Random Amplitude Modulation Research Articles

On the Maximum Rate of Fluctuation in Mode-Stirred Reverberation

Theoretical limits are derived for the maximum permissible rate of mechanical/electronic stirring or spatial/spectral scanning inside a reverberant cavity. These limits are based on upper bounds for the maximum rate of field fluctuations and are obtained by imposing the requirement of quasi-stationarity on the interior cavity field. For a sinusoidal excitation field, the interior field is represented as a narrowband random hybrid amplitude-plus-frequency modulation, as induced by the stirring or scanning process, and is based on an analytic field formulation. Distortion (nonlinearity) of the modal and effective field is quantified for first-order variations of amplitude and frequency. Its dependence on the random amplitude modulation index is demonstrated. The latter is estimated from macroscopic system parameters. The effect of compensation of net input power on the distortion and maximum stirring rate is analyzed. The maximum stirring rate exhibits an inverse power law dependence on the operating frequency. For a specified level of maximum distortion, maximum rates of electronic, mechanical, or electromechanical mode stirring are derived. The effect of the order of the EUT transfer function on the distortion, as well as the detuning, bandwidth, and amplitude distortion of the perceived test field caused by stirring or scanning are quantified and analyzed.

Non-stationary response of structures excited by random seismic processes with time variable frequency content

Seismic random processes are characterized by high non-stationarity and, in most cases, by a marked variability of frequency content. The hypothesis modeling seismic signal as a simple product of a stationary signal and a deterministic modulation function, consequently, is hardly ever applicable. Several mathematical models aimed at expressing the recorded process by means of a system of stationary random processes and deterministic amplitude and frequency modulations are proposed. Models oriented into the frequency domain with subsequent response analysis based on integral spectral resolution and models oriented into the time domain based on the multicomponent resolution are investigated. The resolution into individual components (non-stationary signals) is carried out by three methods. The resolution into intrinsic mode functions seems to possess the best characteristics and yields results almost not differing from the results obtained by stochastic simulation. An example of the seismic response of an existing bridge obtained by two older models and three variants of multicomponent resolution is given.

Stimulus Encoding and Feature Extraction by Multiple Sensory Neurons

Neighboring cells in topographical sensory maps may transmit similar information to the next higher level of processing. How information transmission by groups of nearby neurons compares with the performance of single cells is a very important question for understanding the functioning of the nervous system. To tackle this problem, we quantified stimulus-encoding and feature extraction performance by pairs of simultaneously recorded electrosensory pyramidal cells in the hindbrain of weakly electric fish. These cells constitute the output neurons of the first central nervous stage of electrosensory processing. Using random amplitude modulations (RAMs) of a mimic of the fish's own electric field within behaviorally relevant frequency bands, we found that pyramidal cells with overlapping receptive fields exhibit strong stimulus-induced correlations. To quantify the encoding of the RAM time course, we estimated the stimuli from simultaneously recorded spike trains and found significant improvements over single spike trains. The quality of stimulus reconstruction, however, was still inferior to the one measured for single primary sensory afferents. In an analysis of feature extraction, we found that spikes of pyramidal cell pairs coinciding within a time window of a few milliseconds performed significantly better at detecting upstrokes and downstrokes of the stimulus compared with isolated spikes and even spike bursts of single cells. Coincident spikes can thus be considered "distributed bursts." Our results suggest that stimulus encoding by primary sensory afferents is transformed into feature extraction at the next processing stage. There, stimulus-induced coincident activity can improve the extraction of behaviorally relevant features from the stimulus.

ENCODING CARRIER AMPLITUDE MODULATIONS VIA STOCHASTIC PHASE SYNCHRONIZATION

The firings of excitable systems can phase lock to periodic forcing. In many situations however, the firings are separated by a random number of forcing cycles, even though they occur near a preferred phase of the forcing. Also, the associated interspike interval histograms display peaks over a continuous range of integer multiples of the forcing period, and the peak heights are a unimodal function of increasing multiples of the period. This paper focusses on these patterns of stochastic phase synchronization and their alteration by physiologically relevant stimuli that modulate the amplitude of the periodic forcing. Specifically, two regimes of the FitzHugh–Nagumo system exhibiting stochastic phase locking are considered. We discuss how internal noise, originating from e.g. synaptic or conductance fluctuations, must interact with either suprathreshold or subthreshold dynamics, and in some instances with subthreshold chaos, to produce such firing patterns. These responses to constant amplitude "carriers" are then compared to those from carriers with random band-limited amplitude modulations (AM's). The comparison is based on the mean firing rate, as well as phase synchronization computed using a suitably defined input–output phase difference. Further, using the stimulus reconstruction technique to characterize synchrony between random AM's and spikes, the internal noise is shown to help transmit information about random carrier AM's in the subthreshold and slightly suprathreshold cases. This transmission also depends nonmonotonically on the carrier frequency. Our results provide biophysical insight into the dynamics of neural signal encoding that combines a mean rate code on long time scales and a precise temporal code based on phase locking on the shorter time scale of the carrier period.

