Noise Power Density Research Articles

Models of potassium conduction in excitable membrane examined by spectral analysis

Various models of potassium conduction in neuron membrane are evaluated via computer, as pertain to recently observed deviations from first order kinetics in the form of noise power density spectra with sharp corners, peaks and steep high frequency asymptotic slopes. A certain co-operative lattice model with linear, first order channel kinetics is found to be the only viable alternative to already well explored n-state, noninteractive channels with linear, but higher order kinetics, among a fairly wide range of possibilities. Lattice parameters are optimized with respect to spectral data, and a randomized hexagonal lattice with nearest neighbor interaction is found to be satisfactory. The general class of lattices considered includes spatial inhomogeneities.

FM Television Signal-to-Noise Ratio

For a frequency-modulation relay link carrying television, a simple general form is suggested for the relationship between baseband signal-to-noise ratio and the ratio of carrier power to noise power density applied to the receiver discriminator. The bandlimiting, emphasis, and weighting functions prescribed by various standards are characterized by effective noise bandwidths with respect to triangular noise.

Fluctuations and noise in kinetic systems III. Cycling steady-state models

The noise and fluctuations due to chemical reactions are considered for steady-state kinetic systems in which the Wegscheider relations are not obeyed (i.e. the systems are at a cycling steady state). We derive the noise power density spectrum in the quantity N = ∑ i = 0 x a i N i for an esemble of independent and equivalent systems each of which can exist in a set of discrete states i = 0, 1, 2, …, x. Ni is the number of systems of the ensemble in state i and ai's are constants. The transitions between two arbitrary states (i → j) are linear. The derived noise power spectrum is explicitly expressed as a function of the kinetic rate constants so that numerical calculations can easily be carried out for an arbitrary cycling steady-state model. This extends the derivations in two previous papers of this series in which only non-cycling models were discussed in detail. There are possible applications to optical pumping, photo adsorption-desorption reaction, active membrane transport, muscle contraction, etc. In each case, noise measurements would provide information about the kinetic scheme. Possible applications in biological systems in vivo are discussed in particular.

Potassium and sodium ion current noise in the membrane of the squid giant axon.

1. The spectral density of current noise power from 20 mm segments of giant axons of the squid Loligo vulgaris has been measured under space-clamp and voltage-clamp conditions. From 4 to 1000 Hz the measured noise is larger by several orders of magnitude than the theoretical thermal noise. The amplifier's noise, which may yield appreciable contributions above 200 Hz, could be evaluated and subtracted from the total noise using direct measurements of the membrane impedance...

Measurement of the spectral density of noise power with a selective voltmeter

Measurement of the spectral density of noise power with a selective voltmeter

Fluctuations and Noise in Kinetic Systems: Application to K + Channels in the Squid Axon

We consider the equilibrium or steady-state noise power density spectrum in the quantity N = Sigma(x) (i=0)a(i)N(i) for an ensemble of independent and equivalent systems each of which can exist in the discrete set of states i = 0, 1, ..., x. N(i) is the number of systems of the ensemble in state i and the a(i)'s are constants. There is a transition rate constant alpha(ij) for an arbitrary transition i --> j; the kinetic equations are linear. There are possible applications to enzyme and biochemical kinetics generally, to membrane transport, muscle contraction, binding on macromolecules, etc. In each case, noise measurements would provide information about the kinetic scheme. The particular application considered here is to K(+) channels or gates (one channel = one system) in the squid axon membrane: a(i)g(K) is the K(+) conductance of a channel in state i and the kinetic scheme is of the Hodgkin-Huxley type (HH). Here we allow an arbitrary set of a(i)'s. This is a generalization of our treatment of K(+) channel noise in an earlier paper. The theory is discussed and some calculations made using Fishman's recent experimental results on K(+) channel noise as a guide. Preliminary indications are that the HH choice of a(i)'s may be oversimplified and that a(0) congruent with 0, a(1) not equal a(0), a(x) not equal a(x-1). Quite possibly the a(i)'s increase from a(0) to a(x), though the early a(i)'s must be relatively small to give the observed induction behavior in g(K)(t). An increase in equal steps is unsatisfactory because this is essentially HH with x = 1 (no induction). More refined experiments may modify these tentative conclusions. In any case, it appears from Fishman's work that noise measurements will probably be very useful in distinguishing between rival models of K(+) channels.

Current noise in thin discontinuous films

Measurements have been made of the current noise in thin discontinuous platinum films deposited on glass substrates with surface sensitivities in the range 1.5 to 5.0*103 k Omega sq-1. The influence of film temperature and gaseous ambients on the variation of the spectral noise power density current flowing through the film, noise-channel frequency and surface resistance is described. The experimental data are interpreted in terms of a noise model based on quantum mechanical tunnelling through a surface layer containing adsorbed gaseous ions. The relationship between activation energies determined from conductance temperature and noise against temperature plots is investigated and it is shown that for activation energies epsilon >or=kT the noise mechanism is thermally activated.

