Probability Distribution Of Noise Research Articles

Characteristics of atmospheric radio noise observed at Singapore

Measurements of the amplitude probability distributions of atmospheric radio noise in a power bandwidth of approximately 400c/s, made at the Radio Research Station, Singapore, from September 1958 to July 1960, are presented for frequencies of 24 kc/s, 145 kc/s, 11 Mc/s and 20 Mc/s. Results are normalised to the r.m.s. amplitude to show the diurnal and seasonal variations of noise structure.The temporal variations in parameters derived from the distributions are also illustrated and the results explained by reference to the prevailing meteorological and ionospheric conditions. Parameters relating to noise amplitude are the mean power and the average value of the noise-envelope voltage; those relating to noise structure are the ratio of the r.m.s. to the average value and the dynamic range.The programme of measurements was similar to that made at the Radio Research Station in England during the International Geophysical Year. Wherever possible, the Singapore data are compared with the corresponding results for England.

Intermodulation Distortion in Analog FM Troposcatter Systems

In broadband transmission over troposcatter paths, selective fading will be encountered with resultant transmission impairments, depending on the modulation method. An analysis has been made in a companion paper of such selective fading, based on an idealized model of troposcatter paths. It indicated that selective fading will be accompanied by phase nonlinearity which in a first approximation can be regarded as quadratic over a narrow band. A probability distribution for such quadratic phase distortion was derived. On the premise of quadratic phase distortion, the error probability owing to selective fading was determined for digital transmission by various methods of carrier modulation. The same idealized model and basic premise of quadratic phase distortion is used here to determine intermodulation distortion in FM for a signal with the statistical properties of random noise. An approximate expression for intermodulation noise owing to specified quadratic phase distortion has been derived, applying for any method of frequency pre-emphasis in FM. In turn, median intermodulation noise as well as the probability distribution of intermodulation noise has been determined, as related to certain basic system parameters. A comparison is made of predicted with measured intermodulation noise in four troposcatter systems with lengths from 185 to 440 miles. The results indicate that phase nonlinearity owing to selective fading can be approximated by quadratic phase distortion, or linear delay distortion, over an appreciable part of the transmission band ordinarily considered for troposcatter systems, with a probability distribution that can be determined from certain basic parameters of troposcatter links, such as the length and antenna beam angles. However, to predict intermodulation distortion on any system, further experimental data than are now available are required on beam broadening by scatter. The present random multipath FM distortion theory is shown to afford

Detection Theory Applied to the Absolute Sensitivity of Sensory Systems

Mainly the skin senses touch and warmth have been investigated. It is shown that the decision model describes the experimental data better than the threshold model. The experiments lead to the assumption that an internal noise exists, which is a neural activity being undistinguishable from the neural activity caused by small stimuli and which adds to the neural activity caused by the stimulus. The probability distribution of this internal noise can be considered to be gaussian. The relation between stimulus and neural activity is alinear for the touch sense. The question of whether noise of a multiplicative nature must be assumed is discussed.

A class of definitions of “duration” (or “uncertainty”) and the associated uncertainty relations

A new class of definitions for “time duration” and “bandwidth” (or “time uncertainty” and “frequency uncertainty”), in terms of norms of Lp spaces, is suggested. Some properties of the definitions and the associated uncertainty relations are derived. As examples of the application of these concepts, the problems of the approach of the probability distribution of shot noise towards the normal law, and the “beamwidth”—“aperture width” product in antenna theory are considered.

Probability Distribution of Noise Due to Fading on Multisection FM Microwave Systems

The probability distribution of expected baseband noise during fading at the end of a multisection microwave radio system is an important consideration in the engineering of a long system. This paper gives measurements of fading on a single path, and derives an estimate of the probability distribution of expected noise due to fading on a particular 68-section system of which the single path is a typical part. A comparison is shown with a measured cumulative distribution curve of noise at baseband subsequently obtained on the long system under operating conditions. A numerical method of combining distribution curves was used in this case and the so-called breaking effect, due to deep fades, is included. This method is described in the Appendix. While this paper is directed specifically to a particular microwave system, the principles described can be applied equally well to others.

On the Theory of Prediction of Nonstationary Stochastic Processes

We consider the following problem of prediction: During a finite time interval T the real valued function S(t)+N(t) is observed, in which S(t) is a signal and N(t) is a linearly superimposed noise disturbance. The problem is to predict the value of a given linear functional of S(t), the predictor formula having certain preassigned ``optimum properties'' among a certain class of predictors. In the case in which the mean value of S(t) is known, the random components of S(t) and N(t) are strictly stationary, and the time interval T is infinite, a complete solution to this problem has been given by N. Wiener. (In the case of discrete time series, the solution was given by A. Kolmogoroff.) This theory has been extended by L. Zadeh and J. Ragazzini [J. Appl. Phys. 21, 645 (1950] to the case in which T is a finite time interval and the mean value of S(t) is unknown but is restricted to be a polynomial in time. We extend the above theories to the case in which the random components of both S(t) and N(t) are nonstationary in time and merely possess finite continuous covariance and cross-covariance functions. The analytical tools of probability theory which we use are those developed independently by M. Loève and K. Karhunen in their studies of a class of stochastic processes usually termed processes of second order. Apparently these techniques are practically unknown outside of certain mathematical circles. In the opinion of the author these techniques are extremely powerful in the analysis of transient random phenomena in linear systems. Finally we give an exposition of a method of prediction by the theory of conditional probabilities. This method is applicable when the form of the joint probability distribution of signal and noise is known and hence is applicable to many practical problems, since this distribution is often Gaussian. In this particular case the predictor formula given by the theory of conditional probabilities is identical with the usual linear predictor formula given by the theory of least squares. In case the signal is a Markoff process, the method of conditional probabilities yields a much simpler prediction formula than the usual method of least squares.