Waveform equalizer apparatus formed of neural network, and method of designing same

A waveform equalizer for reducing distortion of a digital signal produced from a digital data recording and playback system or transmission system is formed of a neural network having fixed weighting coefficients. Respective values for the coefficients are established by generating a corresponding simulated neuron network, by software implementation using a computer, and by executing a neuron network learning operation using input values obtained from a distorted digital signal and teaching values obtained from an original digital signal which resulted in the distorted digital signal.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
The present invention relates to a waveform equalizer for removing signal 
distortion which arises when a digital signal is recorded and subsequently 
reproduced, or is transmitted and subsequently received, and to a method 
of designing such a waveform equalizer. In particular, the invention 
relates to a waveform equalizer which is formed as a neural network having 
fixed weighting coefficients. 
2. Description of the Related Art 
In recent years, systems which utilize recording and playback or 
transmission/receiving of digital signals have come to be widely utilized. 
However in such a system, even if an original digital signal which is 
recorded or transmitted has a substantially ideal digital waveform, the 
resultant signal that is subsequently produced from a playback apparatus 
or a receiving apparatus will have a waveform that is very different from 
such an ideal digital signal waveform, and must be regarded as an analog 
signal for the purposes of signal processing. The following description 
will be directed to a digital signal recording and playback system, 
however similar considerations apply to a digital signal transmission and 
receiving system. The general term "digital signal transfer system" as 
used in the following description and in the appended claims is intended 
to designate a system such as a magnetic or optical recording and playback 
system, or a digital signal transmission system, in which an original 
signal is recorded and reproduced to obtain a corresponding distorted 
digital signal, or is transmitted and received, to obtain a corresponding 
distorted digital signal. 
In the specific case of a digital data magnetic recording and playback 
system, a phenomenon known as "peak shift" occurs whereby portions of the 
playback digital signal waveform are shifted in time with respect to other 
portions of the waveform, as a result of the recording and playback 
process, thereby causing distortion of the signal and resulting in errors 
in judging the 0 and 1 logic level states of the playback signal data. In 
the case of an optical recording and playback system too, signal 
distortion (intersymbolic interference) arises due to such factors as lens 
aberration, etc. as described in detail hereinafter. 
To overcome such problems, a type of waveform equalizer has been used in 
the prior art which is based on a transversal filter, as illustrated in 
the circuit diagram of FIG. 1. The waveform equalizer is assumed to 
receive as input signal a distorted digital signal produced from a 
recording and playback system. The output signal from the playback 
apparatus is delayed by successive identical amounts in delay lines 130a 
to 130d respectively. The directly supplied input signal and the delayed 
input signal outputs produced from the delay lines are amplified by 
amplifiers 131a to 131d respectively, which have predetermined 
respectively different amplification factors. The resultant amplified 
output signals are then summed by the adder circuit 132, to obtain a 
waveform-equalized output signal. However such a waveform equalizer 
apparatus does not provide satisfactory results. 
The digital signal distortion which arises in a magnetic recording and 
playback system will be described in the following. Diagrams (A) to (E) of 
FIG. 2 are waveform diagrams for illustrating how such distortion occurs 
in a magnetic recording and playback system. It is assumed here that NRZ 
(Non Return to Zero) code is recorded and played back, and that the 
original recording current signal has an ideal digital waveform, i.e. with 
rapid transitions between fixed 0 and 1 state digital levels as 
illustrated in diagram (A). However the magnetic pattern that is actually 
recorded will be of the form shown in diagram (B). At the time of 
playback, assuming that such an ideal current waveform has been recorded, 
then since during playback (if there were no distortion in the 
record/playback process) the waveform of the output signal from the 
playback apparatus is differentiated, the resultant waveform would be as 
shown in diagram (C) of FIG. 2. In this case there is no waveform 
distortion, and no peak shift has occurred. 
However in practice, as shown in diagram (D) of FIG. 2, the playback signal 
that is actually obtained in this case will be substantially distorted. 
When such a playback signal is differentiated, then it is found an amount 
of peak shift such as the amount .DELTA.t has occurred in the 
differentiated waveform, as shown in diagram (E). Here, a peak value in 
the differentiated playback signal which should correspond to a recording 
signal level transition at point t2 of the original recording signal has 
been displaced. That is to say, for some portions of the playback signal 
waveform, peak values of the differentiated playback signal will be 
time-displaced from the correct positions of these peak values. In the NRZ 
code, one bit is represented by a magnetic polarity inversion. However as 
a result of such distortion, the positions of inversions of the playback 
signal waveform will not be clear, so that satisfactory waveform 
reproduction cannot be achieved. That is to say, although polarity 
inversions have occurred at the time points t2 and t3, it will be judged 
(by a circuit which converts the differentiated playback signal of diagram 
(E) to a data stream) that magnetic polarity inversions have occurred at 
the time points t1 and t4, or (due to the fact that the signal level at 
these portions is low) it may be judged that no polarity inversions have 
occurred in the region from t1 to t4. Conversely, it may be erroneously 
judged that polarity inversions have occurred at some low-amplitude 
portions of the playback signal, for example it may be mistakenly judged 
that inversion has occurred at the time points t5 or t7. 
Moreover in the case of an optical type of recording and playback 
apparatus, even greater degrees of signal distortion can arise. In an 
optical recording and playback system, defocussing or lens aberration may 
occur in the optical system of an optical pickup which focusses a small 
spot of light on the optical disk, and this is a source of overall signal 
distortion (intersymbolic interference). There are 5 basic types of 
aberration, and of these, astigmatism, spherical aberration, and coma 
aberration will result in distortion and intersymbolic interference in the 
digital signal. In addition, optical aberration can arise as a result of 
an optical disk being tilted, and this can also result in intersymbolic 
interference. 
Diagrams (A) to (D) of FIG. 3 illustrate how signal distortion can arise in 
an optical recording and playback system. Here, Tmin designates a minimum 
duration for which the recorded data remains continuously at the digital 1 
or 0 state. In a standard audio signal CD (compact disk) digital 
recording/playback system, the data that are actually recorded on the disk 
(i.e. as elongated surface pits, of varying length) represent data that 
are referred to as "channel bits", which are synchronized with a clock 
signal known as the channel clock signal, having a frequency of 
approximately 4.32 MHz. In the field of CD techology the period of that 
channel clock signal is commonly referred to simply as T, and that 
designation will be used in the following. The minimum interval between 
successive inversions of that recorded data will be designated as Tmin. In 
standard CD operation, the value of Tmin is three periods of the channel 
clock signal, i.e. 3 T, as illustrated by FIG. 4. However for the purposes 
of obtaining suitably distorted digital signals to be used in a neural 
network learning operation as described hereinafter, CDs may be utilized 
in which the recorded data has a value of Tmin that is less than 3 T. 
In diagram (B) of FIG. 3, t1, t2, t3 and t4 denote respective time points 
which are defined by a the aforementioned channel clock signal. Looking 
first at the waveform of diagram (A), the data inversion point X in the 
original data, which occurs at a time point t2, is preceded by 1 Tmin 
period at the digital 0 state, and succeeded by 3 Tmin periods at the 
digital 1 state. Conversely, the data inversion point Y is preceded by 3 
Tmin periods at the digital 1 state and is succeeded by one Tmin period at 
the digital 0 state. 
Playback of an optical disk is based upon energy, and such playback 
operation does not include elements which are of mutually opposite kind, 
such as the N and S polarities of a magnetic recording and playback 
system. For that reason, when a lack of sharpness due to spherical 
aberration in the optical system arises, then as shown in diagram (B) of 
FIG. 3, the ends of the long code portion (3 Tmin of data) will become 
lengthened so that the portion of the waveform at time point t2 is shifted 
towards the time point t1 and the portion of the waveform at t3 is shifted 
towards t4. In addition, the distortion that results from coma aberration 
can cause even more serious effects. Diagram (C) of FIG. 3 shows a case in 
which coma aberration is produced which is oriented in the opposite 
direction to the direction of disk rotation, while diagram (D) shows a 
case in which coma aberration is produced which is oriented along the 
direction of disk rotation. It can be seen that the amount and shape of 
the waveform distortion of the playback signal will differ in accordance 
with these two types of coma aberration. 
When reading data from an optical recording and playback system, e.g. from 
an optical disk (referred to in the following simply as a CD), there will 
generally be high levels of these different types of aberration in the 
lens and the optical system, and it is not possible to quantitatively 
determine the respective amounts of distortion that arise from the various 
types of aberration. Thus it has been almost impossible to achieve 
effective waveform equalization in the prior art. Taking for example the 
prior art waveform equalizer shown in FIG. 1, respectively different 
coefficient values would be required, i.e. different values of 
amplification factors for the amplifiers 131a to 131e, depending upon the 
degree of intersymbolic interference (i.e. degree of code distortion) and 
the causes of the distortion. Thus the coefficient values cannot be 
unconditionally defined, so that it has not been possible to achieve 
satisfactory results with the such prior art types of waveform equalizer, 
which have linear input/output characteristics. 
