Method for processing signals, particularly for oximetric measurements on living human tissue

A method is used for processing signals, particularly for oximetric measurements on living human tissue. Spurious signals are suppressed with respect to information signals. The spurious signals have a frequency lying in a first frequency range, and the information signals have a frequency lying in a second frequency range being different from said first frequency range. The signals are conducted over a filter having essentially a blocking characteristic in said first frequency range and having essentially a transmission characteristic in said second frequency range. An output signal of the filter is further processed. In order to eliminate distorting effects from the filter on the information signal, a first function is determined representing the deviation of the frequency response of the filter in said frequency range from an ideal transmission characteristic. A second function inverted with respect to said first function is generated. The output signal is weighted by the second function to generate a weighted output signal.

BACKGROUND OF THE INVENTION 
The invention relates to a method for processing signals, particularly for 
oximetric measurements on living human tissue, in which spurious signals 
are suppressed with respect to information signals, said spurious signals 
having a frequency lying in a first frequency range and said information 
signals having a frequency lying in a second frequency range being 
different from said first frequency range, said signals being conducted 
over a filter having essentially a blocking characteristic in said first 
frequency range and having essentially a transmission characteristic in 
said second frequency range, an output signal of said filter being further 
processed. 
It is well-known in the art to perform measurements of various physical 
quantities by using detectors, to convert the physical quantity into 
electric voltages. However, when processing the electrical signal, derived 
from such detectors, one has to take into account that the information 
signals, i.e. the signals, representing the desired physical quantities, 
are mostly superimposed by spurious signals coming from various sources. 
The effect of spurious signals becomes more important, the more the 
sensitivity of the measuring circuitry is enhanced. Typical examples for 
spurious signals are drift signals, i.e. low-frequency aberrations being 
generated by thermal effects, by slow alterations of supplying voltages, 
etc. 
When the frequency of such spurious signals is different from the frequency 
of the information signals, one can easily suppress the spurious signals 
by inserting filter circuits into the measuring circuitry which have a 
blocking characteristic in the frequency range of the spurious signals and 
which have a transmission characteristic in the frequency range of the 
information signals. 
In the field of oximetric measurements on living human tissue, it is known 
to use photoelectric probe heads exhibiting a plurality of light-emitting 
elements, e.g. light-emitting diodes (LED) which are tuned to different 
wavelengths so that light beams of different wavelength may be emitted on 
the human tissue under investigation. The light beams, having penetrated 
the tissue, are then directed on a photo-sensitive device which converts 
the impinging light beams into electrical signals. 
However, when performing such measurements, one potential source of 
spurious signals is the ambient light at the location where the 
measurement is performed. Considering that human tissue is partially 
transparent to light, it can easily be understood that the photo-sensitive 
device used in oximetric measurements is not only subject to the light 
beams, generated by the light-emitting elements but also to ambient light, 
be it generated by electric lamps or be it natural day-light. Ambient 
light may vary in amplitude during the time where the measurement is 
performed so that the photo-sensitive device will detect a mixture of 
slowly varying ambient light and of the light beams generated by the 
light-emitting elements. 
In order to overcome these deficiencies, it is well-known in the art to use 
multiplex techniques. For this purpose, pulse trains are generated, being 
composed by individual pulses, each of which being generated by a 
light-emitting element and, thus, corresponding to a light beam of 
different wavelength. One can, for example, use pulse trains having three 
individual pulses corresponding to short light pulses of three different 
wavelengths. One can, further, timely separate the pulse trains by a short 
break, during which no light is emitted so that the electrical signal, 
generated by the photo-sensitive device during such break, is only 
dependent on ambient light. 
As long as the influence of ambient light is constant, one can easily 
measure an offset-value corresponding to the electrical signal during the 
break and can subtract the offset-value from any succeeding electrical 
signals received when the pulse trains appear. Such offset-compensation 
is, however, only effective if the influence of ambient light is constant 
within the desired precision of measurement. 
However, in most cases, this is not true, because the influence of ambient 
light varies with time and can, therefore, not be compensated by simply 
subtraction measures. 
