MSc Sound and Vibration Studies

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  • Objectives
    The programme aims to provide engineering, science or mathematics graduates from a diversity of backgrounds with an academically challenging exposure to modern developments in sound, vibration and signal processing. The range of subjects offered is linked to the internationally recognised research activities of staff and covers engineering acoustics, structural dynamics, applied digital signal processing, automotive NVH and human effects of sound and vibration.
  • Entry requirements
    Candidates should normally have a good bachelor's degree in engineering, mathematics or physics from an approved university. In exceptional circumstances students with other qualifications may be accepted.
  • Academic title
    MSc Sound and Vibration Studies
  • Course description
    The MSc courses in Sound and Vibration Studies, Engineering Acoustics, Structural Dynamics, Applied Digital Signal Processing and Automotive Noise and Vibration form a 12 month full-time programme. This is based on two semesters of lectures and practical instruction, followed by 4 months of full-time work on a research project leading to a dissertation.

    Semester 1

    Fundamentals of Acoustics

    Introduction to the propagation of acoustic disturbances

    Longitudinal wave motion, introduction to plane acoustic waves. Sound speed, frequency, wavelength, wavenumber, characteristic acoustic impedance. Thermodynamics of acoustic compressions; the isentropic assumption.
     One-dimensional acoustic wave motion

    Conservation equations in one dimension; linearisation of governing equations; derivation of one-dimensional wave equation. Solutions to the one-dimensional wave equation. Complex exponential representation of wave motion. Helmholtz Equation. Linearity and the Superposition principle. Specific acoustic impedance. Acoustic energy density and intensity. Standing waves.
     Waves in three-dimension

    Conservation equations in three dimensions; derivation of the three-dimensional wave equation. Solutions to the three dimensional wave equation. Spherical waves. Point sources of spherical radiation. Acoustic power output.
     Sound in enclosures

    Solution to the three-dimensional wave equation in a room with rigid walled boundaries; eigenfunctions and eigenvalues. Modal statistics; modal density, modal overlap and the Schroeder frequency. The concept of a diffuse field. Average absorption coefficient and the energy balance equation, reverberation time.
     Sound radiation

    Radiation from a plane vibrating piston. On axis radiation in near and far fields of a circular piston. Directivity and interference. Radiation impedance. Wave matching at a plane boundary. Radiation efficiency for infinite and finite vibration panels.
     Multipole sources

    The point monopole source. The point dipole source; vector dipole strength.
    Fundamentals of Vibration

    Semester 1


    -Vibration problems in engineering.
    -Basic principles.

    Single degree of freedom system

    -Free vibration of mass-spring system: natural frequency.
    -Free vibration with damping: damping factor.
    -Energy methods.
    -Time harmonic forced vibration: resonance.
    -Isolation, base excitation and other applications.
    -Structural damping.
    -Transient vibration: response to transient excitation: impulse response; shock spectra.

    Multiple degree of freedom systems

    -Free vibration of two degree of freedom systems: modes of vibration, natural frequencies and mode shapes.
    -Multiple degree of freedom systems: matrix methods.
    -Time harmonic forced vibration with damping: modal decomposition.
    -Introduction to vibration treatment; vibration absorbers.

    Continuous systems

    -Free vibrations of strings, bars and shafts: equation of motion, boundary conditions.
    -Modes of vibration: natural frequencies and mode shapes.
    -Bending vibration of beams.
    -Forced vibration of continuous systems: modes and resonance.
    -Introduction to structural wave motion in one dimension: propagation, reflection and transmission; coincidence.

    Modelling methods

    -Rayleigh’s method.
    -Lagrange’s equations for free undamped vibration.

    Vibration measurement and analysis

    -Vibration transducers and measurement.
    -Experimental modal analysis.

    Signal processing

    Semester 1

    Time histories and their classification

    Deterministic signals, periodic signals and Fourier series, almost periodic signals, transients and the Fourier integral. Amplitude, phase, energy and power spectra.
    Convolution and the effect of linear filters, time and frequency domain considerations, impulse response functions, transfer functions and frequency response functions, system identification. Data windowing and resolution.
    Uniform sampling of continuous time histories. Fourier transforms of sampled data, aliasing and anti-aliasing filters. The discrete Fourier transform and the fast Fourier transform algorithm.
    Random signals, the concepts of probability, expectation and moments. Stationary and nonstationary processes. Auto- and cross-correlation (covariance) functions: auto (power) and cross spectra. Linear system input-output relationships in the time and frequency domains.
    System identification using estimators H1, H2 and H3. The coherence function and its interpretation.
    Estimators for stochastic processes; bias and variability errors and confidence intervals. Spectral estimators, raw and smoothed spectra. Transfer function and coherence function estimators and their properties.

    Digital systems

    Semester 1

    Digital Systems

    -Auto-regressive (AR) modelling (through population models)
    -Moving average (MA) systems
    -ARMA processes
    The Z-Transform

    -Representing the z-plane
    -Poles and zeros
    -Regions of convergence
    -Inversion using, power series, partial fractions and contour integration
    FIR Filter Design

    -General filter design issues
    -The windowing design method
    -Frequency sampling
     IIR Filter Design

    -General comments on how to map analogue to digital systems
    -Analogue filter designs
    -Method of mapping differentials
    -Impulse variance
    -Bilinear transforms
    High Resolution Spectral Estimation

    -Time series models and the contrast between parametric and non-parametric estimation
    -Auto-regressive moving-average models and parameter estimation
    -Auto-regressive models and the Yule-Walker equations; maximum entropy methods; model order determination
    -Capon's method
    -Eigen-based methods; the MUSIC algorithm

    Noise Control

    Semester 1

    Noise control requirements

    -The need for noise control.
    -EC directives on machinery noise and outdoor equipment.
    -Specification of noise control targets.