In the case of the signal distortion conditions which arise in a magnetic 
recording and playback system, as illustrated in diagrams (D) and (E) of 
FIG. 2, it would be possible for an individual who is highly experienced 
in the characteristics of a magnetic recording and playback system and the 
NRZ code to make correct judgements concerning the playback signal, by 
examining such a static waveform diagram. That is to say, the polarity 
inversions always occur in pairs, so that each positive-going inversion of 
the playback signal should always be followed by a negative-going 
inversion, i.e. there should be a sequence of positive-negative, 
positive-negative, inversions. Hence, considering the time points t2 and 
t3, it can be judged that inversions occur in that portion of the waveform 
of diagram (D) of FIG. 2 within a short time interval, and since the 
period has been lengthened as a result of bit shifting in that portion, 
the inversion points could be correctly judged as being at the time points 
t2, t3, rather than at the points t1, t4 (which erroneous judgement might 
be made based on the results of differentiation, shown in diagram (E)). 
Similarly, since the playback signal waveform is positive at each of the 
time points t5, t6 and t7, i.e. positive-negative inversion pairs do not 
appear, it would be judged by an experienced individual that t6 is a data 
inversion point. 
Furthermore, in the case of the signal distortion conditions in an optical 
recording and playback system that are illustrated in diagrams (B) to (D) 
of FIG. 3, it would be possible for an experienced individual who is very 
familiar with the characteristics of such an optical recording and 
playback system to make correct judgements of the playback signal 
waveform. Specifically, from the slope of the 3 Tmin data portion 
extending betweeen t2 and t4, it would be possible for such an individual 
to estimate the direction and the amount of coma aberration, and based on 
that knowledge, to correctly judge the transition points (t2, t3) of the 
playback signal. 
However it is not practicable to execute real-time elimination of signal 
distortion that arises in a digital signal recording and playback system 
or transmission system, by a method which uses human experience and 
analysis as described above. Prior art types of waveform equalizer cannot 
provide satisfactory performance, and in addition the design of such a 
waveform equalizer (for example, to determine the amplification factors in 
accordance with the characteristics of a particular recording and playback 
system) is complex. 
Recently, signal processing by neural networks has been proposed in various 
types of applications. A neural network consists of a plurality of neuron 
units, each having a non-linear input/output characteristic, and 
interconnected by linking elements which have respective mutually 
independent weighting coefficients. The weighting coefficients can be 
altered by a learning operation, which involves comparing an output value 
produced from the neural network (while a specific combination of input 
values are being inputted to the neural network) with a desired value 
(referred to as a teaching value), and modifying the values of the 
weighting coefficients such as to bring the output value from the neural 
network closer to the teaching value, by using a learning algorithm. The 
learning process is successively repeated for a number of different 
teaching values and corresponding input value combinations. The operation 
of a neural network is generally implemented by simulation using a 
computer. As a result, it has not been possible to achieve a sufficiently 
high performance with a neural network (due to the limited processing 
speed capabilities of the usual types of computer) to execute real-time 
signal processing for such a waveform equalizer type of application. 
Moreover, it is difficult to realize neuron units as practical hardware 
circuits which have non-linear input/output characteristics. 
Due to the above factors, it has not been considered practicable to use a 
neural network to learn the characteristics of a magnetic recording and 
playback system or an optical recording and playback system and to thereby 
execute real-time equalization of a distorted digital signal that is 
produced from a transmission or playback system. 
SUMMARY OF THE INVENTION 
It is an objective of the present invention to overcome the disadvantages 
of the prior art as set out above, by providing a waveform equalizer 
having a simple circuit configuration, which can be easily designed to 
match the specific characteristics of a particular recording and playback 
system or transmission/receiving system, and which provides greater 
accuracy of waveform equalization than has been possible in the prior art. 
With the present invention, a waveform equalizer is configured as a neural 
network circuit formed of a plurality of circuit units functioning as 
neuron units each having a non-linear input/output characteristic, which 
are interconnected by linking elements having fixed, respectively 
independently established weighting coefficients. These weighting 
coefficients are established beforehand by generating a simulated neural 
network having variable weighting coefficients, whose configuration is 
equivalent to that of the waveform equalizer neural network, by means of a 
suitably programmed computer. While inputting successive values of a 
distorted digital signal to the simulated neural network and comparing the 
resultant output values produced from that simulated neural network with 
desired (i.e. original, undistorted) digital signal values, the weighting 
coefficients of the simulated neural network are successively varied until 
suitable values are obtained, by using a known type of learning algorithm 
such as a back-propogation algorithm which operates on the basis of 
results obtained from the aforementioned comparisons. The weighting 
coefficients which are obtained as final values (at the end of the neural 
network learning processing) are then used to determine respective values 
for the corresponding fixed weighting coefficients for the neural network 
of the actual waveform equalizer circuit, for example to determine the 
respective values of resistors which are used as linking elements 
providing fixed weighting coefficients. 
As a result,the learning function and the actual signal processing function 
can be optimally executed mutually separately, enabling a waveform 
equalizer to be provided which performs effective real-time equalization 
of a distorted digital signal produced from a playback system or 
transmission system. 
The finally obtained waveform equalizer (formed as a neural network, with 
fixed weighting coefficients) can be implemented by a hardware circuit 
configuration that is based on generally available types of analog 
components such as operational amplifiers, diodes and resistors. 
During the actual waveform equalization signal processing, the learning 
function is of course unnecessary, so that the waveform equalizer 
configuration can be simple, and high-speed processing can be achieved. 
More specifically, according to a first aspect the present invention 
provides a waveform equalizer for processing an input distorted digital 
signal, comprising: 
delay means coupled to receive the input distorted digital signal, for 
delaying the distorted digital signal by successive fixed amounts to 
obtain a plurality of delayed distorted digital signals; and 
a plurality of neuron units, and a plurality of linking elements having 
respectively fixed weighting coefficients, the linking elements 
interconnecting the neuron units to form a neural network which is coupled 
to receive the input distorted digital signal and delayed distorted 
digital signals as input signals thereto, and which produces a 
waveform-equalized output digital signal in response to the input signals. 
Respective values for the fixed weighting coefficients are established by a 
learning procedure employing a computer-simulated neural network having 
variable weighting coefficients and having a network configuration 
corresponding to that of the neural network of the waveform equalizer. 
The learning operation includes supplying to the computer-simulated neural 
network an input distorted digital signal while comparing with an output 
signal obtained from that neural network a teaching signal which is an 
undistorted digital signal corresponding to the distorted digital signal, 
and applying a predetermined learning algorithm to alter the variable 
weighting coefficients in accordance with differences between the teaching 
signal and the neural network output signal. 
Preferably, a range of values of the aforementioned teaching signal include 
at least one value that is intermediate between a digital 1 value and a 
digital 0 value. 
The neural network of such a waveform equalizer is preferabley formed of a 
plurality of layers of neuron units, wherein an output one of the layers 
receives a plurality of weighted input signals from a preceding one of the 
layers, and wherein the weighted input signals may include signals of 
mutually opposite polarity. 
Each of the neuron units of the waveform equalizer is configured as a 
signal conversion unit which executes non-linear conversion of a sum of 
weighted input signals applied thereto, and each of the conversion units 
includes at least one semiconductor device, such as a pair of diodes 
connected with opposing directions of polarity, for providing a non-linear 
input/output characteristic. Each of the neuron units of the waveform 
equalizer can thereby be configured to have a non-linear input/output 
characteristic which is formed of a plurality of respectively different 
linear regions. 
Furthermore, each of the neuron units of such a waveform equalizer 
preferably comprises a pair of series-connected signal inverting elements, 
such that of a plurality of weighted input signals supplied to each neuron 
unit, each of the weighted input signals is selectively supplied to a 
first one or a second one of the inverting elements in accordance with 
whether an effectively positive or effectively negative value of weighting 
coefficient is to be applied to each input signal. 