Therefore, one has tried to overcome these problems by inserting 
appropriate filter circuitry into the signal path behind the 
photo-sensitive element. Considering that the pulse frequency is 
relatively high, i.e. in the order of magnitude of several hundred cps, 
and considering, further, that the variation of ambient light is in the 
order of a few cps, one has used high-pass filter circuits to suppress 
spurious signals generated by the variation of ambient light. 
However, due to the fact that all filters have a frequency characteristic 
influencing frequency bands lying octaves away, inserting a high-pass 
filter into the signal path of an oximetric measuring instrument would 
result in a distortion of the information signal even if the frequency of 
the information signals is several orders of magnitude away from the 
spurious signal frequency. This holds true the more the sensitivity of the 
oximetric system shall be enhanced which requires a high-precision of 
amplitude measurement on the light pulses received by the photo-sensitive 
element. 
It is, therefore, an object of the present invention to improve the method 
mentioned above by effectively suppressing spurious signals and, 
concurrently, preserving the precision of high-sensitivity measurements. 
BRIEF DESCRIPTION OF THE INVENTION 
This object is achieved according to the invention by determining a first 
function representing the deviation of the frequency response of said 
filter in said second frequency range from an ideal transmission 
characteristic, generating a second function inverted with respect to said 
first function and weighting said output signal by said second function to 
generate a weighted output signal. 
The object of the invention is, thus, fully achieved, because all 
distortions, generated by the filter, are fully eliminated, since the 
signal, appearing at the output of the filter, is electrically processed 
exactly the opposite way as was the case in the filter with respect to the 
distorting characteristic from the spurious signal frequency range still 
being effective in the information frequency range. 
Therefore, irrespective of what these distortional effects are and how 
effective they may be, these distorting effects are fully compensated for 
by using an inverted characteristic and applying such characteristic on 
the signal at the output of the filter. 
In a preferred embodiment of the invention, the information signal is a 
multiplexed signal having pulse trains of a high frequency, said spurious 
signals having a low frequency, and said filter being a high-pass filter. 
As explained above, this embodiment of the invention can advantageously be 
used for all measurements where spurious signals appear in the 
low-frequency range, as is the case with thermal variations, long-term 
variations of supply voltages and, above all, in the case of measurements 
using light beams in the presence of varying ambient light. 
In another preferred embodiment of the invention, the inverted function is 
a first square matrix having a number of lines and columns being equal to 
the number of pulses of said pulse trains, said output signal being 
represented as a second square matrix of amplitudes of pulses of pulse 
trains appearing at the output of said high-pass filter, said first and 
second matrices being multiplied by each other to generate a third square 
matrix of amplitudes of pulses of pulse trains of said weighted output 
signal. 
This embodiment of the invention is particularly advantageous, because one 
can easily perform matrix operations by using digital electronics to 
convert incoming signals into weighted output signals. Once the first 
function representing the deviation of the frequency response of the 
filter in the second frequency range is known, one can easily convert the 
first function into a matrix, store such matrix in an electronic memory 
and performing weighting operations on the incoming measuring signal by 
transforming the pulse train signals into a matrix and multiplying this 
matrix with the one matrix stored in the memory. 
According to another preferred embodiment of the invention, one can 
determine coefficients of said first matrix in that a number of test pulse 
trains of a predetermined first amplitude is fed to said high-pass filter, 
said number of test pulse trains as well as the number of test pulses of 
each of said test pulse trains corresponding to said number of lines and 
columns of said first matrix, second amplitudes of pulses appearing at 
said output of said high-pass filter in response to said test pulses being 
measured, and said coefficients being determined by dividing a fourth 
matrix defined from said first amplitudes by a fifth matrix defined from 
said second amplitudes. 
This embodiment of the invention has the particular advantage of allowing 
to determine the first function representing the deviation of the 
frequence response of the filter in the second frequency range by once 
testing the filter with test pulse trains of known amplitudes. When 
applying the test pulse trains on the filter in the absence of any 
spurious effects, one can, thus, determine the characteristic of the 
filter as a matrix of coefficients in order to then perform the 
afore-explained operations on incoming measuring signals during actual 
measurements. 
