Amplitude Frequency Response Measurement: A Simple Technique

A simple method is described to combine a modern function generator and a digital oscilloscope to configure a setup that can directly measure the amplitude frequency response of a system. This is achieved by synchronously triggering both instruments, with the function generator operated in the ``Linear-Sweep'' frequency mode, while the oscilloscope is operated in the ``Envelope'' acquisition mode. Under these conditions, the acquired envelopes directly correspond to the (input and output signal) spectra, whose ratio yields the amplitude frequency response. The method is easy to configure, automatic, time-efficient, and does not require any external control or interface or programming. This method is ideally suited to impart hands-on experience in sweep frequency response measurements, demonstrate resonance phenomenon in transformer windings, explain the working principle of an impedance analyzer, practically exhibit properties of network functions, and so on. The proposed method is an inexpensive alternative to existing commercial equipment meant for this job and is also an effective teaching aid. Details of its implementation, along with some practical measurements on an actual transformer, are presented.

On using peak amplitude and rise time for AE source characterization

Acoustic Emission (AE) signals, which are electrical version of acoustic emissions, are usually analysed using a set of signal parameters. The major objective of signal analysis is to study the characteristics of the sources of emissions. Peak amplitude (P-a) and rise time (R-t) are two such parameters used for source characterization. In this paper, we theoretically investigate the efficiency of P-a and R-t to classify and characterize AE sources by modelling the input stress pulse and transducer. Analytical expressions obtained for P-a and R-t clearly indicate their use and efficiency for source characterization. It is believed that these results may be of use to investigators in areas like control systems and signal processing also.

Ultrasound-modulated optical tomography: recovery of amplitude of vibration in the insonified region from boundary measurement of light correlation

We address a certain inverse problem in ultrasound-modulated optical tomography: the recovery of the amplitude of vibration of scatterers [p(r)] in the ultrasound focal volume in a diffusive object from boundary measurement of the modulation depth (M) of the amplitude autocorrelation of light [phi(r, tau)] traversing through it. Since M is dependent on the stiffness of the material, this is the precursor to elasticity imaging. The propagation of phi(r, tau) is described by a diffusion equation from which we have derived a nonlinear perturbation equation connecting p(r) and refractive index modulation [Delta n(r)] in the region of interest to M measured on the boundary. The nonlinear perturbation equation and its approximate linear counterpart are solved for the recovery of p(r). The numerical results reveal regions of different stiffness, proving that the present method recovers p(r) with reasonable quantitative accuracy and spatial resolution. (C) 2011 Optical Society of America

Developments in amplitude-comparator techniques for distance relays

The paper reports the development of new amplitude-comparator techniques which allow the instantaneous comparison of the amplitude of the signals derived from primary line quantities. These techniques are used to derive a variety of impedance characteristics. The merits of the new relaying system are: the simple mode of the relay circuitry, the derivation of closed polar characteristics (i.e. quadrilateral) by a single measuring gate and sharp discontinuities in the polar characteristics. Design principles and circuit models in their schematic form are described and, in addition, a comprehensive theoretical basis for comparison is also presented. Dynamic test results are presented for a quadrilateral characteristic of potentially general application.

New possibilities in amplitude- and phase-comparison techniques for distance relays

The paper reports further work on the amplitude-comparison technique described by the same authors in a previous paper. This technique is extended to develop improved polar characteristics. Discontinuous polar characteristics, like directional parallelograms, are obtained by a single measuring gate with a simple mode of relay circuitry, whereas two measuring gates are required to provide a directional-quadrilateral characteristic of potentially general application. The paper also describes some new possibilities in phase-comparison methods for distance-protection schemes. Comparator models which effect the amplitude and phase comparison of the relaying signals are described in their schematic form. A comprehensive theoretical basis for comparison is also presented.

Dynamic shear modulus as affected by displacement amplitude

The realistic estimation of the dynamic characteristics for a known set of loading conditions continues to be difficult despite many contributions in the past. The design of a machine foundation is generally made on the basis of limiting amplitude or resonant frequency. These parameters are in turn dependent on the dynamic characteristics of soil viz., the shear modulus/stiffness and damping. The work reported herein is an attempt to relate statistically the shear modulus of a soil to its resonant amplitude under a known set of static and dynamic loading conditions as well as wide ranging soil conditions. The two parameters have been statistically related with a good correlation coefficient and low standard error of estimate.