According to another aspect, the present invention provides a method of 
designing a waveform equalizer for waveform equalization of a a distorted 
digital signal produced from a digital signal recording and playback 
apparatus, the waveform equalizer being formed as a neural network 
comprising a plurality of neuron units which are interconnected by linking 
elements providing respective fixed weighting coefficients, wherein 
respective values for the fixed weighting coefficients are mutually 
independently established by: 
generating a set of original data, and storing the original data in a first 
memory means; 
recording the original data as digital data values on a recording medium, 
and subsequently executing playback of the recorded original data, to 
obtain a playback digital signal; 
periodically sampling the playback digital signal with a sampling period 
that is less than or equal to a data period of the digital data values, to 
obtain successive digital sample values to be used as learning input 
values, and storing the learning input values in a second memory means; 
generating a simulated neural network having variable weighting 
coefficients, by using a computer, the simulated neural network being an 
equivalent circuit of the waveform equalizer neural network; 
supplying successive ones of the learning input values from the second 
memory means to the computer to be sequentially inputted to the simulated 
neural network; 
supplying successive data values of the original data, respectively 
corresponding to the learning input values, from the first memory means to 
the computer to be used as teaching signal values for comparison with 
respective output values produced from the simulated neural network; 
repetitively executing a learning algorithm utilizing results obtained from 
the comparison, to successively alter the variable weighting coefficients 
of the simulated neural network, until a predetermined degree of 
convergence is obtained for values of the variable weighting coefficients; 
and 
establishing respective values for the fixed weighting coefficients of the 
waveform equalizer neural network, based upon final values obtained for 
corresponding ones of the variable weighting coefficients of the simulated 
neural network. 
With such a method of designing a waveform equalizer the sampling can be 
executed utilizing a sampling clock signal generated by a phase locked 
loop, the phase locked loop being coupled to receive the playback digital 
signal and functioning to extract a clock signal from the playback digital 
signal and to generate the sampling clock signal based on the extracted 
clock signal. 
Alternatively, the invention provides a method of designing a waveform 
equalizer wherein the teaching values are derived by: 
dividing the original data into successive discrete digital values 
respectively corresponding to the sample values; 
transferring the discrete digital values through a digital low-pass filter 
to obtain filtered data values; and 
obtaining the teaching values by selecting successive ones of the filtered 
data values by an identical selection operation to the operation for 
selected the learning input values from the digital sample values.

DESCRIPTION OF PREFERRED EMBODIMENTS 
An embodiment of a waveform equalizer formed of a neural network according 
to the present invention and a method of designing and manufacturing such 
a waveform equalizer will be described in the following referring to the 
drawings. 
FIG. 5 shows a neural network which is an equivalent circuit to an 
embodiment of a waveform equalizer according to the present invention, and 
which is implemented by simulation using a computer in order to design 
such a waveform equalizer. This is a multilayer neural network formed of 
successive layers of neuron units, with interconnections by linking 
elements which are connected between the neuron units of a layer and 
neuron units of the preceding and succeeding layers. The neuron units are 
designated in general as U.sub.n,i, where "n" and "i" respectively denote 
the position of the layer containing that neuron unit and the position of 
the neuron unit within that layer, i.e. with U.sub.n,i indicating the 
i.sup.th neuron unit of the n.sup.th layer, while U.sub.n-1, j designates 
the j.sup.th neuron unit of the (n-1).sup.th layer In FIG. 5, an input 
signal is supplied to a series-connected set of four delay lines DL1, DL2, 
DL3, DL4, so that a set of five output signals are obtained. These five 
output signals correspond to five output signals which are distributed 
successively along the time axis. However in the simulated neural network, 
each of these delay lines DL can be considered to be a data register, 
through which input data values (described hereinafter, and referred to as 
learning input values) are successively shifted. These five output signals 
are respectively inputted to a set of units designated as U'.sub.1,1 to 
U'.sub.1,4 which constitute an input layer of the neural network. In this 
embodiment each of these units of the input layer represents a linear 
amplifier which serves as an input buffer amplifier in the actual hardware 
neural network. The output signals from the input layer are coupled to 
respective ones of a set of neuron units U.sub.2,1, U.sub.2,2, U.sub.2,3 
which constitute an intermediate layer of the neural network, with the 
output signals from the input layer being coupled through the 
aforementioned linking elements which multiply the output signals by 
respective weighting coefficients, these weighting coefficients being 
designated in general as W. Each of the neuron units has a specific 
non-linear input/output characteristic. In general, each weighting 
coefficient is designated as W.sub.n,i,j, which indicates that the 
weighting coefficient is applied to the output signal from the j.sup.th 
neuron unit of the (n-1).sup.th layer that is supplied to the i.sup.th 
neuron unit of the n.sup.th layer. During a neural network learning 
operation described hereinafter, these weighting coefficients W are 
variable and are determined mutually independently, however in the neural 
network of the actual waveform equalizer (i.e. the hardware configuration) 
the values of the weighting coefficients W are fixed (by respective 
resistor values). The values of these weighting coefficients W which 
connect the input layer to the intermediate layer can be considered to 
represent respective strengths of coupling between neuron units of the 
intermediate layer and neuron units of the input layer. 
In a similar way, respectively output signals produced from the neuron 
units of the intermediate layer are transferred through linking elements 
having respective weighting coefficients W to be inputted to a neuron unit 
of the output layer of the neural network. In this embodiment, the output 
layer of the neural network consists of only a single neuron unit, that is 
to say a single output value is produced from that final neuron unit of 
the neural network in response to a specific combination of input signal 
values supplied to the input layer of the neural network. That final 
neuron unit is designated as U.sub.3,1. 
As described above, each of the units of the input layer of this embodiment 
is a linear amplifier. However each of the neuron units of the input layer 
and output layer has a predetermined non-linear input/output 
characteristic, whereby the level of output signal produced therefrom 
varies in a known non-linear manner in accordance with the sum of the 
weighted input signal values applied thereto, and whereby respective 
weighting coefficients are selected to be positive or negative. This is 
illustrated in FIG. 6, which is a conceptual diagram to illustrate the 
input connections and operation of a neuron unit U.sub.n,i. Such a neuron 
unit can be considered to consist of an input section 50 and an output 
section 51. The input section 50 sums the weighted input signal values 
supplied thereto, with each of these input signal values having been 
multiplied by a corresponding weighting coefficient which is designated as 
W.sub.n,i,j. The resultant sum output signal that is produced from the 
input section 50 of the neuron unit is designated as X.sub.n,i, and is 
supplied to the output section 51 of the neuron unit. The output section 
executes processing in accordance with the non-linear function Y=F(X), to 
obtain the output signal Y.sub.n,i, which is supplied to one or more 
neuron units of the succeeding layer after having been multiplied by 
respective weighting coefficients. 
The basic principles of learning operation (i.e. during the computer 
simulation stage of designing the neural network) can be summarized as 
follows. A sequence of input signal values and a corresponding sequence of 
desired output values from the neural network (the latter being referred 
to as teaching values) are derived beforehand as described hereinafter, 
and stored in memory. During the learning operation, these input values 
and teaching values are successively read out from memory, with the input 
values being supplied to the chain of "delay lines" DL1 to DL4. During 
each interval after an input value has thus been supplied and prior to 
supplying the next input value to the delay line chain, a specific 
combination of output values will be inputted in parallel to the neural 
network (i.e. in this embodiment, a set of five values), and these 
simulate a set of input values which are distributed at fixed intervals 
along the time axis. At that time, a corresponding teaching value is read 
out from memory, to be compared with the output value produced from the 
neural network (i.e. from the final neuron unit U.sub.3,1 in this 
embodiment). The difference between that teaching value and the output 
value from the neural network is then applied in a learning algorithm, for 
modifying the respective values of the weighting coefficients W of the 
neural network, in a manner such as to reduce the amount of that 
difference. In this embodiment, the learning operation is executed by 
using a back-propogation type of learning algorithm, whereby weighting 
coefficient updating processing proceeds from the output layer back to the 
input layer, i.e. in the reverse direction to the normal forward direction 
of processing. Such types of learning algorithm are now well known in the 
art, so that detailed description will be omitted. 
As mentioned above, in the computer-simulated neural network of FIG. 5, the 
units indicated as DL1 to DL4 would not be actual delay lines, but might 
be for example a set of four data registers. During the learning 
operation, each time that a new input signal value is supplied (with a 
corresponding teaching value also being supplied, to be compared with the 
new output value that will be produced from the neural network), the 
contents of DL3 are shifted into DL4, the contents of DL2 are shifted into 
DL3, the contents of DL1 are shifted into DL32, and the most recent input 
signal value is set into DL1. Thus, a new combination of five input signal 
values are being supplied to the input layer of the neural network, and 
the resultant output value from the neural network is compared with the 
new teaching value. 
FIG. 8 is a basic circuit diagram of this waveform equalizer embodiment. 