According to a further preferred embodiment of the invention, the test 
pulse trains exhibit each one pulse having a high first amplitude, the 
other pulses having low first amplitudes. 
When doing so, one can enhance the precision of succeeding matrix 
calculations and one can obtain matrices of diagonal form which, further, 
enhance the precision of measurements and reduce the expenditures of 
weighting operations. 
According to a further embodiment of the invention, one can decrease the 
principal diagonal coefficients of said first matrix by unity, factor out 
the value of a n-th power of two, and digitally multiply said second 
matrix by said first matrix using digital words having a number of bits 
smaller than n. 
These measures allow to reduce the amount of operations on the measured 
signal. If, e.g., the matrix coefficients are processed with a precision 
of 16 bits, the multiplication of matrices would require nine multiplying 
operations in 16.times.16 bit technology or thirty six operations in 
8.times.8 bit technology, respectively. However, when proceeding according 
to the afore-mentioned embodiment of the invention, one can reduce these 
operations to one half, i.e. to nine operations in 8.times.16 bit 
technology or eighteen operations in 8.times.8 bit technology. In 
practical examples, one has found that in spite of this drastic reduction 
in operations, the residual error is negligible, because it is smaller 
than 10.sup.-3. 
According to another embodiment of the invention, one can, alternately, 
standardize the principal diagonal coefficients of said first matrix on 
unity, then, again, factor out the value of a n-th power of two, and 
digitally multiply said second matrix by said first matrix using digital 
words having a number of bits smaller than n. 
This embodiment of the invention, too, has the particular advantage of 
reducing the number and extent of operations, necessary to process the 
signal from the output of the high-pass filter. Making again reference to 
the above-mentioned example with the necessity of performing nine 
multiplications in 16.times.16 bit technology without the particular 
measures of the embodiment of the invention, one can achieve a reduction 
to six operations in 8.times.16 bit technology or twelve operations in 
8.times.8 bit technology, respectively. 
According to a further embodiment of the invention, one can weight an 
offset-value by said first matrix, having its principal diagonal 
coefficients standardized to unity to generate a sixth matrix of 
correction values, said correction values being subtracted from said 
weighted signals generated from pulse trains exhibiting said offset-value. 
This embodiment of the invention has the particular advantage of avoiding 
bipolar operations. If the offset-value of constant amplitude were 
compensated for at the input of the high-pass filter, the distortion, 
generated by the high-pass filter, could result in negative polarities of 
output signals which, again, would generate the necessity of performing 
bipolar operations on the output signal of the high-pass filter. In 
contrast, the afore-mentioned measures of this particular embodiment of 
the invention allows to compensate for constant offset-values at the 
output of the high-pass filter by introducing a correction operation in 
which the constant offset-value, too, is weighted by the transmission 
characteristic of the high-pass filter. 
Although the present invention may be applied in various fields of 
measuring technology, it is particularly preferred to use the invention in 
the field of oximetric measurements on living human tissue. In that case, 
one preferably uses a plurality of light-emitting elements sending in 
timely spaced relationship first pulsed light beams of different 
wavelength on a living human tissue supplied with blood, second light 
beams having passed said tissue being guided on a light-receiving element, 
said light-receiving element generating said multiplexed signal. 
Thus, the invention allows to use all of the afore-mentioned advantages in 
connection with oximetric measurements so that the oxygen saturation of 
blood may be measured on a patient with unparalleled precision, because 
one can effectively eliminate all measuring errors generated by spurious 
signals, particularly by slowly varying ambient light. 
Further advantages of the invention will become apparent from the 
description of embodiments as well as from the accompanying drawings. It 
goes, further, without saying that all of the afore-mentioned elements may 
be used separately or in other combinations as expressedly mentioned 
without deviating from the scope of the present invention.

DETAILED DESCRIPTION OF THE INVENTION 
As already explained hereinbefore, the present invention may be used for a 
wide range of measuring problems. However, for the sake of clarity, the 
following description of embodiments makes reference to oximetric 
measurements on human tissue supplied with blood. 