Amplitude death in complex networks induced by environment

We present a mechanism for amplitude death in coupled nonlinear dynamical systems on a complex network having interactions with a common environment like external system. We develop a general stability analysis that is valid for any network topology and obtain the threshold values of coupling constants for the onset of amplitude death. An important outcome of our study is a universal relation between the critical coupling strength and the largest nonzero eigenvalue of the coupling matrix. Our results are fully supported by the detailed numerical analysis for different network topologies.

A Technique to Compute Smooth Amplitude, Phase, and Frequency Modulations From the Analytic Signal

Gabor's analytic signal (AS) is a unique complex signal corresponding to a real signal, but in general, it admits infinitely-many combinations of amplitude and frequency modulations (AM and FM, respectively). The standard approach is to enforce a non-negativity constraint on the AM, but this results in discontinuities in the corresponding phase modulation (PM), and hence, an FM with discontinuities particularly when the underlying AM-FM signal is over-modulated. In this letter, we analyze the phase discontinuities and propose a technique to compute smooth AM and FM from the AS, by relaxing the non-negativity constraint on the AM. The proposed technique is effective at handling over-modulated signals. We present simulation results to support the theoretical calculations.

Analysis of large-amplitude stratospheric mountain wave event observed from the AIRS and MLS sounders over the western Himalayan region

Mountain waves in the stratosphere have been observed over elevated topographies using both nadir-looking and limb-viewing satellites. However, the characteristics of mountain waves generated over the Himalayan Mountain range and the adjacent Tibetan Plateau are relatively less explored. The present study reports on three-dimensional (3-D) properties of a mountain wave event that occurred over the western Himalayan region on 9 December 2008. Observations made by the Atmospheric Infrared Sounder on board the Aqua and Microwave Limb Sounder on board the Aura satellites are used to delineate the wave properties. The observed wave properties such as horizontal (lambda(x), lambda(y)) and vertical (lambda(z)) wavelengths are 276 km (zonal), 289 km (meridional), and 25 km, respectively. A good agreement is found between the observed and modeled/analyzed vertical wavelength for a stationary gravity wave determined using the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis winds. The analysis of both the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis and MERRA winds shows that the waves are primarily forced by strong flow across the topography. Using the 3-D properties of waves and the corrected temperature amplitudes, we estimated wave momentum fluxes of the order of similar to 0.05 Pa, which is in agreement with large-amplitude mountain wave events reported elsewhere. In this regard, the present study is considered to be very much informative to the gravity wave drag schemes employed in current general circulation models for this region.

Analysis of large-amplitude stratospheric mountain wave event observed from the AIRS and MLS sounders over the western Himalayan region

Mountain waves in the stratosphere have been observed over elevated topographies using both nadir-looking and limb-viewing satellites. However, the characteristics of mountain waves generated over the Himalayan Mountain range and the adjacent Tibetan Plateau are relatively less explored. The present study reports on three-dimensional (3-D) properties of a mountain wave event that occurred over the western Himalayan region on 9 December 2008. Observations made by the Atmospheric Infrared Sounder on board the Aqua and Microwave Limb Sounder on board the Aura satellites are used to delineate the wave properties. The observed wave properties such as horizontal (lambda(x), lambda(y)) and vertical (lambda(z)) wavelengths are 276 km (zonal), 289 km (meridional), and 25 km, respectively. A good agreement is found between the observed and modeled/analyzed vertical wavelength for a stationary gravity wave determined using the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis winds. The analysis of both the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis and MERRA winds shows that the waves are primarily forced by strong flow across the topography. Using the 3-D properties of waves and the corrected temperature amplitudes, we estimated wave momentum fluxes of the order of similar to 0.05 Pa, which is in agreement with large-amplitude mountain wave events reported elsewhere. In this regard, the present study is considered to be very much informative to the gravity wave drag schemes employed in current general circulation models for this region.

On Computing Amplitude, Phase, and Frequency Modulations Using a Vector Interpretation of the Analytic Signal

The amplitude-modulation (AM) and phase-modulation (PM) of an amplitude-modulated frequency-modulated (AM-FM) signal are defined as the modulus and phase angle, respectively, of the analytic signal (AS). The FM is defined as the derivative of the PM. However, this standard definition results in a PM with jump discontinuities in cases when the AM index exceeds unity, resulting in an FM that contains impulses. We propose a new approach to define smooth AM, PM, and FM for the AS, where the PM is computed as the solution to an optimization problem based on a vector interpretation of the AS. Our approach is directly linked to the fractional Hilbert transform (FrHT) and leads to an eigenvalue problem. The resulting PM and AM are shown to be smooth, and in particular, the AM turns out to be bipolar. We show an equivalence of the eigenvalue formulation to the square of the AS, and arrive at a simple method to compute the smooth PM. Some examples on synthesized and real signals are provided to validate the theoretical calculations.