While all of the components shown in FIG. 5 are simulated by computer 
processing during the learning operation, i.e. implemented by software, 
the components of the circuit shown in FIG. 8 are generally-available 
hardware analog circuit elements, such as operational amplifiers, 
resistors etc. The circuit shown in FIG. 8 is equivalent to the neural 
network of FIG. 5, but with fixed values for the weighting coefficients W, 
with these fixed values being determined by by respective values of 
resistors R1 to R53. These fixed weighting coefficient values are 
determined beforehand by a neural network learning operation using the 
computer-simulated neural network of FIG. 5, as described in detail 
hereinafter. 
In FIG. 8, an input signal (i.e. a distorted digital signal which is 
produced from a recording and playback apparatus after having been 
recorded and reproduced, or is outputted from a digital signal 
transmission system after being received) is applied to a chain of four 
series-connected delay lines 14, 15, 16, 17 which respectively 
corresponding to the four simulated "delay lines" DL1 to DL4 of the neural 
network circuit of FIG. 5. That output signal and the respective output 
signals from the delay lines 14 to 17 are amplified by respective ones of 
a set of linear amplifiers 5, 6, 7, 8, and 9 which respectively correspond 
to the amplifiers U'.sub.1,1 to U'.sub.1,5 of the input layer of the 
equivalent neural network circuit of FIG. 5. The output signals produced 
from the amplifiers 5 to 9 are coupled through the set of resistors R11, 
R21, R31, R41, R51, R12, R22, R32, R42, R52, R13, R23, R33, R43, and R53 
to circuit units which function as the neuron units of the intermediate 
layer. These circuit units are signal conversion units each of which 
executes non-linear conversion of an input signal applied thereto. The 
conversion units of the intermediate layer respectively correspond to the 
neuron units U.sub.2,1 to U.sub.2,3 of the neural network of FIG. 5. In 
this embodiment, each conversion unit of the intermediate layer is formed 
of a pair of operational amplifiers connected in series, with a diode pair 
connected at the output of the second operational amplifier, to provide a 
non-linear input/output characteristic. Of the weighted input signals that 
are applied to such a neuron unit, some of the input signals are inputted 
to the inverting input terminal of the first operational amplifier of the 
series-connected pair (e.g. to the operational amplifier 1b, in the case 
of the neuron unit U.sub.2,1), with the non-inverting input terminal of 
that operational amplifier being connected to ground potential, while 
other ones of these weighted input signals are applied to the inverting 
input terminal of the second one of the pair of series-connected 
operational amplifiers (e.g. to the operational amplifier 1a, in the case 
of the neuron unit U.sub.2,1), with the non-inverting input terminal of 
that operational amplifier being connected to ground potential. It can 
thus be understood that each signal that is applied to the first 
operational amplifier (e.g. to operational amplifier 1b) of such a 
series-connected pair will be inverted twice in succession, i.e. will in 
effect not be inverted, whereas each signal which is supplied to the 
second one (e.g. operational amplifier 1a) of a pair of series-connected 
operational amplifiers will be inverted. Hence, each input signal that is 
supplied to the first operational amplifier of the pair can be considered 
to be multiplied by a fixed positive weighting coefficient (whose value is 
determined by the value of the resistor through which that signal is 
transferred), while each input signal that is supplied to the second 
operational amplifier of such a pair is in effect multiplied by a fixed 
negative weighting coefficient (whose absolute value is determined by the 
value of the resistor through which that signal is transferred). 
The output terminal of the second operational amplifier of each neuron unit 
is connected to ground potential through a pair of diodes which are 
connected in parallel with mutually opposing directions of polarity, i.e. 
the diode pairs 10, 11 and 12 connected to the outputs of the operational 
amplifiers 1a, 2a and 3a respectively of the actual neuron units in FIG. 8 
which correspond to the neuron units U.sub.2,1, U.sub.2,2, U.sub.2,3 of 
the neural network circuit of FIG. 5. 
The three neuron units of the intermediate layer in FIG. 8 are respectively 
formed of the series-connected pair of inverting-type operational 
amplifiers 1a, 1b, with the diode pair 10 connected at the output of 
operational amplifier 1a, the operational amplifiers 2b, 2a with the diode 
pair 11 connected at the output of operational amplifier 2a, and the 
operational amplifiers 3b, 3a with the diode pair 12 connected at the 
output of operational amplifier 3a. 
The output signals produced from the neuron units of the intermediate layer 
in FIG. 8 are transferred through weighting resistors R1, R2, R3 
respectively to the output neuron unit, corresponding to the output layer 
U.sub.3,1 of the neural network circuit of FIG. 5. That output neuron unit 
is made up of series-connected inverting-type operational amplifiers 4b, 
4a, with a diode pair 13 connected to the output of the second operational 
amplifier 4a. The output signal from the neural network is thereby 
developed across the diode pair 13. 
Each of the diode pairs 10 to 13 functions to provide a known form of 
non-linear input/output characteristic for the corresponding neuron unit. 
This will be described referring to FIG. 9, which shows the input/output 
characteristic of such a diode pair. Such a characteristic can be 
considered to consist of three different linear regions, which are 
designated as E1, E2 and E3 in FIG. 9. In the regions E1 and E3 the level 
of signal voltage appearing across the diode pair is substantially 
constant (i.e. diode clipping occurs), while in the region E2 the output 
signal Y (i.e. the signal voltage appearing across the diode pair) varies 
substantially linearly with respect to input signal X. It can thus be 
understood that each of the neuron units of the actual waveform equalizer 
formed of a neural network shown in FIG. 8 can be configured from readily 
available circuit components, can have a simple circuit arrangement, can 
provide effectively negative or positive values for the weighting 
coefficients applied to the input signals applied thereto from neuron 
units of the preceding layer, and can have a known non-linear input/output 
characteristic that is formed of three linear regions. 
In FIG. 9, the central potential is assumed to be 0 V, i.e. the output 
signal Y produced from the output neuron unit varies between fixed 
positive and negative voltage levels. In the following, these positive and 
negative levels will be assumed to correspond to the digital 1 and 0 
potentials respectively, while in addition the 0 V level of that output 
signal Y will be taken to represent a level of 0.5, i.e which is midway 
between the 1 and 0 digital potentials. 
The set of resistors (R11, R21, R31, R41, R51, R12, R22, R32, R42, R52, 
R13, R23, R33, R43, R53) which couple the output signals from the input 
layer of the neural network circuit in FIG. 8 to the neuron units of the 
intermediate layer, i.e. which transfer the output signals from the 
amplifiers 5, 6, 7, 8, 9 to the neuron units U.sub.2,1, U.sub.2,2, 
U.sub.2,3, will be collectively designated as the resistors R.sub.ji. 
These neuron units U.sub.2,1, U.sub.2,2, U.sub.2,3 in FIG. 8 are 
respectively formed of the pair of (inverting type) operational amplifiers 
1a and 1b with the diode pair 10, the pair of operational amplifiers 2a, 
2b with the diode pair 11, and the pair of operational amplifiers 3a, 3b 
with the diode pair 12, The resistors (R1, R2, R3) which couple the output 
signals from the intermediate layer of the neural network circuit in FIG. 
8 to the neuron units of the output layer, i.e. which transfer the output 
signals from the neuron units U.sub.2,1, U.sub.2,2, U.sub. 2,3 to the 
output neuron unit U.sub.3,1 will be collectively designated as the 
resistors R.sub.j. The output neuron unit U.sub.3,1 is formed of pair of 
operational amplifiers 4a, 4b with the diode pair 13. Thus the weighting 
coefficients W.sub.2,i,j in the neural network of FIG. 5 correspond to the 
resistors R.sub.ji and the weighting coefficients W.sub.3,i,j of the 
neural network of FIG. 5 correspond to the resistors R.sub.j. 
After respective values for the weighting coefficients W have been 
established by the learning operation, using computer simulation of the 
neural network, the respective values for the resistors R.sub.ji, R.sub.j 
are determined based upon the values obtained for the corresponding 
weighting coefficients. 
During the learning operation, in the simulated operation of the neural 
network, successive input signal values (which will be referred to in the 
following as learning signal values) are successively supplied to the 
neural network (i.e. to the "delay line" DL1 and the input layer unit 
U'.sub.1,1) at intervals which correspond to a fixed (real-time) period. 
In this embodiment, each of these intervals will be assumed to correspond 
to one half of the bit period T of the digital playback signal from a CD, 
i.e. to one half of the minimum bit duration. Thus, in the simulated 
neural network system, the successive sets of learning input values that 
are outputted from the "delay lines" DL1 to DL4 are in effect distributed 
at successive T/2 intervals. 