Oximetric measurements of this kind are performed in order to determine the 
saturation of oxygen within the blood of a patient. It is well-known in 
the art to evaluate the oxygen supply in the circulation of a patient by 
determining the amount of the patient's hemoglobin, carrying chemically 
bound oxygen molecules compared to the amount of the total patient 
hemoglobin as a percentage. 
Common techniques use light beams emitted on the patient's tissue, e.g. on 
the finger of a patient, where the light beam penetrates a part of the 
patient's tissue either in a transmission or a reflection mode. By 
measuring the light absorption for various wavelengths in the visible and 
the infrared range, one can calculate transmission or reflection 
characteristics and, thus, determine the oxygen saturation. 
Referring now to FIG. 1, 1 designates a finger of a patient under 
investigation. A pick-up 2 is provided with a plurality of light-emitting 
elements 3, one of which being shown in FIG. 1 by means of example. The 
light-emitting elements 3 can be made as light-emitting diodes or any 
other comparable elements, capable of emitting light within the visible 
and the infrared range. The elements 3 are designed such to emit light of 
different wavelengths. 
The pick-up 2 is, further, provided with one or more light-receiving 
elements 4, e.g. a photo-sensitive transistor. 
A cable 5 is provided for feeding both the light-emitting elements 3 as 
well as the light-receiving element or elements 4 with electrical energy 
and for feeding signals to and from the pick-up 2. 
When the pick-up 2 is pressed to the patient's finger 1 and appropriate 
control signals are fed to the pick-up 2 via cable 5, first beams of light 
6 are emitted on the patient's tissue, designated by reference numeral 7. 
The hemoglobin in the patient's tissue 7 is shown at 8. When the first 
light beams 6 impinge on hemoglobin 8, a second beam of light is reflected 
onto light-receiving element or elements 4. An appropriate electrical 
signal is then generated and transmitted via cable 5 to an electronic 
circuitry, not shown in FIG. 1. 
According to the amount of hemoglobin 8, being chemically bound to oxygen 
molecules or not, the first beams of light 6 are more or less absorbed by 
hemoglobin 8 and, thus, the second beams of light 9 vary in amplitude 
depending on the amount of oxygen saturation of hemoglobin 8 and, further, 
depending on the particular wavelength used. 
FIG. 2 shows a block diagram of an oximetric measuring circuit, indicated 
as a whole at 10. 11 designates a pulse generator, delivering control 
pulses to a multiplexer 12. The multiplexer 12 is used to generate pulse 
patterns in order to activate light-emitting elements 3a, 3b, and 3c, 
respectively. The wavelength of the light beams, emitted by light-emitting 
elements 3a, 3b, and 3c are designated by .lambda..sub.1, .lambda..sub.2 
and .lambda..sub.3, respectively. 
After having passed through the patient's tissue, schematically designated 
at 7 in FIG. 2, the light beams impinge on light-receiving element 4, 
being represented as a photo-sensitive transistor in FIG. 2. The output 
signal of light-receiving element 4 is designated as U. 
Voltage U is then fed to a high-pass filter 14, the output signal of which 
is designated by L. In a specific mode of operation, high-pass filter 14 
may be bypassed by closing a switch 15, as will be explained below. Output 
signal L is then fed to an evaluation circuit, indicated at 16. 
The purpose of circuitry 10 of FIG. 2 is to generate light pulses by 
activating light-emitting elements 3a, 3b, and 3c, respectively, in timely 
spaced relationship, i.e. by activating the said elements one after the 
other. Thus, pulse trains of light beams with varying amplitude and 
varying wavelength are generated and received in light-receiving element 4 
after having passed through tissue 7. However, when performing such 
measurements, light-receiving element 4 is, further, subjected to ambient 
light, schematically indicated at 17. Thus, output signal U is a mixture 
of information signals, i.e. absorption response of tissue 7 with respect 
to the light pulses emitted from light-emitting elements 3a through 3c and 
spurious signals as generated by ambient light 17. The purpose of 
high-pass filter 14 and evaluation circuit 16 in combination with switch 
15 is to eliminate any error signals generated by ambient light 17, as 
will now be described in further detail. 