Nonlinear viscoelasticity of entangled wormlike micellar fluid under large-amplitude oscillatory shear: Role of elastic Taylor-Couette instability

The role of elastic Taylor-Couette flow instabilities in the dynamic nonlinear viscoelastic response of an entangled wormlike micellar fluid is studied by large-amplitude oscillatory shear (LAOS) rheology and in situ polarized light scattering over a wide range of strain and angular frequency values, both above and below the linear crossover point. Well inside the nonlinear regime, higher harmonic decomposition of the resulting stress signal reveals that the normalized third harmonic I-3/I-1 shows a power-law behavior with strain amplitude. In addition, I-3/I-1 and the elastic component of stress amplitude sigma(E)(0) show a very prominent maximum at the strain value where the number density (n(v)) of the Taylor vortices is maximum. A subsequent increase in applied strain (gamma) results in the distortions of the vortices and a concomitant decrease in n(v), accompanied by a sharp drop in I-3 and sigma(E)(0). The peak position of the spatial correlation function of the scattered intensity along the vorticity direction also captures the crossover. Lissajous plots indicate an intracycle strain hardening for the values of gamma corresponding to the peak of I-3, similar to that observed for hard-sphere glasses.

Effect of amplitude correlations on coherence in the local field potential

Neural activity across the brain shows both spatial and temporal correlations at multiple scales, and understanding these correlations is a key step toward understanding cortical processing. Correlation in the local field potential (LFP) recorded from two brain areas is often characterized by computing the coherence, which is generally taken to reflect the degree of phase consistency across trials between two sites. Coherence, however, depends on two factors-phase consistency as well as amplitude covariation across trials-but the spatial structure of amplitude correlations across sites and its contribution to coherence are not well characterized. We recorded LFP from an array of microelectrodes chronically implanted in the primary visual cortex of monkeys and studied correlations in amplitude across electrodes as a function of interelectrode distance. We found that amplitude correlations showed a similar trend as coherence as a function of frequency and interelectrode distance. Importantly, even when phases were completely randomized between two electrodes, amplitude correlations introduced significant coherence. To quantify the contributions of phase consistency and amplitude correlations to coherence, we simulated pairs of sinusoids with varying phase consistency and amplitude correlations. These simulations confirmed that amplitude correlations can significantly bias coherence measurements, resulting in either over-or underestimation of true phase coherence. Our results highlight the importance of accounting for the correlations in amplitude while using coherence to study phase relationships across sites and frequencies.

Event-triggered sampling using signal extrema for instantaneous amplitude and instantaneous frequency estimation

Event-triggered sampling (ETS) is a new approach towards efficient signal analysis. The goal of ETS need not be only signal reconstruction, but also direct estimation of desired information in the signal by skillful design of event. We show a promise of ETS approach towards better analysis of oscillatory non-stationary signals modeled by a time-varying sinusoid, when compared to existing uniform Nyquist-rate sampling based signal processing. We examine samples drawn using ETS, with events as zero-crossing (ZC), level-crossing (LC), and extrema, for additive in-band noise and jitter in detection instant. We find that extrema samples are robust, and also facilitate instantaneous amplitude (IA), and instantaneous frequency (IF) estimation in a time-varying sinusoid. The estimation is proposed solely using extrema samples, and a local polynomial regression based least-squares fitting approach. The proposed approach shows improvement, for noisy signals, over widely used analytic signal, energy separation, and ZC based approaches (which are based on uniform Nyquist-rate sampling based data-acquisition and processing). Further, extrema based ETS in general gives a sub-sampled representation (relative to Nyquistrate) of a time-varying sinusoid. For the same data-set size captured with extrema based ETS, and uniform sampling, the former gives much better IA and IF estimation. (C) 2015 Elsevier B.V. All rights reserved.

Correlation Between Decay Rate and Amplitude of Solar Cycles as Revealed from Observations and Dynamo Theory

Using different proxies of solar activity, we have studied the following features of the solar cycle: i) The linear correlation between the amplitude of cycle and its decay rate, ii) the linear correlation between the amplitude of cycle and the decay rate of cycle , and iii) the anti-correlation between the amplitude of cycle and the period of cycle . Features ii) and iii) are very useful because they provide precursors for future cycles. We have reproduced these features using a flux-transport dynamo model with stochastic fluctuations in the Babcock-Leighton effect and in the meridional circulation. Only when we introduce fluctuations in meridional circulation, are we able to reproduce different observed features of the solar cycle. We discuss the possible reasons for these correlations.