Thus in the actual waveform equalizer circuit of FIG. 8, each of the delay 
lines 14, 15, 16, 17 (respectively corresponding to the aforementioned 
"delay lines" DL1 to DL4 which apply input signals to the simulated neural 
network) provides a delay of T/2 in this embodiment. 
The input signal values supplied to the neuron units of the waveform 
equalizer neural network of FIG. 8 are the weighted output values from the 
preceding layer, i.e. in the case of the intermediate layer the input 
values are the output values from the input layer, after these have been 
respectively weighted by being transferred through the resistors R(j, i) 
(i.e. R11, R21, R31, R41, R51, R12, R22, R32, R42, R52, R13, R23, R33, 
R43, R53), which provide respectively independent fixed weighting 
coefficients. The resultant input values from the resistors are supplied 
to the neuron units of the intermediate layer, i.e. the units U.sub.2,1 to 
U.sub.2,3. Specifically, these weighted input signal values are applied to 
the inverting input terminals of the operational amplifiers 1a, 1b, 2a, 
2b, 3a, 3b, to be additively combined. After having been amplified (and 
inverted or re-inverted) by the operational amplifiers of a neuron unit of 
the intermediate layer, the input signal sum is subjected to non-linear 
conversion by the diode pair of that neuron unit (10, 11 or 12) and then 
outputted to the next layer, which is the output neuron unit. 
If the respective values for the resistors R.sub.j,i, R.sub.j of the 
waveform equalizer have been suitably established, based on the weighting 
coefficient values that are obtained by the neural network learning 
operation described hereinafter, then the circuit of FIG. 8 will in effect 
execute a similar type of judgement of the distorted playback signal that 
is supplied thereto as would an experienced human observer. Thus the 
output signal produced from the waveform equalizer circuit of FIG. 8 will 
be closely similar to a signal that was originally recorded on a CD from 
which the playback signal is obtained, with level transitions of that 
output signal (corresponding to transitions between digital 1 and 0 
levels) corresponding to those of the originally recorded signal. Accurate 
waveform equalization is thereby achieved. 
It should be noted that various other configurations for the neural network 
of the waveform equalizer could be utilized, other than that of FIGS. 5 
and 8. It may be found advantageous for example to apply respective 
weighted fixed DC bias inputs to each of the neuron units, as illustrated 
in FIG. 7. The respective values for the weighting coefficients W applied 
to these bias inputs, supplied from a common DC bias source E.sub.B, are 
determined together with the other weighting coefficients W by a learning 
operation which is described hereinafter. 
It should also be noted that the circuit arrangement shown in FIG. 8 is 
intended only to show the basic elements of that circuit in a simple 
manner, for ease of understanding, and does not necessarily show all of 
the components (such as resistors for local negative feedback) which may 
be required in a practical circuit. In particular, if the weighted input 
signals are inputted to the operational amplifiers as current signals, and 
all of the operational amplifers are of identical type, then it would be 
necessary to connect a resistor between the output of the first 
operational amplifier of each neuron unit (e.g. 1b) and the input of the 
second amplifier of that unit (e.g. 1a), and to scale down the values of 
the input weighting resistors of each first operational amplifier 
accordingly. 
The procedure for determining suitable values for the resistors R.sub.j,i, 
R.sub.j of the waveform equalizer of FIG. 8 is as follows. The procedure 
utilizes a suitably programed workstation (computer), and is based upon 
generating a simulated neural network of the form shown in FIG. 5, 
executing a learning operation to obtain suitable values for the weighting 
coefficients of that neural network, and then determining the respective 
values for the fixed weighting coefficients (i.e. resistor values) in the 
actual hardware neural network of the waveform equalizer. 
The basic principles of the learning operation for successively varying the 
values of the weighting coefficients W of the simulated neural network of 
FIG. 5 will be first described, referring to FIG. 10. In FIG. 10, diagram 
(A) shows a portion of the waveform of an original signal which is used 
for learning. For the purpose of achieving maximum accuracy of 
equalization, the learning operation utilizes data recorded on a CD in 
which the value of the aforemention minimum interval between transitions 
of the recorded data, Tmin, is made smaller than the standard value of 3 
T. In the example of FIG. 10, Tmin is made equal to T. As shown in diagram 
(B), specific sample values (designated in the following as teaching 
values) are derived from the original signal, with these teaching values 
occurring periodically with a period that is equal to or less than the 
period T, and which is equal to T/2 in this example. These T/2 periods 
will be referred to as learning intervals. As shown, each teaching value 
which occurs immediately before a transition of the original signal from 
the digital 0 to digital 1 state takes the value digital 0, each teaching 
value which occurs immediately following a transition of the original 
signal from the digital 0 to digital 1 state takes the value digital 1, 
and each teaching value which coincides with a transition of the original 
signal between the digital 0 and digital 1 states takes a value which is 
midway between the digital 1 and 0 levels, which is indicated as a value 
of 0.5. Thus the teaching values are tri-state values, rather than digital 
values in this example. 
Referring to diagram (C) of FIG. 10, the playback signal waveform from a 
CD, corresponding to the original signal waveform portion shown in diagram 
(A) will as shown in general be highly distorted. Periodic sampling of the 
playback signal is executed (as described hereinafter) to obtain 
successive values referred to in the following as learning input values, 
which respectively correspond to the aforementioned teaching values. Five 
of these learning input values are designated in diagram (C) as LV.sub.1 
to LV.sub.5, which respectively correspond to the teaching values TV.sub.1 
to TV.sub.5. Here, the term "respectively corresponding" signifies 
"occurring at respectively identical positions along the data sequence". 
These positions, within the playback signal, can be established (starting 
from a specific initial position, identified by a reference marker portion 
within the playback data) by using an appropriate clock signal as 
described hereinafter. Assuming that the playback signal varies about a 
central 0 V value, then for example the learning input value designated as 
LV.sub.3 should ideally be 0 V, to correspond to the transition value 0.5 
of the corresponding teaching value TV.sub.3. Similarly, the learning 
input value LV.sub.4 should ideally be a positive voltage value 
corresponding to a predetermined digital 1 level. However due to 
distortion effects such as aberration distortion described hereinabove, 
the learning input values will actually differ substantially from these 
ideal values. 
Basically, the learning operation is as follows. The learning input values 
are successively inputted to the "delay lines" DL1 to DL4 of the simulated 
neural network, such that during each learning interval (corresponding to 
T/2 ) there will be a set of five learning input values being supplied to 
the input layer of the neural network. While the learning input value 
LV.sub.3 is being supplied from DL2 (i.e. when the learning input values 
LV.sub.1 and LV.sub.2 are being supplied from the input and output of DL1 
and LV.sub.4 and LV.sub.5 are being supplied from the respective outputs 
of DL3 and DL4), with resultant combinations of weighted input values 
being applied to the neuron units of the intermediate layer and a 
resultant combination of weighted input values being supplied to the final 
neuron unit U.sub.3,1, the output value that is thereby produced from that 
final neuron unit is compared with the teaching value TV.sub.3 that 
corresponds to LV.sub.3. Based on the difference value obtained from that 
comparison, respective updated values for the weighting coefficients W of 
the neural network are computed, by using a backward propogation type of 
learning algorithm. In the next learning interval, i.e. when the learning 
input value LV.sub.4 is being outputted from the delay line DL2, the 
resultant output value produced from the neural network as a result of the 
new combination of five input learning input values is compared with the 
teaching value TV.sub.4, corresponding to LV.sub.4, and the weighting 
coefficients are again updated accordingly based on the result of that 
comparison. 
As mentioned hereinabove, the blocks designated as DL1 to DL4 in FIG. 5 do 
not represent actual delay elements, can be considered as respective data 
registers, through which the learning values are sequentially shifted, to 
obtain successive sets of five learning values that are inputted to the 
simulated neural network during respective learning intervals. Considering 
for example the first three learning input values to be supplied, after 
learning operation begins. The first learning input value is inputted to 
the unit U'.sub.1,1 of the first layer of the neural network, and a 
resultant output signal value obtained from the output unit U.sub.3,1 of 
the neural network (although there is no teaching value actually 
corresponding to that output value). The second learning input value is 
then inputted to the unit U'.sub.1,1 while the first learning input value 
is being inputted to the second unit U'.sub.1,2 of the first layer, and a 
resultant output value obtained from the neural network. Again, there is 
no corresponding teaching value to that output value. Next, the third 
learning input value is inputted to the unit U'.sub.1,1 while the second 
learning input value is being inputted to the second unit U'.sub.1,2 and 
the first learning input value is being inputted to the third unit 
U'.sub.1,2 of the input layer. A resultant output value is obtained from 
the neural network. In this case, as will be understood from the above 
description of FIG. 10, there is a teaching value which is to be compared 
with that output value from the neural network (i.e. The teaching value 
that corresponds to the first learning input value), and so the learning 
algorithm will be executed for the first time. 
