Bayesian estimation of simultaneous musical notes based on frequency domain modelling

This paper proposes a Bayesian method for polyphonic music description. The method first divides an input audio signal into a series of sections called snapshots, and then estimates parameters such as fundamental frequencies and amplitudes of the notes contained in each snapshot. The parameter estimation process is based on a frequency domain modelling and Gibbs sampling. Experimental results obtained from audio signals of test note patterns are encouraging; the accuracy is better than 80% for the estimation of fundamental frequencies in terms of semitones and instrument names when the number of simultaneous notes is two.

A comparison of methods for the coupled analysis of floating structures

The dynamic analysis of a deepwater floating platform and the associated mooring/riser system should ideally be fully coupled to ensure a reliable response prediction. It is generally held that a time domain analysis is the only means of capturing the various coupling and nonlinear effects accurately. However, in recent work it has been found that for an ultra-deepwater floating system (2000m water depth), the highly efficient frequency domain approach can provide highly accurate response predictions. One reason for this is the accuracy of the drag linearization procedure over both first and second order motions, another reason is the minimal geometric nonlinearity displayed by the mooring lines in deepwater. In this paper, the aim is to develop an efficient analysis method for intermediate water depths, where both mooring/vessel coupling and geometric nonlinearity are of importance. It is found that the standard frequency domain approach is not so accurate for this case and two alternative methods are investigated. In the first, an enhanced frequency domain approach is adopted, in which line nonlinearities are linearized in a systematic way. In the second, a hybrid approach is adopted in which the low frequency motion is solved in the time domain while the high frequency motion is solved in the frequency domain; the two analyses are coupled by the fact that (i) the low frequency motion affects the mooring line geometry for the high frequency motion, and (ii) the high frequency motion affects the drag forces which damp the low frequency motion. The accuracy and efficiency of each of the methods are systematically compared. Copyright © 2007 by ASME.

Nonlinear phenomena in thermoacoustics: A comparison between single-mode and multi-mode methods

Nonlinear analysis of thermoacoustic instability is essential for prediction of frequencies and amplitudes of limit cycles. In frequency domain analyses, a quasi-linear transfer function between acoustic velocity and heat release rate perturbations, called the flame describing function (FDF), is obtained from a flame model or experiments. The FDF is a function of the frequency and amplitude of velocity perturbations but only contains the heat release response at the forcing frequency. While the gain and phase of the FDF provide insight into the nonlinear dynamics of the system, the accuracy of its predictions remains to be verified for different types of nonlinearity. In time domain analyses, the governing equations of the fully coupled problem are solved to find the time evolution of the system. One method is to discretize the governing equations using a suitable basis, such as the natural acoustic modes of the system. The number of modes used in the discretization alters the accuracy of the solution. In our previous work we have shown that predictions using the FDF are almost exactly the same as those obtained from the time-domain using only one mode for the discretization. We call this the single-mode method. In this paper we compare results from the single-mode and multi-mode methods, applied to a thermoacoustic system of a premixed flame in a tube. For some cases, the results differ greatly in both amplitude as well as frequency content. This study shows that the contribution from higher and subharmonics to the nonlinear dynamics can be significant and must be considered for an accurate and comprehensive analysis of thermoacoustic systems. Hence multi-mode simulations are necessary, and the single-mode method or the FDF may be insufficient to capture some of the complex nonlinear behaviour in fhermoacoustics.

On applications of high-frequency asymptotics in aeroacoustics.

The aim of this paper is to survey a range of applications of high-frequency asymptotic methods in aeroacoustics. Specifically, we are concerned with problems associated with noise generation, propagation and scattering as found in large modern aeroengines. With regard to noise generation, we consider the interaction between high-frequency vortical waves and thin aerofoils, with particular emphasis being placed on the way in which the vortical waves act on the non-uniform mean flow around the aerofoil. A ray-theoretic description of the resulting sound as it propagates along the engine intake is then presented, followed by consideration of the diffraction of these rays by the (possibly asymmetric) intake lip to produce sound in the far field. A range of more detailed possible extensions is also presented.