FIG. 3 shows a voltage vs. time characteristic of a signal 20 as appearing 
at the output of light-receiving element 4. As can easily be seen from 
FIG. 3, signal 20 is a mixture of an information signal 21 shaped as pulse 
trains and a spurious signal 22 having the shape of a slowly varying 
background signal. 
Referring now to FIG. 4, one can see the information signal 21 in a 
somewhat larger scale. Information signal 21 consists of a pulse train 23' 
in which a break is followed by three pulses having voltage amplitudes of 
U.sub.1, U.sub.2, and U.sub.3, respectively. In the break preceding the 
three pulses, an offset-value U.sub.0 is measurement, and the subsequent 
voltage amplitudes U.sub.1, U.sub.2, and U.sub.3 are measured with respect 
to offset-value U.sub.0. 
Pulse train 23' of FIG. 4 would represent an ideal signal in the absence of 
spurious signal 22. 
However, when considering the mixture of the two afore-mentioned signals, 
one would come to a representation as shown in FIG. 5 where 23 indicates a 
real pulse train as actually measured in the presence of spurious signal 
22. 
As can easily be seen from FIG. 5, pulse train 23 is distorted with respect 
to the ideal pulse train 23' of FIG. 4 in that deviation signals d.sub.1, 
d.sub.2, and d.sub.3 must be taken into account when measuring the actual 
voltage amplitude of the pulses of pulse train 23. If spurious signal 22 
has a stochastic amplitude vs. time characteristic, it is not possible to 
eliminate deviation values d.sub.1 through d.sub.3 by using extrapolation 
techniques. 
However, considering that in the case of low-frequency spurious signals the 
frequency range of the spurious signals is orders of magnitude lower than 
the frequency range of the information signals, one can use a frequency 
band separation technique. 
FIG. 6 is a transmission factor vs. frequency diagram in which 30 
represents a high-pass filter characteristic. 31 designates the filter 
attenuation in the blocking band whereas 32 designates the filter 
transmission in the transmission band. 33 indicates frequency f.sub.L of 
the pulses used for pulse trains 23. 
In contrast, 36 designates the spectral distribution of spurious signals as 
occurring during oximetric measurements in the presence of ambient light. 
As one can clearly see from FIG. 6, the frequency range of the spurious 
signals is different from the frequency range of transmission band 32 of 
high-pass filter 14. In a practical example, spurious signals occur in a 
frequency band below 5 cps whereas frequency f.sub.L of pulse trains 23 
may be set to be 400 cps up to several thousand cps. 
However, in practice a strict separation between blocking band and 
transmission band of a high-pass filter cannot be achieved. As a result, 
the attenuating behaviour of a high-pass filter in its blocking range 
becomes also effective in its transmission band, as indicated by a 
dash-dot-line in FIG. 6. 
The result of such practical behaviour of high-pass filters is depicted in 
FIG. 7. 
The left upper corner of FIG. 7 shows an ideal pulse train 23a composed of 
pulse signals S.sub.1, S.sub.2, and S.sub.3. When pulse train 23a is 
subjected to high-pass filter 14, as indicated by arrow 40 in FIG. 7, an 
output signal L is generated having the shape of pulse train 23b in the 
right upper corner of FIG. 7 with pulse signals L.sub.1, L.sub.2, and 
L.sub.3, respectively. 
The conversion of pulse train 23a into pulse train 23b corresponds to the 
frequency response of high-pass filter 14. In other words, if the 
conversion characteristic of high-pass filter 14 is known, one can 
re-convert pulse train 23b by electronic manipulation as indicated by 
arrows 41 in FIG. 7 in order to re-transform distorted pulse train 23b 
into ideal pulse train 23a. 
In order to do so, one can write down the conversion of distorted pulse 
train 23b into ideal pulse train 23a as a system of equations (1) in which 
signals S.sub.1, S.sub.2, and S.sub.3 are calculated from pulse signals 
L.sub.1, L.sub.2, and L.sub.3, respectively, by using coefficients 
a.sub.ik. In other words, a matrix of signals S may be determined by 
multiplying a matrix of signals L by a matrix A according to equation (2) 
where matrix A is written down with its coefficients a.sub.ik. 