However there is a basic practical problem in executing such a learning 
operation, in the case of a playback signal from a magnetic or optical 
recording and playback system. Referring to FIG. 11, a sequence of 
teaching values TV.sub.1, TV.sub.2, . . . are shown as occurring in a data 
sequence that is to be recorded on a recording medium, for example a CD. 
When a playback signal is subsequently obtained from that CD, then due to 
such factors as disk rotation drive system inaccuracy during recording and 
playback, the values LV.sub.1, LV.sub.2 etc which respectively correspond 
to the teaching values TV.sub.1 etc. will not occur at regular intervals 
as measured with respect to a standard timebase. That is to say, if the 
playback signal is sampled at regularly spaced time points, which should 
ideally coincide with the respective positions of the learning input 
values in the playback data flow, in fact the sample values that are 
obtained will differ from the desired values. In FIG. 11, for example, (in 
which the degree of deviation is of course greatly exaggerated), sampling 
the playback signal at the 8.sup.th reference time point R8 would result 
in a signal level near the learning input value LV.sub.7 being selected, 
rather than the correct value LV.sub.8 (i.e. the 8.sup.th learning input 
value in the data sequence). Thus, correct learning operation will be 
impossible, unless the playback disk rotation speed is controlled to a 
very high degree of accuracy. 
In a preferred embodiment of the present invention described in the 
following, the above problem is overcome by using a PLL (phase locked 
loop) circuit to derive the clock signal component of the playback signal, 
and to use the derived clock signal to determine the sampling time points 
(i.e. The points R.sub.1, R.sub.2, . . . in the example of FIG. 5). In 
that case, the time-axis deviations of the learning input values LV.sub.1, 
LV.sub.2, etc. will be identical to those of the sampling time points, so 
that the correct learning input values (i.e. respectively corresponding to 
the predetermined teaching values TV.sub.1, TV.sub.2, etc.) can be 
accurately extracted from the playback signal by sampling that signal. 
Thus, the operation will be unaffected by deviations in the rotational 
speed of the CD 22. 
The basic features of this embodiment will be described referring first to 
the general block diagrams of FIGS. 13, 14 and 15, assuming that a 
learning interval of T/2 is utilized (as in the example of FIG. 10 
described above). FIG. 13 shows the apparatus required to record on a 
recording medium (in this case, a CD) data to be used in the neural 
network learning operation, which data will be referred to in the 
following as the learning data. The learning data are generated as a 
portion of original data that are produced from an original data source 20 
and are supplied to a recording apparatus (i.e. cutting apparatus) 21 to 
be recorded on a CD 22. In addition to the learning data, this original 
data includes an identifying marker portion, preceding the learning data, 
for use in precisely identifying the start of the learning data, and a 
preamble portion preceding the identifying marker portion, for initial 
stabilization of PLL operation. The original data are also supplied, as 
text data, to be recorded on a floppy disk 25 by a disk drive unit 24. If 
for example a portion of the original data is of the form shown in diagram 
(A) of FIG. 12, i.e. a sequence of 2 T periods at the digital 1 state, 2 T 
at the 0 state, followed by 1 T at the digital 1 state, then that portion 
could be represented as text data as a sequence of numeric symbols . . . 
0, 1, 1, 0, 0, 1, 0, . . . . 
When the above recording operations have been completed, the apparatus 
shown in FIG. 14 are put in operation. A playback apparatus 26 rotates the 
CD 22 to derive a playback signal from an optical pickup, with that 
playback signal being supplied to an A/D converter 28 and to a PLL 27. The 
A/D converter 28 periodically converts the playback signal to successive 
digital sample values at a sampling rate that is substantially higher than 
the data rate of the recorded data, i.e. with a sampling period that is 
much shorter than the aforementioned period T. It will be assumed that 
this sampling rate is 100 MHz. These digital samples are supplied to a 
sampling circuit 29. The PLL 27 extracts the data clock signal (having the 
1 T period) from the playback signal, and also frequency-multiplies that 
extracted clock signal by 2 to obtain a sampling clock signal having the 
desired period of T/2 (described above referring to FIG. 10). That 
sampling signal is supplied to the sampling circuit 29, for selecting 
successive digital samples, e.g. to select the first digital sample which 
occurs at or immediately after each sampling time point defined by the 
sampling clock signal applied to the circuit 29. These selected sample 
values are stored in a sample data memory 30. 
Next, the apparatus shown in FIG. 15 is used to set the learning input 
values and teaching values into a computer 33 (used as a work station) 
which executes the neural network simulation and learning operations. The 
learning data are read out as text data from the floppy disk 25 by a disk 
drive unit 32 which is controlled by the computer 33, are transferred into 
the computer 33 through an input port 35, and are then converted to 
suitable form for use as teaching values in the neural network learning 
operation. Specifically, assuming that the learning values are of the form 
described in FIG. 10 hereinabove (i.e. tri-state values of either digital 
1 or 0 or the intermediate level 0.5), the text data sequence is converted 
by the computer 33 into a corresponding teaching value sequence, for 
example the sequence shown in diagram (C) of FIG. 12 in the case of the 
text data sequence of diagram (B) of FIG. 12. The teaching values thus 
obtained are successively stored in a teaching data region of an internal 
memory 34 of the computer 33. 
The sample data values are successively read out from the sample data 
memory 30 under the control of read command signals supplied from the 
computer 33, to be transferred through an input port 36 to the computer 
33. The computer 33 judges each of these input sample values, to determine 
when these correspond to learning input values, and stores the learning 
input values in a learning input data region of the internal memory 34. 
Specifically, the computer 33 examines the flow of input sample values 
from the memory 30 to detect the start of the learning data, as indicated 
by the aforementioned marker portion of the playback data from the CD. For 
example, the computer 33 can then for example simply transfer each sample 
value which occurs, following that marker portion, into the learning input 
data memory as a learning input value (assuming that all of the sample 
values in the learning data portion are to be used as learning input 
values). Alternatively, as described hereinafter, the computer 33 can 
operate on successive groups (e.g. successive pairs) of these sample 
values which occur after the start of the learning data, to derive 
respective learning input values. 
With the teaching values and learning input values having now been stored 
in the internal memory 34, the neural network learning operation described 
hereinabove is started, and continued until all of the learning data have 
been utilized, and a sufficient degree of convergence has been reached for 
the successively obtained values of neural network weighting coefficients 
derived in the learning operation. 
The basic operations executed during the neural network learning operation 
and during normal functioning of the waveform equalizer (after fixed 
weighting coefficients have been established by the learning operation) 
are illustrated in FIGS. 16 and 17 respectively. During the learning 
operation as illustrated in FIG. 16, the learning input values and 
teaching values that have been stored in the internal memory of the 
computer as described hereinabove are successively read out, with the 
learning input values being inputted to the neural network of FIG. 5, with 
the resultant output values produced from the simulated neural network 
being compared with respective teaching values, and the comparison results 
used in the learning algorithm, to establish updated values for the 
weighting coefficients of the neural network. 
Upon completion of that learning operation, fixed values for the resistors 
in the waveform equalizer (i.e. for the fixed weighting coefficients of 
the neural network of that waveform equalizer) are determined based on the 
final values obtained for the respectively corresponding weighting 
coefficients of the neural network. When a distorted playback signal is 
now inputted to the waveform equalizer, an accurately waveform-equalized 
optical signal is obtained, as illustrated in FIG. 17. 
To establish weighting coefficient values for the neural network such that 
satisfactory equalization will be achieved by the waveform equalizer even 
when the playback signal may be distorted in various ways, a plurality of 
respectively differently distorted types of learning data are used in the 
learning operation. These different types of learning data will be 
referred to in the following as respective learning data categories, and 
can be generated for example by operating the playback apparatus 26 under 
respectively different conditions of incorrect adjustment of the optical 
pickup which reads data from the CD 22. In that way, respective learning 
data categories can be obtained in which distortion of the digital 
playback signal from the CD is the result of defocussing, spherical 
aberration, coma aberration along the direction of disk rotation, coma 
aberration that is opposite to the direction of disk rotation, etc. In the 
learning operation, learning is first executed for one of these learning 
data categories, to obtain a final set of weighting coefficients for the 
neural network, then the learning is repeated using the next category of 
learning data, and so on for each of the categories. 