LDA measurement of sound: amplitude modulation of laser Doppler signals

Laser-Doppler-anemometry measurements of instantaneous acoustic particle velocity are presented. The Doppler signals, from measurements in air, display quasi-periodic amplitude modulation with a fundamental frequency equal to the frequency of the acoustic field. This effect can cause signal-processing problems. Periodic amplitude modulation is investigated by studying the power spectral densities of the envelopes of measured Doppler signals. Various seeding and acoustic conditions are considered. It is shown that the periodic amplitude modulation is much more significant with water-droplet seeding than it is with smoke-particle seeding. Random amplitude modulation replaces periodic amplitude modulation when a significant steady flow is superimposed on the acoustic field. The harmonic content of the Doppler-signal envelope increases with the intensity of the acoustic field. A simple computational model is used to simulate Doppler-signal envelopes. The simulation is in good qualitative agreement with many experimental observations. However, there is is some discrepancy with experimental measurements, notably a 90° phase difference between the positions of measured and simulated envelope maxima. The paper briefly considers the possibility of exploiting the periodic amplitude modulation effect in a new type of anemometer for acoustic velocity measurement in sound fields with low acoustic frequency and high acoustic particle velocity amplitude.

Cramer-Rao bounds and maximum likelihood estimation for random amplitude phase-modulated signals

The problem of estimating the phase parameters of a phase-modulated signal in the presence of colored multiplicative noise (random amplitude modulation) and additive white noise (both Gaussian) is addressed. Closed-form expressions for the exact and large-sample Cramer-Rao Bounds (CRBs) are derived. It is shown that the CRB is significantly affected by the color of the modulating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is small. Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed. These estimators are shown to be equivalent to the nonlinear least squares estimators, which consist of matching the squared observations with a constant amplitude phase-modulated signal when the mean of the multiplicative noise is forced to zero. Closed-form expressions are derived for the efficiency of these estimators and are verified via simulations.

Feature Extraction by Burst-Like Spike Patterns in Multiple Sensory Maps

In most sensory systems, higher order central neurons extract those stimulus features from the sensory periphery that are behaviorally relevant (e.g.,Marr, 1982; Heiligenberg, 1991). Recent studies have quantified the time-varying information carried by spike trains of sensory neurons in various systems using stimulus estimation methods (Bialek et al., 1991; Wessel et al., 1996). Here, we address the question of how this information is transferred from the sensory neuron level to higher order neurons across multiple sensory maps by using the electrosensory system in weakly electric fish as a model. To determine how electric field amplitude modulations are temporally encoded and processed at two subsequent stages of the amplitude coding pathway, we recorded the responses of P-type afferents and E- and I-type pyramidal cells in the electrosensory lateral line lobe (ELL) to random distortions of a mimic of the fish's own electric field. Cells in two of the three somatotopically organized ELL maps were studied (centromedial and lateral) (Maler, 1979; Carr and Maler, 1986). Linear and second order nonlinear stimulus estimation methods indicated that in contrast to P-receptor afferents, pyramidal cells did not reliably encode time-varying information about any function of the stimulus obtained by linear filtering and half-wave rectification. Two pattern classifiers were applied to discriminate stimulus waveforms preceding the occurrence or nonoccurrence of pyramidal cell spikes in response to the stimulus. These signal-detection methods revealed that pyramidal cells reliably encoded the presence of upstrokes and downstrokes in random amplitude modulations by short bursts of spikes. Furthermore, among the different cell types in the ELL, I-type pyramidal cells in the centromedial map performed a better pattern-recognition task than those in the lateral map and than E-type pyramidal cells in either map.

Random changes in envelope of AM tones and their detection.

The aim of this investigation was to determine the detection thresholds of sinusoidal and random changes in envelope of amplitude modulated (AM) signals. The envelope changes were obtained as a result of modulation of a pure-tone carrier by chosen types of modulators, which gave either sinusoidal, pseudorandom, or random (Gaussian) amplitude modulation. For pseudorandom and random modulation, the detection thresholds were determined when only modulation depth (m) of AM signals was changed randomly (fm const) or when both modulation depth and modulation frequency (fm) were changed randomly (fm random). The data showed that for low modulation frequency (fm≤64Hz) the detection thresholds for sinusoidal amplitude modulation (SAM), pseudorandom amplitude modulation (PAM) and random amplitude modulation (RAM) overlapped one another in the limit of the standard deviation (SD). However, for higher modulation frequencies, the average threshold for the RAM (fm, const) was about 3dB lower (around fm=128Hz) than that for sinusoidal amplitude modulation. In this case the PAM threshold was similar, within the limit of SD, to the SAM threshold. However, when random changes in amplitude were combined with random changes in frequency, the PAM (fm, random), and RAM (fm random) thresholds decreased about 5 dB relative to the SAM threshold.