Thus, ideal signals S may be determined as a matrix S as shown in equation 
(3). 
In order to perform the conversion as explained before, one has first to 
determine matrix A according to equation (2). 
In order to do so, one can use a technique in which test pulse trains are 
applied to the input of high-pass filter 14 in the FIG. 2 circuit in two 
operational modes, the first of which having switch 15 open and the second 
of which having switch 15 closed. 
To do so, test pulse trains may be used as shown in FIGS. 8 through 10. 
A first test pulse train 50 as shown in FIG. 8 has a first pulse 50a of a 
high amplitude succeeded by two further pulse trains 50b and 50c of lower 
but different amplitudes, respectively. A second test pulse train as shown 
in FIG. 9 has a first low-amplitude pulse 51a, a second high-amplitude 
pulse 51b, and a third low-amplitude pulse 51c. Finally, a third test 
pulse train as shown in FIG. 10 has a first low-amplitude pulse 52a, a 
second low-amplitude pulse 52b, and a third high-amplitude pulse 52c. 
The reason for using test pulse trains 50 through 52 with one 
high-amplitude pulse and two low-amplitude pulses each, is to enhance the 
precision in the determination of matrix A. 
Having performed the afore-mentioned operations, one has three matrix 
equations in which the undistorted signal (switch 15 closed) is depending 
on the distorted signal (switch 15 opened). 
This matrix equation system as written down in equation (4) may be reduced 
to one S-matrix and one L-matrix as written down in equations (5) and (6), 
respectively. In equations (5) and (6), respectively, numerical values are 
given as an example for one practical application where a standard 
commercial oximetric measuring system SaO.sub.2 -Clover D of the applicant 
was used in connection with a second order high-pass filter having a 
cut-off frequency of 30 cps. The S-matrix numerical values were achieved 
with the high-pass filter 14 bypassed whereas the L-matrix numerical 
values were measured with the high-pass filter inserted into the 
circuitry. 
The A-matrix may be determined from the S- and the L-matrix, respectively, 
by dividing the S-matrix by the L-matrix. Considering the numerical values 
as written down in equations (5) and (6), respectively, one comes to the 
numerical values for the A-matrix as written down in equation (7). 
As one can easily see from equation (7), this matrix is to a high degree 
diagonal, because its principal diagonal coefficients a.sub.11, a.sub.22, 
a.sub.33, respectively, are almost exactly equal to unity. This is because 
in view of the great distance between the respective frequency bands of 
the spurious signals and the information signals, the amplitudes of 
distorted signals L are at a first glance equal to the amplitudes of 
undistorted signals S. 
In a practical test, one has applied the A-matrix according to equation (7) 
to operational pulse trains of the oximetric system used and has found 
that the accuracy of the coefficients as written down in equation (7) is 
better than 10.sup.-3 and, thus, is below the noise level of the 
particular system used. 
When performing matrix division on the values as written down in equations 
(5) and (6), respectively, one has to perform nine multiplications in 
16.times.16 bit technology considering that the principal diagonal 
coefficients of equations (5) and (6) have five decimal digits. 
In order to reduce the necessary operations, one may recall that the 
A-matrix of equation (7) is highly diagonal as again represented in 
equation (8) where the principal diagonal coefficients are said to be 
unity and all coefficients of the upper half are negative and all 
coefficients of the lower half are positive. 
In view of the symmetry of the A-matrix, one can make a modification on 
this matrix by creating a modified matrix Eps as written down in equation 
(9). Matrix Eps is determined by subtracting a unity matrix from matrix A. 
The signal matrix S may now be written as equation (10) by combining 
equations (1) and (9). 
Factoring now out powers of two, namely 2.sup.8 and 2.sup.3, one can write 
a one-Byte coefficient matrix C as shown in equation (11). As a result, 
the coefficients used for the necessary matrix division as explained above 
with respect to equations (5) through (7) are reduced to one-Byte 
coefficients having a maximum of three decimal digits, as can be seen in 
equation (11). 