The overall flow of such learning operation is illustrated by the flow 
diagram of FIG. 22. Firstly, the teaching data from the floppy disk 25 are 
transferred into the computer 33 as text data, and are then converted into 
a corresponding sequence of teaching values, e.g. tri-level teaching 
values as illustrated in diagram (C) of FIG. 12, with each transition 
between the digital 1 and 0 levels in the original signal being converted 
to an intermediate (0.5) level, and with the teaching values corresponding 
to sample values occurring at T/2 intervals. 
For example, referring to diagrams (A) and (B) of FIG. 10, the set of 
teaching values TV.sub.1 to TV.sub.5 would be obtained as the sequence of 
values 0, 0, 0.5, 1, 1 (where "1" and "0" here represent digital 1 and 0 
levels). The teaching values thus obtained are stored in the teaching data 
memory region of the internal memory 34. The playback signal for the first 
learning data category is then obtained from the CD 22, and the selected 
digital sample values are stored in the sample data memory 30 (step S3). 
Next in step S4, initial values for the weighting coefficients of the 
simulated neural network are established, e.g. as random values. 
The first of the sample values that were stored in the sample data memory 
30 is then read into the computer 33 and a simulated output is calculated 
(step S5), and a decision is made as to whether or not the timing of the 
output corresponds to that of the teaching values. If so, it is stored in 
the learning input value data memory region of the computer, then if the 
end of the playback data has not yet been reached (judged in step S8) the 
next sample value is read out from the sample data memory 30 and the above 
process repeated. When the end of the playback data for that learning data 
category is reached, the neural network learning operation is commenced 
(step S10), with successive ones of the stored learning input values being 
read out and supplied to the simulated neural network of FIG. 5. When the 
end of that processing is reached, i.e. when all of the teaching values 
have been used in the learning operation, a decision is made as to whether 
or not a satisfactory set of weighting coefficient values has been 
derived. This can be decided either by repetitively executing that 
learning operation (step S5 to S11) until the values obtained for the 
weighting coefficients cease to change (as they are successively updated), 
or by judging whether the differences between the output values produced 
from the neural network and the teaching values have become sufficiently 
small. 
The final set of weighting coefficients thus obtained are then stored, and 
in step S13 a decision is made as to whether or not all of the learning 
data categories have been processed. If not, a playback signal for 
obtaining the next learning data category is generated (step S14) and the 
operation then returns to step S3, in which that playback signal is 
sampled. In this case, the initial values to which the weighting 
coefficients are set in step S4 can be the values obtained for the 
preceding learning data category, which were stored in step S12. 
The above process is successively repeated for each of the learning data 
categories, to obtain a final set of weighting coefficients. 
It should be noted that it would be equally possible to supply successive 
sample values from the sample data memory 30 to be directly used in the 
neural network learning operation, instead of temporarily storing all of 
the output values in an internal memory of the computer. 
In the above it has been assumed for simplicity of description that the 
time points defined by the clock signal from the bit PLL 27 in FIG. 14 
coincide precisely with the desired learning input value points, in the 
playback data stream. That assumes for example, referring to FIG. 11, that 
sampling time points are defined which respectively coincide in time with 
the learning input values LV.sub.1 etc. in the playback signal. However in 
practice that is not necessarily so, i.e. there will be some degree of 
fixed displacement between the sampling points defined by the PLL output 
and the learning input value positions. If the learning period (which is 
T/2 in the embodiment described above) is made sufficiently small in 
relation to the data period T then that deviation of the sampling points 
is not a significant problem. However if the learning period is relatively 
large, as illustrated in FIG. 18 (in which the arrows in diagram (C) 
indicate the time points defined by the sampling signal produced from the 
bit PLL, and diagram (B) shows the corresponding teaching signal waveform) 
then for example there may be a significant deviation between a desired 
learning input value time point t2 in the playback data (shown in diagram 
(A)) and the preceding sampling time point, i.e. t1. In that case, a 
sample value SV.sub.a will be obtained which is significantly different 
from the desired value LV.sub.a, as shown. 
In such a case, it may be preferable to obtain each learning input value by 
interpolation of two successive sample values, as illustrated in FIG. 19. 
Here, a learning input value LV.sub.m is obtained by interpolation between 
two adjacent sample values SV.sub.n and SV.sub.n+1. 
It should also be noted that although in the learning operation of the 
embodiment described above, each of the sample values obtained in the 
learning data portion of the playback signal is used as a learning input 
value, in practice it may preferable to use a greater number of samples to 
obtain each learning input value. For example, the playback signal could 
be sampled at T/8 intervals, with the learning interval being T/2, and 
with each learning input value being calculated based on a combination of 
four successive sample values. 
Furthermore, there are various types of CD playback apparatus which utilize 
an optical pickup which provides four playback signal channels, i.e. 
respectively derived from a set of four spatially separated pickup 
elements. These four playback signals can provide information to be used 
in systems which control the optical system of the pickup, for example the 
focussing. These four playback channel signals are preferably used to 
extract a more accurate data clock signal by the bit PLL of the above 
embodiment, as illustrated in FIG. 21. Here, the playback signals of the 
four channels, designated as C1 to C4, are combined in a signal combining 
circuit 61, to obtain an input signal for the bit PLL 27. Higher stability 
and accuracy of PLL operation is thereby achieved. In addition, these four 
channel signals can be separately sampled, using the output signal from 
the PLL, to obtain 4-channel digital sample values which are stored in the 
sample data memory 30, to be subsequently transferred to the computer 33 
for the learning operation. In that case, after each of these 4-channel 
sample values is inputted to the computer, the four sample values are 
combined by the computer to obtain a single sample value, which is then 
operated on by the computer as described hereinabove for the case of 
single-channel operation. 
As described hereinabove it is essential, for accurate learning operation 
of the embodiment described above, for the computer 33 to precisely 
identify the start of the learning data portion of the playback data which 
are inputted thereto. This is done by inserting an initial marker portion 
in the playback signal, containing a data pattern which will not otherwise 
occur in the playback data. Specifically, that marker portion consists of 
successive sets of 15 T periods of data at the digital 1 level and 15 T of 
data at the digital 0 level, as illustrated in FIG. 20 which shows the 
data format of the playback signal used for learning operation. Firstly 
there is a preamble portion, i.e. a burst of data which is suitable for 
stabilizing the bit PLL operation. This is followed by the aforementioned 
marker portion, which is succeeded by a preparatory data portion, i.e. 
another burst of data which is suitable for stabilizing the PLL operation, 
since the long 15 T data states at the 1 and 0 levels do not occur during 
normal operation. The starting point of the learning input data is thereby 
identified (by the clock signal extracted by the PLL) as occurring at 
exactly the end of the preparatory data portion. Such highly precise 
identification of the start of the data to be used for neural network 
learning operation, in conjunction with corresponding predetermined 
teaching data, is a necessary feature of the present invention. It has 
been found that satisfactory results are obtained if the length of the 
learning data portion is made approximately 3000 T. 
In the embodiment described above, teaching values which are intermediate 
between the digital 0 and 1 levels (i.e. 0.5) are utilized, and it has 
been found that this feature greatly increases the speed with which the 
learning operation can be executed to obtain final values for the 
weighting coefficients, and the accuracy of the waveform equalization that 
is provided by the finally designed waveform equalizer. It would be also 
possible to use a shorter value of learning interval than the value of T/2 
used in the above embodiment. In that case, a plurality of intermediate 
values (between the digital 0 and 1 levels) could be used for the possible 
levels of the teaching values, in addition to the digital 0 and 1 levels. 
A second method of establishing the teaching values and learning input 
values to be used in the neural network learning operation will now be 
described. This method differs from that described above in that the bit 
PLL is not used to extract a clock signal from the playback signal. That 
is to say, referring to FIG. 14, the PLL 27 and sampling circuit 29 are 
omitted in this case. Apart from that, the system used can be as 
illustrated in FIGS. 13, 14 and 15. The playback signal from the CD 22 is 
converted to digital sample values at the very high sampling rate of the 
A/D converter 28 (e.g. 100 MHz), and these sample values are stored in the 
memory 30. A portion of the resultant data stored in the sample data 
memory 30 can for example be considered to be as illustrated in diagram 
(A) of FIG. 23. The text data representing the corresponding portion of 
the teaching data (i.e. corresponding to the playback data sequence of 5 T 
periods at a positive level, 3 T at a negative level, 4 T at the positive 
level, and 6 T at the negative level in this example) could be as shown in 
diagram (B), or alternatively as shown in diagram (C) or diagram (D). When 
these text data are transferred into the computer 33, they are converted 
into a sequence of digital 1 or 0 values, which occur at spacings 
corresponding to those of the learning input values, as illustrated in 
diagram (E) of FIG. 23. That is to say, if for example a certain portion 
of the playback signal data sequence has been converted into a set of 
1,000 sample values by the 100 MHz sampling operation, then the 
corresponding portion of the teaching value data sequence is converted 
into 1,000 discrete digital values. These discrete digital teaching values 
are then transferred through a suitable digital low-pass filter, i.e. a 
FIR filter, to be converted into a sequence of discrete values which can 
take the 0 and 1 digital levels and also a plurality of levels which are 
intermediate between these digital levels, such that these teaching values 
conform to to an ideal teaching signal waveform as illustrated in diagram 
(F) in FIG. 23. 