Experimental Evaluation of Noise Parameters in Gunn and Avalanche Oscillators

Equations are presented that express noise-to-carrier ratio and rms frequency deviation of a negative-resistance oscillator with a multiple-resonant circuit in terms of effective available noise power densities of both 1/f and white-noise sources, an effective saturation factor, and an appropriate Q/sub L/ of the oscillator. Experimental evaluation of the noise parameters in Gunn and avalanche oscillators by use of these equations is described. AM and FM noise measurements have been made on X-band Gunn oscillators and Si and GaAs avalanche oscillators for frequency off carriers extending from 1 kHz to 10 MHz. Both 1/f and white noise have been observed in these oscillators. The validity of the above equations has been verified for Gunn oscillators from the dependence of the noise spectra on Q/sub L/. For Gunn oscillators and Si and GaAs avalanche oscillators, the effective noise-temperature ratio for white noise, N/kT/sub 0/, has been found to be 23~29, 41~51, and 38~44 dB, and the effective saturation factor to be 2~2.9, 0.5~2.4, and 2, respectively. An increase of N/kT/sub 0/ with the RF voltage across the diode has been observed in Si avalanche oscillators. Parameters for 1/f noise have also been evaluated approximately.

Noise spectrum for fluctuations of contact resistance and mechanism of noise generation in sliding contact

Noise voltage due to fluctuations in contact resistance arising from sliding contact varies with the kind of contact metals. The frequency spectrum of the noise power density resulting from sliding motion is assumed to be influenced by the properties of the metal surface. Moreover, the causes of the noise generation due to fluctuations in contact resistance are considered to be fairly well understood by investigating the frequency spectrum of the noise. By analyzing the frequency spectrum of the noise it was found that there are three types of noise spectra depending on the properties of the metal surface. Noise spectra with an f − 1 2 characteristic are found in metals with large values of W P , those with an f −1 characteristic in noble or like metals, and those with an f −2 characteristic in hard base metals.

Performance of a Two-Sample Mann-Whitney Nonparametric Detector in a Radar Application

The detection of signals in an unknown, typically non-Gaussian noise environment, while attempting to maintain a constant false-alarm rate, is a common problem in radar and sonar. The raw receiver data is commonly processed initially by a bank of frequency filters. The further processing of the outputs from the filter bank by a two-sample Mann-Whitney detector is considered. When the noise statistics in all filters are identical, the Mann-Whitney detector is distribution free, i. e., the false-alarm probability may be prescribed in advance regardless of the precise form of the noise statistics. The primary purpose of this paper is to demonstrate the potential advantage of nonparametric detectors over conventional detectors. The signal detection performance of the Mann-Whitney detector is compared to that of an ordinary linear envelope detector plus integrator in the presence of Gaussian and several hypothetical forms of non-Gaussian noise. This comparison is made for both uniform and nonuniform distributions of noise power across the filter bank. Besides providing a much more constant false-alarm rate than the conventional detector, the Mann-Whitney detector's signal detection performance is found also to be much less sensitive to the form of the noise statistics. In one case, its detection sensitivity is found to be 11 dB better than that of the conventional detector. Even when the noise power density is made moderately nonuniform across the filter bank, the detection performance of the Mann-Whitney detector is found not to be significantly affected.

Fluctuating Target Detection in Clutter Using Sidelobe Blanking Logic

In an earlier paper, Maisel [6] considered two-channel detection systems using a sidelobe blanking logic when a nonfluctuating target was present. This paper is an extension of the earlier work to include fluctuating targets. The Swerling I, II, III, and IV models are considered when single-pulse detection is of interest. An adaptive threshold procedure is also briefly discussed whereby the probability of false alarm at any given resolution cell is maintained constant, even though the input clutter level may vary from cell to cell or from beam position to beam position. Useful data are presented for detection probabilities in the range 0.5 to 0.9, for false alarm probabilities in the range 104 to 10-8, and for a false detection probability of 0.1 for a sidelobe target yielding an apparent signal to total noise power density ratio of 13.0 dB in the main beam receiver.

Noise Spectrum Received by an Antenna in a Plasma

A general expression for the noise spectrum received by an antenna in an isotropic plasma is derived by using a combination of plasma fluctuation theory and the reciprocity theorem. The special case of Maxwellian velocity distributions of the constituents is then considered. In the still more special case of thermal equilibrium Nyquist's theorem is shown to be satisfied. It is shown that a 'Maxwellian' energetic electron constituent carrying only a small fraction of the total thermal energy can enhance the spectral power density of antenna noise just above the plasma frequency. The maximum enhancement factor is equal to the square of the ratio of the 'thermal' velocities of the high‐ and low‐energy electrons. There is no such enhancement in the resistance of the antenna.