Detection thresholds of random amplitude modulation

The main objective of this study was to determine the detection thresholds of random amplitude modulation (RAM) as a function of modulation and carrier frequency. Two experiments were performed. Experiment 1 concerned the detection thresholds of AM stimuli for only random amplitude changes at constant modulation frequency. Experiment 2 dealt with detection thresholds for simultaneous, random changes in amplitude and modulation frequency. The data obtained showed that for low modulation frequency, the detection thresholds for sinusoidal amplitude modulation (SAM), random amplitude modulation at constant modulation frequency [RAM(fm const)], and random amplitude and modulation frequency [RAM(fs random)] overlapped one another in the limit of SD. However, for higher carriers and modulation frequencies the RAM(fm const) thresholds were, in a limited range offm , much lower than the SAM ones. When random changes in modulation frequency were combined with random changes in amplitude, the RAM(fm random) thresholds decreased relative to the RAM(fm const) thresholds. a)Permanent address: Institute of Acoustics, Adam Mickiewicz University, Poznan ul. Matejki 48/49, Poland.

Modulation detection interference using random and sinusoidal amplitude modulation

The detection of amplitude modulation (AM) of a target sound is made more difficult by the presence of a modulated sound some spectral distance from the target. This effect (modulation detection interference, or MDI) was examined for stimuli with random amplitude modulations (RAM) and for sounds with sinusoidal amplitude modulations (SAM) as a function of average modulation depth (m) of the interferer. In an experiment comparing comodulated and independent RAM targets and interferers, the amount of interference was not related to the modulation coherence of the target and interferer. Elevations in AM threshold increased as a function of m in a similar way for both conditions. The MDI for RAM and SAM targets and interferers was also compared. While no difference was found for AM detection of RAM and SAM, MDI was found to be greater for the RAM stimuli than for the SAM stimuli. A subsidiary experiment comparing RAM and SAM modulation depth discrimination indicated that RAM discrimination is more difficult than SAM discrimination. Taken together, these results are quantitatively consistent with a mechanism resembling AM discrimination as the underpinning of MDI in conditions where the target and interferer are synchronously gated.

Numerical analysis of nonlinear transient light scattering by hypersound

A numerical analysis is made of nonlinear transient light scattering by hypersound in a nonlinear medium. It is shown that random amplitude modulation of a Stokes wave excited by stimulated Brillouin scattering initiated from a seed noise disappears on transition to the nonlinear regime. It is also shown that two pairs of light waves may undergo mutual phase locking as a result of their four-wave interaction with the same hypersonic wave.

Influence of noise on the formation of optical solitons in waveguides

An analysis is made of the propagation of an electromagnetic pulse in a nonlinear fiber waveguide. A numerical solution of a nonlinear Schrodinger equation with an initial condition in the form of pulses subjected to random amplitude or phase modulation demonstrates that if a soliton is formed, then its position and propagation velocity experience fluctuations whereas the amplitude is affected very little. This should result in broadening of the average envelope of a pulse, but in each of the realizations of the random initial condition the resultant pulse may not experience broadening.

Bloch equations driven by a random telegraph signal

Input-output cross-correlations are derived for the Bloch equations driven by a sinusoid near the Larmor frequency with random telegraph binary amplitude modulation. The correlations decrease with time as a superposition of four exponential functions. Two time constants may be conjugate complex giving rise to damped oscillations for certain values of relaxation times, resonance offset, excitation amplitude, and modulation bandwidth. The dependence of the correlations on these parameters is similar to the behavior of the magnetization in Torrey nutations, except that the relaxation rates are enhanced by the modulation bandwidth. In the limit of zero or infinite bandwidth, the results agree with cw or white Gaussian noise excitation, respectively. Measurements using the proton magnetic resonance of a doped water sample show agreement for a case with intermediate bandwidth.

Detection of frequency modulation by normally hearing and severely‐to‐profoundly hearing‐impaired listeners

Listeners with a severe to profound hearing loss often perceive changes in loudness when the frequency of a stimulus is changed. As a result, researchers who have studied frequency discrimination in impaired listeners may have underestimated the extent of the frequency impairment. In this study, we compare normal and impaired listeners in three frequency modulation detection experiments, in which the amplitudes of the test signals were either fixed, sinusoidally modulated at a constant rate of 3 Hz, or randomly modulated at rates of 3 Hz and below. Results for listeners with normal hearing showed that modulation of signal amplitude yielded Δ FMs that were 2–3 times larger than those obtained with fixed amplitude. Results for one impaired listener tested thus far show abnormally large Δ FMs for all conditions, and, in addition, that Δ FMs obtained with random amplitude modulation are as much as 45 times larger than those found for listeners with normal hearing. [Work supported by NIH.]