TWO TUTORIAL EXAMPLES OF MULTIVARIABLE CONTROL SYSTEM DESIGN.

Two tutorial examples are presented which illustrate different methods of designing practical multivariable control systems using frequency-domain techniques. In the first case eigenvector alignment techniques are used to manipulate and shape the generalized Nyquist diagrams, while in the second case LQG theory in conjunction with singular value plots is employed. In both cases the designs are carried out on a modern computer-aided control-system design package.

Rhythm generation in monkey motor cortex explored using pyramidal tract stimulation.

We investigated whether stimulation of the pyramidal tract (PT) could reset the phase of 15-30 Hz beta oscillations observed in the macaque motor cortex. We recorded local field potentials (LFPs) and multiple single-unit activity from two conscious macaque monkeys performing a precision grip task. EMG activity was also recorded from the second animal. Single PT stimuli were delivered during the hold period of the task, when oscillations in the LFP were most prominent. Stimulus-triggered averaging of the LFP showed a phase-locked oscillatory response to PT stimulation. Frequency domain analysis revealed two components within the response: a 15-30 Hz component, which represented resetting of on-going beta rhythms, and a lower frequency 10 Hz response. Only the higher frequency could be observed in the EMG activity, at stronger stimulus intensities than were required for resetting the cortical rhythm. Stimulation of the PT during movement elicited a greatly reduced oscillatory response. Analysis of single-unit discharge confirmed that PT stimulation was capable of resetting periodic activity in motor cortex. The firing patterns of pyramidal tract neurones (PTNs) and unidentified neurones exhibited successive cycles of suppression and facilitation, time locked to the stimulus. We conclude that PTN activity directly influences the generation of the 15-30 Hz rhythm. These PTNs facilitate EMG activity in upper limb muscles, contributing to corticomuscular coherence at this same frequency. Since the earliest oscillatory effect observed following stimulation was a suppression of firing, we speculate that inhibitory feedback may be the key mechanism generating such oscillations in the motor cortex.

Dynamical behavior of damped driven coupled single electron simple harmonic oscillators

Coherent coupling between a large number of qubits is the goal for scalable approaches to solid state quantum information processing. Prototype systems can be characterized by spectroscopic techniques. Here, we use pulsed-continuous wave microwave spectroscopy to study the behavior of electrons trapped at defects within the gate dielectric of a sol-gel-based high-k silicon MOSFET. Disorder leads to a wide distribution in trap properties, allowing more than 1000 traps to be individually addressed in a single transistor within the accessible frequency domain. Their dynamical behavior is explored by pulsing the microwave excitation over a range of times comparable to the phase coherence time and the lifetime of the electron in the trap. Trap occupancy is limited to a single electron, which can be manipulated by resonant microwave excitation and the resulting change in trap occupancy is detected by the change in the channel current of the transistor. The trap behavior is described by a classical damped driven simple harmonic oscillator model, with the phase coherence, lifetime and coupling strength parameters derived from a continuous wave (CW) measurement only. For pulse times shorter than the phase coherence time, the energy exchange between traps, due to the coupling, strongly modulates the observed drain current change. This effect could be exploited for 2-qubit gate operation. The very large number of resonances observed in this system would allow a complex multi-qubit quantum mechanical circuit to be realized by this mechanism using only a single transistor.

CLADP - THE CAMBRIDGE LINEAR ANALYSIS AND DESIGN PROGRAMS USER REFERENCE MANUAL (4TH ISSUE: APRIL 1983).

CLADP is an engineering software program developed at Cambridge University for the interactive computer aided design of feedback control systems. CLADP contains a wide range of tools for the analysis of complex systems, and the assessment of their performance when feedback control is applied, thus enabling control systems to be designed to meet difficult performance objectives. The range of tools within CLADP include the latest techniques in the field whose central theme is the extension of classical frequency domain concepts (well known and well proven for single loop systems) to multivariable or multiloop systems, and by making extensive use of graphical presentation information is provided in a readily understood form.

HEAVY VEHICLE VIBRATION - A CASE STUDY.