Intermodulation in parametric amplifiers

Third-order intermodulation products due to the charge-voltage nonlinearity of the varactor diode in a parametric amplifier have been computed. Some experimental data obtained from a two-carrier measurement have been reported. Finally, the noise power density in a telephone channel due to parametric amplifier intermodulation has been calculated as a function of total input power into the amplifier.

Analysis of Airborne VHF/UHF Incidental Noise over Metropolitan Areas

The computation of VHF band incidental radio noise levels over the centers of several cities, based upon measured surface noise data, is performed and the results compared with airborne data at several frequencies, altitudes, and urban locations. The functional dependence of airborne incidental noise upon detector altitude is computed and compared with available VHF measurements. Comparison is also made between man-made surface noise power density obtained from both airborne and surface measurements. Finally, the use of airborne measurements for determining surface incidental noise distributions in urban areas is noted and discussed.

Effect of duration on amplitude discrimination in noise.

Amplitude-discrimination performance is found to be independent of the duration of the signals to be discriminated for durations ranging from 20 to 200 msec provided that the ratio of signal energy to noise-power density is kept constant. If the ratio of signal energy to noise-power density is manipulated by altering either the noise-power density or the signal duration, then discrimination performance is also independent of that ratio once it exceeds 20 dB. The implication of these findings is discussed.

Current noise in thin gold films

Measurements have been made of the current noise in gold films deposited on glass substrates with surface resistivities in the range 10 to 104 Ω/sq. The experimental results have shown that the spectral noise power density may be expressed by where I is the direct current flowing through a gold film of surface resistance R at a temperature T, f is the noise-channel frequency, F(T) is a function of T and G(S) is a function of film structure. Observations have also been made on the phenomenon of noise bursts. The experimental data are interpreted in terms of a trap-assisted tunnelling conduction mechanism with a range of barrier widths. Further support is given to the proposed model from current-noise measurements made on cermet films.

Quasistationary noise in resistors

Carbon resistors, operated at very low currents, showed a quasistationary noise spectrum at very low frequencies. Over long periods the stationary noise power density followed S(ω) = Kω-s, with s close to unity. Then sudden large fluctuations occurred ending in another stationary period, but K may have changed its value. This behaviour explains a difficulty in repeating l.f. noise measurements.

A High-Performance Digital Data-Transmission System

A family of practical data-transmission systems, whose design is motivated by a desire to reduce the required energy per bit (for a specified noise power density) while operating in a well-defined part of the frequency spectrum, is described. The blocks of j information bits that are periodically fed to the transmitter are encoded into equal energy waveforms whose design is based upon the use of truncated \sin(kt + b)/(kt + b) impulse response networks, together with an n -dimensional unit hypersphere code. The same waveform generation equipment is used for matched filtering at the receiver terminal. This design approach leads to equipment that performs well in the presence of impulse noise as well as Gaussian noise.

Least-square-error amplitude measurement of pulse signals in presence of noise

This paper attempts to provide an insight into the mechanism of optimum amplitude measurement of pulse signals, in particular nuclear detector signals, with the purpose of summarizing the results and indicating the approach to the remaining problems. It is recalled that the optimum way to perform amplitude measurements in the presence of additive white gaussian noise - according to the least-square-error criterion - is to perform the “weighting” on the observed signal by evaluating the integral g m = ∫ −∞ ∞ s m ·(t)dt , where s m( t) is the observed signal plus noise and f( t) is the expected signal waveform. It is shown that this relation follows from both the matched filter approach (linear circuit theory) and from the statistical estimation theory. The optimum operation can be performed by two methods: the matched filter measurement and the correlation measurement. The resulting best signal-to-noise ratio is invariant of the method and is equal simply to the ratio of the signal energy in the measurement time interval and the noise power density. This gives directly the relationship between the signal-to-noise ratio and the measurement time. The time invariant matched filter and its approximations presently in use are very inefficient with respect to the ratio of the measurement time actually required to extract the amplitude information and the time in which they are unable to perform another measurement. This is a basic limitation of time-invariant linear filters. The solution to optimization of both the signal-to-noise ratio and the time requires time variant filters.

NOISE STUDIES IN UNIFORM AVALANCHE DIODES

This Letter reports avalanche noise studies on microplasma-free guard-ring avalanche diodes. The low and high frequency approximations of Hines' theory are compared with experimental results at 1 kHz and 3 to 9 GHz, respectively. Good agreement is found between experiment and theory at both low and high frequencies. The open-circuit spectral voltage density is white up to the avalanche frequency ωa and decreases inversely with current. For ω ≫ ωa the spectral noise power density falls off with ω4.