Analysis of the response of linear dynamic systems to product random processes

A method is presented for the analysis of the response of linear dynamic systems to product random processes, with application to processes with random amplitude modulation. The Fokker-Planck equation is used to develop equations for the statistical moments of the system response, including relations for the moments of all orders of the response of systems which have linear time-invariant state equations. The quasi-steady approximation, which omits the dynamic properties of the random amplitude modulation, is developed as a limiting case of the exact solution for the moments of the system response. The quasi-steady approximation is generally accurate for well-damped systems, but can be inaccurate for lightly damped systems.

Effect of simultaneous random amplitude and frequency modulation on ECG power spectra

The periodic approximation to a typical electrocardiograph signal is found to be inaccurate as the residuals from the actual ECG and the periodic approximation failed consistently to satisfy the hypothesis of being a realization from a white noise process. The authors, therefore, considered the model which is the simultaneously amplitude- and frequency-modulated version of the periodic model and obtained the average spectrum of the more comprehensive model. The average spectrum is displayed in a manner in which the “spike” part corresponding to the periodic part of the ECG (QRS complex) and the part corresponding to the underlying nonperiodic part of the ECG are identified and displayed.

Propagation of a coherent acoustic wave through a turbulent shear flow

A collimated ’’monochromatic’’ acoustic wave (sinusoidal wave of 3–90 kHz) was directed across a two-dimensional turbulent jet perpendicular to its plane of symmetry. Extensive study of the statistical properties both of the turbulent medium and of the received signal (random amplitude and phase modulation) offers physical insight into the general phenomenon of a periodic wave (pressure) scattered by random inhomogeneities (solenoidal velocity field). Subject Classification: [43]28.60.

Parametric instability thresholds and their control

It is shown that the “swelling” of the laser electric field must be included in threshold estimates for the electrostatic instabilities excited by a laser near the critical density. Random amplitude modulation of the laser is found to lead to an increased instability threshold.

Unified analysis of fan stator noise

A theory is developed which predicts the acoustic radiation of an axial-flow fan stator due to interaction with rotor viscous wakes. Calculations are compared in detail with experimental data. Both the harmonic and broadband noise-spectrum components are calculated from a unified model using methodology from the theories of random pulse amplitude modulation, PAM, and pulse position modulation, PPM. The stator is modeled as a circular array of pulsed dipoles. The amplitude and arrival time of each pulse are random variables whose means correspond to the values calculated from harmonic rotor-stator interaction theory. The standard deviations of these random variables are measures of the turbulence levels in the blade wakes. For the model proposed the solution is exact: when PAM is imposed on a periodic stator source, new broadband energy is generated whose spectrum shape is similar to the envelope of harmonics at high frequencies and the harmonic radiation is unchanged; however, when PPM occurs, new broadband energy is radiated but at the expense of harmonic energy. At frequencies significantly above duct cutoff it is shown for a fixed stator solidity that the spectrum is essentially independent of the number of stator vanes.

Ocean Surface Bias on Doppler System Output

Usually, the Doppler output of a sonar system is assumed to be monochromatic. The random variation of ocean surface and bottom significantly alter this assumed monochromatic nature of the Doppler signal into a frequeucy band-limited output. The surface heights are assumed to be normally distributed; the facet approach is used to show their effect on the Doppler term. For instance, a transmitted signal: et(t) = sin ωct becomes: ẽr(t) = à sin(ωcf+φ̃d+φ̃a). The random amplitude modulation à and its associated phase-angle modulation φ̃a have been previously shown to be strictly surface-caused effects, whereas φ̃d is the surface-caused randomly varying Doppler term, if one takes out the transmitter beam-modulalation effects. The long time averages of à and φ̃d have been shown to be statistically independent, Rayleigh and uniformly distributed, respectively. Beating of the received signal ẽr(t) with the local oscillator producing the carrier frequency ωc and passing it through the low-pass filter to get rid of 2ωc term results in ēr′ = à sin(φd+φa). Under quite general conditions, the probability density function of ẽr′ was shown to be Gaussian. This result was then verified from experimental data obtained by an underwater Doppler system as well as by its laboratory ultrasonic simulation at the University of Houston in a 20-ft-, 25-ft-deep water tank. Results of the experimental data analysis seem to support the theoretical results discussed earlier. [Work sponsored by the Office of Naval Research (Acoustics Branch).]