Referring now to FIG. 17, to obtain the learning input values that are to 
be set into the internal memory 4 for use in the neural network learning 
operation, the first part of the sample data held in the sample data 
memory 30 is transferred into the computer 33, to detect the 
aforementioned marker portion. After the start of the learning data is 
thereby detected, and successive sample values are transferred from the 
sample data memory 30 in response to read command signals sent from the 
computer 33, successive periodically occurring ones of these sample values 
are selected to be used as learning input values. This can be done for 
example by counting the number of times the read command signal is 
generated, to thereby determine the size of the learning interval, i.e. 
The separation between successive learning input values. If for example 
the desired learning interval is 231 ns and a 100 MHz sampling frequency 
is used to obtain the sample values (so that the period of the sample 
values is 10 ns), then it can be arranged that each time a count of 23 is 
reached for the sample values read out from the sample data memory 30, the 
sample value then read out is selected by the computer 33 to become a 
learning input value and stored in the internal memory 34, while in 
addition that count number is increased to 24 each time 10 successive 
sample values have been selected. In that way, the average value of 
learning interval will be 231 ns, i.e. sample values will be periodically 
selected at spacings corresponding to 231 ns. 
In order to obtain a set of teaching values which will respectively 
correspond to the learning input values thus obtained, a similar type of 
periodic selection operation is executed on the aforementioned discrete 
digital teaching values which correspond to the 100 MHz sample values. 
When these mutually corresponding sets of teaching values and learning 
input values have thus been derived and stored, the subsequent neural 
network learning operation can be carried out as described hereinabove. 
This method of obtaining the learning input values has the basic 
disadvantage of requiring a very high accuracy of control of the speed of 
rotation of the CD 22, since only a fixed-frequency clock signal is used 
for sampling the playback signal to obtain the learning input values. With 
the method which utilizes a PLL to extract the clock signal component of 
the data in the playback signal, on the other hand, a sampling signal can 
be generated (e.g. by frequency-multiplying the extracted clock signal) 
that is phase-locked to the contents of the playback signal data, 
irrespective of changes in the speed of rotation of the CD from which the 
playback signal is obtained. 
As described hereinabove referring to FIG. 8, that waveform equalizer 
circuit is based on a neural network having fixed weighting coefficients, 
whose values are determined by respective resistors R11, R21, etc. In 
addition, by forming each neuron unit (i.e. signal conversion unit) of 
that circuit as a pair of series-connected inverting operational 
amplifiers, it becomes possible to select the weighting coefficient values 
to be either negative or positive. Thus a combination of weighted input 
signals of either polarity can be inputted to each neuron unit, and in 
particular to the final (output) neuron unit. This has been found to 
provide substantially improved accuracy of waveform equalization, 
particularly when a very high frequency signal is to be equalized, by 
comparison with a more simple circuit configuration in which only which 
only weighted signals of identical polarity are inputted to each of the 
neuron units. 
It should be noted that it might be possible to simplify the circuit of 
FIG. 8, by arranging that signals of appropriately different polarity are 
outputted from the neuron units of the intermediate layer, to be supplied 
to the output layer, i.e. to the final neuron unit. In that case it would 
be possible to eliminate one of the two operational amplifiers 4a, 4b of 
that final neuron unit. 
Furthermore as a result of providing non-linear input/output 
characteristics for the neuron units (i.e. conversion units) of the 
waveform equalizer circuit of FIG. 8 by using diode clipping circuits, 
each having three input/output regions E1, E2 and E3, which have 
respectively different linear characteristics, the circuit of the waveform 
equalizer can have a very simple configuration. Moreover due to the fact 
that the learning computation processing based on the simulated neural 
network will also utilize such a form of non-linear input/output 
characteristic, the learning processing can be simple and efficient. 
A waveform equalizer formed of a neural network WE was constructed, using 
the design method described hereinabove in which a PLL is utilized in 
extracting sample values to be used as learning input values for the 
neural network learning operation. The circuit configuration was as shown 
in FIG. 8. FIG. 24(A) is a waveform photograph showing the effects of 
equalization by that waveform equalizer. FIG. 25(A) shows the analysis 
results obtained for the waveform equalizer, obtained by using a time 
interval analyzer. The test conditions were as follows: 
a. Recording medium 
The recording medium used was a CD having a 2.8 times increase in recording 
density by comparison with the standard CD recording density 
(specifically, with the track pitch made 0.95 micron, to obtain a 1.68 
times increase in recording density, and with the linear direction density 
increased by 1.67 times), and using optical recording with a linear 
velocity of 2.5 m/s for scanning the CD tracks by the pickup. That linear 
velocity is approximately twice the standard value of linear velocity used 
for a CD. 
b. Playback apparatus 
An optical type of playback apparatus employing an optical pickup was used. 
Laser light wavelength=670 nm 
Lens NA (numerical aperture)=0.6 
c. Learning conditions for neural network 
All learning was executed by using a back-propogation method. Five 
categories of learning data were derived for use in the learning 
operation, by executing specific misadjustment of the optical system of 
the playback apparatus. These learning data categories were respectively 
obtained under conditions of: 
(1) Defocussing of the optical system, 
(2) Coma aberration directed along the positive radial direction 
(3) Coma aberration directed along the negative radial direction, 
(4) Coma aberration directed along the positive tangential direction, and 
(5) Coma aberration directed along the negative tangential direction. 
d. Results 
FIG. 24(A) shows eye pattern waveforms of an equalized digital signal 
obtained using the above embodiment of a waveform equalizer according to 
the present invention, and FIG. 25(A) shows the corresponding analysis 
results obtained, using a time interval analyzer. FIG. 24(B) similarly 
shows waveforms obtained for the case of waveform equalization using the 
prior art waveform equalizer of FIG. 1, and FIG. 25(B) shows the analysis 
results obtained for that prior art apparatus. FIG. 24(C) shows the eye 
pattern waveforms for a playback signal with no waveform equalization 
applied. FIG. 25(C) shows the corresponding analysis results obtained for 
the case of a playback signal with no waveform equalization applied. 
The above results were obtained, in each case, for a playback signal having 
distortion due to coma aberration which is directed along the positive 
tangential direction. 
As will be clear from FIGS. 24(A) to (C), this waveform equalizer 
embodiment removes intersymbolic interference from the playback signal, 
and provides a distortion-free eye pattern. Furthermore as will be clear 
from FIGS. 25(A) to (C), showing the results of analysis of the waveform 
equalization by using a time interval analyzer (using a timebase of 1 ns 
and 10.sup.5 samples), the data bits are spaced substantially 
equidistantly, as a result of the operation of the waveform equalizer WE, 
and clearly are well separated, with the amount of jitter standard 
deviation being small. 
Thus with this waveform equalizer, it becomes possible to achieve accurate 
reproduction of a digital signal which contains various types of 
distortion resulting from intersymbolic interference, caused by various 
types of optical aberration. Results are obtained which have not been 
possible in the prior art. Moreover, since the design method is based on a 
neural network, the design process is simple. 
It can be understood from the above that with a waveform equalizer 
according to the present invention, the apparatus configuration is simple, 
and high-speed signal processing is made possible. Hence the invention 
enables effective removal of distortion in a digital signal produced from 
a playback system or from a transmission system, by real-time operation, 
and with a level of performance being attained that has not been possible 
with prior art types of waveform equalizer. 
Although the present invention has been described in the above with 
reference to an embodiment of a waveform equalizer for use with an optical 
type of data recording and playback system, it will be clear that the 
invention could also be applied to a waveform equalizer for use with a 
distorted digital signal produced from a magnetic type of recording and 
playback system, or produced from a receiving apparatus of a digital data 
transmission system. 
It should also be noted that various modifications to the described 
embodiment could be envisaged, such as using a different number of neuron 
units in the circuit of FIG. 8, for example using a different number of 
neuron unit layers, etc., which fall within the scope claimed for the 
present invention. 
Furthermore, in the method of designing such a waveform equalizer, various 
other arrangements other than those described hereinabove could be 
envisaged for deriving a set of learning input values and a corresponding 
set of teaching values for use in the neural network learning operation.