A method is presented for the digital simulation of multiple degrees-of-freedom lumped parameter vibrating systems with arbitrary constitutive elements in an inertial frame of reference. The geometry of the system is treated independently of the constitutive elements and as a result nonlinear (time domain) or linearised (frequency domain) calculations may be performed using a single input description. The method is used to simulate a 3-axle rigid heavy commercial vehicle for harsh vibrating conditions. Some of the assumptions to which the calculations are sensitive are examined. Agreement between the response of a 3-dimensional whole vehicle model and measurements on the test vehicle is satisfactory.

Multivariable toolbox for use with MATLAB.

The authors describe a toolbox for the frequency-domain analysis and design of multivariable feedback systems, to be used with PC-Matlab, or Pro-Matlab. The principal model representations used by the toolbox are described. Its capabilities are illustrated by a worked design example, which shows the use of a Nyquist array method. Other design techniques supported by the toolbox are briefly reviewed.

A three-dimensional tunnel model for calculation of train-induced ground vibration

The frequency range of interest for ground vibration from underground urban railways is approximately 20 to 100 Hz. For typical soils, the wavelengths of ground vibration in this frequency range are of the order of the spacing of train axles, the tunnel diameter and the distance from the tunnel to nearby building foundations. For accurate modelling, the interactions between these entities therefore have to be taken into account. This paper describes an analytical three-dimensional model for the dynamics of a deep underground railway tunnel of circular cross-section. The tunnel is conceptualised as an infinitely long, thin cylindrical shell surrounded by soil of infinite radial extent. The soil is modelled by means of the wave equations for an elastic continuum. The coupled problem is solved in the frequency domain by Fourier decomposition into ring modes circumferentially and a Fourier transform into the wavenumber domain longitudinally. Numerical results for the tunnel and soil responses due to a normal point load applied to the tunnel invert are presented. The tunnel model is suitable for use in combination with track models to calculate the ground vibration due to excitation by running trains and to evaluate different track configurations. © 2006 Elsevier Ltd. All rights reserved.

Natural versus artificial scene classification by ordering discrete fourier power spectra

Holistic representations of natural scenes is an effective and powerful source of information for semantic classification and analysis of arbitrary images. Recently, the frequency domain has been successfully exploited to holistically encode the content of natural scenes in order to obtain a robust representation for scene classification. In this paper, we present a new approach to naturalness classification of scenes using frequency domain. The proposed method is based on the ordering of the Discrete Fourier Power Spectra. Features extracted from this ordering are shown sufficient to build a robust holistic representation for Natural vs. Artificial scene classification. Experiments show that the proposed frequency domain method matches the accuracy of other state-of-the-art solutions. © 2008 Springer Berlin Heidelberg.

Decay of vibrations along deepwater mooring lines

Model tests for global design verification of deepwater floating structures cannot be made at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation techniques. In such a method the upper sections of each line are modelled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model, that aims to simulate the remainder of the line. The rationale for this is that in deep water the transverse elastic waves of a line are likely to decay before they are reflected at the seabed. The focus of this paper is the verification of this rationale and the ongoing work, which is considering ways to produce a truncation model. Transverse dynamics of a mooring line are modelled using the equations of motion of an inextensible taut string, submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. Nonlinear hydrodynamic damping is included; bending and VIV effects are neglected. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it is very useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. Initial efforts in developing a truncated model show that a linearized numerical solution in the frequency domain matches very closely the exact benchmark. Copyright © 2011 by ASME.

Parameters identification by a single point free response measurement

When a thin rectangular plate is restrained on the two long edges and free on the remaining edges, the equivalent stiffness of the restraining joints can be identified by the order of the natural frequencies obtained using the free response of the plate at a single location. This work presents a method to identify the equivalent stiffness of the restraining joints, being represented as simply supporting the plate but elastically restraining it in rotation. An integral transform is used to map the autospectrum of the free response from the frequency domain to the stiffness domain in order to identify the equivalent torsional stiffness of the restrained edges of the plate and also the order of natural frequencies. The kernel of the integral transform is built interpolating data from a finite element model of the plate. The method introduced in this paper can also be applied to plates or shells with different shapes and boundary conditions. © 2011 Elsevier Ltd. All rights reserved.