FIG. 11 shows a digital word 60 in schematic representation as forming part 
of a digital memory or a central processing unit (CPU) of a microcomputer 
signal processing unit. 
As one can see from FIG. 11, one can easily incorporate an 8-bit word into 
a 16-bit memory by placing the 8-bit word (one Byte) into memory positions 
"5" through "12", leaving positions 0 through 4 blank and inserting zero 
values into positions "13" through "15". Thus, a .+-.2.sup.-12 precision 
may be achieved. 
Thus, all coefficients may be stored in one Byte (8-bit) with a precision 
of .+-.2.sup.-12 or 0,25%, respectively. Thus, instead of making nine 
multiplications in 16.times.16 bit technology or thirty six 
multiplications in 8.times.8 bit MUL technology, as explained above, it 
would be sufficient to make nine multiplications in 8.times.16 bit 
technology or eighteen multiplications in 8.times.8 MUL 8-bit technology, 
respectively. 
A further reduction in the amount of operations may be achieved by 
standardizing the principal diagonal coefficients a.sub.11, a.sub.22, and 
a.sub.33, respectively, to unity. This may be achieved by dividing the 
respective lines of the A-matrix by a.sub.11, a.sub.22, and a.sub.33, 
respectively, as written down in equation (12). 
When using the same steps as explained above with respect to equation (11), 
one can obtain a modified 8-bit matrix C. as written down in equation 
(13). As one can easily see by comparing equations (11) and (13), the 
principal diagonal elements of 8-bit matrix C* are now all zero which 
again reduces the amount of operations to six multiplications in 
8.times.16 bit technology or twelve multiplications in 8.times.8 MUL 8-bit 
technology, respectively. 
This can easily be acknowledged when writing down the respective equations 
for signals S.sub.1, S.sub.2, and S.sub.3, respectively, as can be seen in 
equation (14). In equation (14), signals S.sub.1, S.sub.2, and S.sub.3 are 
determined from amplitudes L.sub.1, L.sub.2 , and L.sub.3 by various 
multiplication and addition/subtraction operations with various 
coefficients of the A* and C* matrix as written down in equations (12) and 
(13), respectively. 
Another aspect of the present invention is to further eliminate offset of 
pulse amplitudes appearing at the output of light-receiving device 4 which 
may not be generated by ambient effects but rather by light-receiving 
elements for themselves. 
In principle, one could subtract an appropriate offset-value from the 
signals appearing at the output of light-receiving elements 4 which, 
however, could result in negative polarity signals at the output of 
high-pass filter 4 considering e.g. signals L of FIG. 7 exhibiting 
undershoot effects at trailing edges of pulses L.sub.1, L.sub.2 and 
L.sub.3, respectively. 
In order to avoid bipolar operations in evaluation circuit 16, one can 
introduce correction values COR.sub.1, COR.sub.2, and COR.sub.3, 
respectively, as written down in equation (15). 
Equations (15) are derived under the assumption that a constant 
offset-value H appears at the output of light-receiving elements 4 and 
using a signal processing as explained above with respect to equations 
(12) and (13), respectively. 
Under the assumption of equation (16), one can write a correction value 
matrix COR as written down in equation (17) where correction values 
COR.sub.1, COR.sub.2, and COR.sub.3, respectively, may be calculated from 
constant offset-value H by using the a.sub.ik * coefficients of the 
modified A* matrix of equation (12). 
Combining equations (14) and (17), one comes to equation (18) showing ideal 
signals S.sub.1, S.sub.2, and S.sub.3, respectively, as calculated from 
distorted signals L.sub.1 ', L.sub.2 ', and L.sub.3 ' respectively, where 
the apostrophe was added to indicate that distorted signals L.sub.1 ', 
L.sub.2 ', and L.sub.3 ' were measured in the presence of a constant value 
offset H. 
Thus, additional offset-effects may be compensated for as generated, e.g., 
by the light-receiving elements 4 without the necessity of introducing 
bipolar operations during further signal processing in evaluation circuit 
16.