Most of the quadratic systems are closely connected with the observation of some physical quantity, since the observation essentially coincides with the weighted mean operation in some sense, in view of the fact that an information obtained from the crude physical phenomenon through the observation is a certain mean image. Form of the mean operation (especially the weight function) will be steadily improved with the progress of science. At the stage where the effect of observation on the crude fluctuation is unknown yet, however, a mean squaring operation in the special form seems to be the most natural one to take. The above physical quantity may be random or have a well-defined representation in time, accompanied by noise which interferes with measurement. Quite apart from the instrument problem of realizing a optimum stable detector, there is an inherent limit to the precision of any measurement performed in a finite time, owing to the random nature of noise power itself. A typical input to the mean squaring system is considered as acombination of normal random noise and a regular signal with a definite structure. The random input process is considered to be the noise and signal generated by stationary process, and it will be further assumed that the random input noise has Gaussian probabilityd istribution.
The focus of this paper is to find out how the output probability distributions of signal and noise are given after mean squaring rectification. The above output fluctuation is treated as a probability problem of “distance” in an N-dimensional function space with N=2 TW (W: frequency interval, T: time interval), where the distance is taken as the mean squared fluctuation. From this point of view, many explicit expressions of probability density distribution for normal random noise and a regular signal, after passing a mean squaring circuit and an audio band-pass filter of arbitrary width, are experimentally and theoretically derived in connection with the sampling theorem. In this case, the output fluctuation is reasonably expressed by one ripple parameter m. This parameter m is proved to be approximately equivalent to TW expressed in the samplingtheorem.
The experimental and theoretical results described in this paper are also applicable to the other fields of measurement on random phenomena, since the mean energy (taking a mean squaring form) is a universal physical quantity.

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In proportion to remarkable development of digital instrumentation in recent, many kinds of analog to digital converters which are a basic element for the same instrumentation have been reported. Described in this paper is a digital millivolt meter which consists of a comparator using transistor choppers and arithmometer as main components. The value kept in the arithmometer, which is a measuring value converted into digital value, is modulated into a pulse width (or mark space ratio) having a constant frequency. This pulse width is demodulated into analog voltage E₀ by low pass filter. The analog voltage E₀ and input voltage E_χ are compared by transistor choppers, and ED <E_χ or E₀> E_χ is detected by its output phase. The arithmometer conducts addition and subtraction at the condition of E₀<E_χ or E₀>E_χ and rests at the balancing condition of E₀=E_χ. Since the comparator is composed of transistor choppers, it has very high sensitivity, accuracy, and resolution of 10μV. Employing the pulse width modulation method, the digital to analog converter is composed of smaller number of high-accuracy parts than in ladder-type circuit. Therefore, this digital millivolt meter is in low cost and does not need complicated adjustment.

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In adaptive control system, it is very important to minimize the effect of errors of process identification. For this purpose, the measured value of process has to be statistically processed. This paper describes an adaptive control system in which optimum compensating network is decided so as to satisfy Bayes' solution. Bayes' solution is obtained as a non-data problem by correcting a priori probabilities of parameters every time the measuring value is obtained. If such a compensating network as to satisfy Bayes' solution is used, the expected loss of control system becomes minimum. In this paper, it is assumed that system input is a stationary random process and all the noises are represented by a stationary Gaussian noise of the known characteristcs. It is proved that, in applying Bayes' theorem to nonstationary process such as variation of process parameter, probabilities should be corrected by only a certain number of latest data and older ones must be abandoned. Even if a priori probability is erroneous in the first step, it converges to a right value step by step and for this reason, its control system may be said a sort of learning control system. Furthermore, this paper refers to a new digital filter applying the theory of regression function which is used to decrease noise variance. Experimental results on a single variable system by digital simulation are shown. When a compensating network is decided so as to satisfy Bayes' solution, total loss the number of times and of miscompensations become much smaller than those in the control systems not using this method. This method has the great advan tage that the control characteristics can be quantitatively evaluated by introducing the conception of loss.

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In a digital process control computer, there need multiplexers to sample the transmitting signals in mV DC and convert them in to AC signals. The AC signals are amplified and transmitted to an A-D converter. If the A-D converter can directly convert AC analog signal in to digital signal, there will be such advantages as a rectification system is not needed, common mode noise to come back to the multiplexers is eliminated by use of a coupling transformer and so on. Described in this paper are design and experiment of a few A-D converters for AC signal as shown in the following:
1) Fundamental circuits A-C converters
(a) Voltage comparator of transistor multiar type
(b) Switching circuit for analog signal
(c) Analog decoder
2) A-D converter for AC signal
3) A-D converter for maximum or minimum input signal

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Learntrol IV establishes a clear concept of the hierarchical structure in a learnig control system and the synthesizing method of a high level learning loop necessary to motivate and achieve a want to a higher learning level, and gives a principle of behavior in the high level learning loop.
Learntrol IV is a development of Learntrols I-III presented in previous papers. In Learntrols I & II, a searching method is altered from the step-by-step (gradual) search to the jumping search according to the same previous experience and in Learntrol III, the method is altered from the step-bystep search to the semi-jumping search and finally to the jumping search according to the similar previous experience. Generally, a learning control loop is divided into two parts, one is the alterative part altered according to previous experience and the other the fixed part not altered. Giving an example of the synthesizing method of a high level learning loop for alteration of the fixed part in Learntrol III in order to raise the quality (possibility) of behavior of a learning control system, Learntrol IV shows the learning model method which decides an optimum strategy by means of Gedanken experiment with trial experiment.
As a result of simulation experiment of Learntrol IV with a digital computer, learning curves are shown and discussed.

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