the catheter tip. The oxygen saturation (O.S.) is obtained from O.S.=A-B (Et/Er) where El and Er are proportional to the backscattered infrared and red light intensities, respectively. The constants A and B were found to be hematocrit dependent. This note describes the electronic circuit that has been developed [2] to drive the red (R) and infrared (IR) light emitters (LEDs) and to process the reflected signals to yield (Et/Er). The circuit (Fig. 1) features continuous low-level operation of the LEDs, frequency multiplexing of the R and IR signals, low driving point impedance of the critical photodetector leads, synchronous AM demodulation of the backscattered signals, and automatic gain control (AGC) to obtain
the Eg/Er ratio over a 40 dB denominator range. The complete circuit diagram is shown in detail (Fig. 2).
CIRCUIT DESIGN The R and IR LED brightnesses are modulated by sinusoidal currents at 1.7 kHz and 1 kHz, respectively. These frequencies are low enough to minimize parasitic effects in the long catheter wires, and they are much greater than, and not harmonically related to, 60 Hz. Hence the 60 Hz interference could be better eliminated. The oscillators have a stable amplitude as the sinewaves are obtained from frequency determining active filters whose inputs are driven by square waves of well controlled amplitude. Analysis of the oscillator circuit indicates a third harmonic distortion of approximately -40 dB. The oscillator signals are further amplified in the LED current drivers. The amplitudes
96
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-25, NO. 1, JANUARY 1978
of the modulating currents were adjusted for a signal of 100 mVpp (peak-to-peak) at the photoamplifier output when the reflections from blood with 100% O.S. were measured. Typically the IR LED modulation current was then about 3 mApp, while the R LED current amplitude was larger by an order of magnitude. Different current booster circuits were needed for the R and IR LEDs, since the R LED chip is p-on-n, while the IR LED chip is n-on-p, and both substrates should be connected to ground in order to minimize the number of catheter lead wires. The backscattered light is sensed by the phototransistor Q6 that forms one half of a differential pair. Negative feedback linearizes and stabilizes the operation. The 1 M2 feedback resistor chip RB is mounted on the hybrid tip to eliminate pick-up by the sensitive phototransistor base lead. The signal at the photoamplifier output is 200 mVpp, i.e., 100 mVpp each for the R and IR signal. It is attenuated and ac coupled to the signal processor. The attenuation brings the signal amplitude within the 25 mV input voltage range of the subsequent amplifier. The signal processor consists of an AGC stage, synchronous demodulators, filters, and a feedback amplifier. Demodulation is achieved by the product detector circuits that multiply the composite signal by 1.7 kHz and 1 kHz square waves derived from the R and IR oscillators, respectively. In effect, each product detector alternately connects an inverting and a noninverting amplifier during the negative and positive half cycles of the multiplying square wave, respectively. The two output signals are summed and averaged over about 100 cycles by a single-pole low-pass filter. The averaged red signal VR is maintained constant at -2 V by AGC action. The error signal amplifier controls the bias current of the variable gain operational transconductance amplifier (OTA) stage, and thus the gain. The dynamic response of the AGC loop is, of course, dependent on the red signal amplitude, i.e., on the gain of the system. Typically steady-state was reached within 0.5 s when the input varied between 2 mV and 10 mV, the full scale input range being 25 mV. The averaged signal VIR is proportional to the ratio VIR/VR = Ei/Er, since both signals are amplified equally, with the denominator maintained constant. DISCUSSION Pulsed operation of the LEDs in a fiberoptic oximeter has been reported by Johnson et al. [3] . They used LED current pulses of 3 A amplitude with 0.166% duty cycle, which results in average LED currents comparable to those reported here. For the hybrid-circuit catheter tip oximeter, however, continuous low-level operation of the LEDs is thought to be preferrable for the same reasons that have led to the choice of rather low modulation frequencies. The synchronous detectors act as high Q filters whose passfrequency follows the oscillator frequency, but they also pass the odd harmonics that may be contained in the phototransistor output. As harmonic distortion is likely to depend on amplitude, it could affect the instrument reading. In our experiments, this has not been observed. Also a simple low pass filter prior to the demodulator could eliminate the harmonics. Experimental in vitro results that were obtained with a non-invasive tip using the circuit described here have been reported elsewhere [ 1] . REFERENCES [1] S. S. Yee, E. G. Schibli, and Vedavalli M. Krishnan, "A Proposed Miniature Red/Infrared Oximeter Suitable for Mounting on a Catheter Tip" IEEE Trans. Biomed. Eng., vol. 24, pp. 195-197, 1977. [21 Vedavalli M. Krishnan, "Development of a Hybrid-Tip Oximeter
and in vitro Calibration," master's thesis, Dept. of Elec. Eng., Univ. of Washington, Seattle, 1973. C. C. Johnson, R. D. Palm, D. C. Stewart, and W. E. Martin, "A Solid-State Fiberoptics Oximeter," J. Assn. Advan. Med. Instrum., vol. 5, pp. 77-83, 1971.
[31
Statistical Deconvolution of Electrocardiograms BRUCE A. EISENSTEIN AND LOUIS R. CERRATO Abstract-Distortion caused by the passage of an electrocardiogram (ECG) through a linear, time-invariant system can be removed by deconvolving the impulse response of the distorting system from the observation. By modeling the ECG as a cyclostationary signal, the deconvolution can be done without a priori knowledge of the impulse response of the distorting system.
INTRODUCTION A technique is reported for removal of distortion from signals of the form of an electrocardiogram (ECG). This distortion arises from transmission of the ECG through any linear system and such distortion could conceivably distort the diagnosis. The novel feature of the present technique is that the distorting system may be unknown and yet allow for the removal of distortion and hence diagnostic improvement. The algorithm used to remove the distortion will be referred to as the Statistical Deconvolution Algorithm (SDA). Distortion, in the sense used here, comes from the convolution of the ECG with the impulse response of a linear time-invariant system (LTIS), hence distortion removal is deconvolution. One assumption which is required is that the ECG can be modeled as a sample function from a cyclostationary (CS) random process with known statistics [ 1, 21 . It is not the intent of this note to establish the validity of the CS model but instead to illustrate the applicability of the technique to an ECG-like signal. A random signal s(t) is CS with period T if
E{s (t + T)} = E{s (t)}
(1)
and
E{s(t1 + T)s(t2 + T)} =E{s(t1)s(t2)J.
(2) Many important signals, including ECG's, can be modeled as CS including those signals which are pulse modulated and time and frequency division multiplexed [ 2] . To show how the algorithm applies, assume that a distorted ECG x (t) was formed by passing s(t), an undistorted ECG, through an LTIS with unknown impulse response h (t), as illustrated in Figure 1. The LTIS may represent, for example, a communication channel over which the ECG has been transmitted, or the preamplifier of a chart recorder. The undistorted ECG and the properties of the distorting system are not available for direct observation but the effects of the distorting system on a test signal may be employed. If we wish to remove the effect of the distortion, that is, restore the ECG, we must do so by operating on the observed signal and the "learned" parameters only. Manuscript received December 8, 1975; revised August 2, 1976 and October 29,1976. This work was supported in part by the Pennsylvania Science and Engineering Foundation under Grant ME-928-(340). B. A. Eisenstein is with the Department of Electrical Engineering, Drexel University, Philadelphia, PA 19104. L. R. Cerrato is with the Frankford Arsenal, Philadelphia, PA.
0018-9294/78/0100-0096$00.75 i 1978 IEEE