     Units of noise measurement

    -Sound pressure, intensity and power levels, reference values.
    -Frequency analysis. dB(A) and other frequency weighted units.
    -Combining sound pressures (incoherent and coherent).

     Characterization of noise sources

    -Physical nature of noise sources, idealizations.
    -Mechano-acoustic efficiency.
    -Frequency spectrum.
    -Parametric dependencies including operational speed.

     Noise source quantification

    -Limitations of sound power as a source strength quantity. Effect of reflecting surfaces.
    -Free field (anechoic) test method.
    -Reverberant field method, including Sabine formula.
    -Sound intensity methods.
    -Substitution techniques.
    -Use of surface vibration.
    -Measurement standards ISO 3740 series, ISO 9614.

     Principles of passive noise and vibration control

    -Effect of multiple sources and multiple paths. Noise path models.
    -Control at source. Airborne transmission. Structure-borne transmission.

     Sound radiation from vibrating structures

    -Definition of radiation ratio.
    -Results for monopole and dipole sources.
    -Radiation from bending waves in plates.
    -Corner modes, edge modes, coincidence.
    -Means of reducing radiation ratio.

     Transmission of airborne sound through partitions

    -Transmission loss of a single partition, mathematical derivation for normal incidence.
    -Coincidence and the transmission loss for particular angles of incidence and for a diffuse field (qualitative).
    -Double partitions (qualitative).
    -Measurement methods for sound reduction index.
    -Machinery enclosures using Sabine formula.

     Sound absorbent materials and applications

    -Qualitative treatment of dissipation mechanisms.
    -Surface impedance and its relation to absorption coefficient.
    -Practical forms of sound absorbers including resonant systems to improve low frequency absorption.
    -Measurement techniques for absorption.
    -Use of absorption in rooms and enclosures.

     Vibration control strategies

    -Force and velocity excitation, blocked force and free velocity.
    -Vibration isolation - low and high frequency models.
    -Damping treatments. Effects of damping.

    Matlab computation

    Semester 1

    Introduction to Matlab in an interactive environment

    -Simple maths
    -The working environment
    -Saving and recovering data
    -Display precision
    -Mathematical functions
    -Complex numbers
    -The colon operator
    -Array operations

    Matrix operations

    -Input and screen output of matrices
    -Scalar-matrix operations
    -Transpose operator
    -Matrix-matrix operations
    -The colon operator to access array elements
    -Eigenvalues and eigenvectors in the solution of vibration problems

    Plotting and graphics

    -Simple plots
    -Annotation on plots
    -Linear and logarithmic axes
    -Polar plots
    -The special case of plots of complex quantities
    -Transfer functions of single degree of freedom systems
    -Acoustic radiation patterns in polar form


    -Script files
    -Function files
    -Combining dB values
    -Numerical differentiation

    Program control

    -If and if else
    -Conditional tests
    -Newton Raphson iterations


    -String functions
    -Strings with more than one row
    -Passing strings into and out of functions
    -The ASCII character set
    -The function eval

    Data input and output

    -Importing data into Matlab
    -Exporting data from Matlab
    -To introduce modern spreadsheet package
    -Example sheets and workbooks are provided to support the 'Excel' lectures
    -The students are expected to complete the assignments and will work at their own pace under the supervision of the lecturer
    -Interfacing with Microsoft Word

    Human response to sound and vibration

    Semester 1


    -The human auditory system

    Noise and health

    -Hearing damage risk
    -Non-auditory health risks, vegetative responses

    Disturbance of speech communication



    -At home
    -In other environments

    Sleep disturbance

    Planning and noise


    Effects of vibration on comfort, performance and health

    Underwater acoustics 1

    Semester 1

    History (1 Lecture)

    Sound Speed (4 Lectures)

    Plane wave equation (linear approximation); Sound speed dependencies; Oceanic sound speed profiles.

    Oceanic Ray Bending (5 Lectures)

    Huygen's principle; Reflection of a pressure wave at normal incidence; Oceanic ray bending; Transmission loss; Bottom reflections.

    Oceanic Ambient Noise (4 Lectures)

    Classical ideas (Shallow and water; Knudsen spectra); Rain; Breaking waves; Bubbles.

    Non-linear Acoustics (4 Lectures)

    The propagation of finite amplitude waveforms; Acoustics streaming; Self-interaction, parametric and stimulated scattering effects in liquids.

    Biomedical Ultrasound (4 Lectures)

    Measurement; Clinical ultrasound (diagnosis and therapy); Mechanisms of biohazard (Hyperthermia, Cavitation).

    Vibration standards

    Musical instrument acoustics

    Semester 1

    -Introduction to musical instrument acoustics.
    -The perception of musical sounds.
    -Struck and plucked strings.
    -Bowed string instruments.
    -Introduction to fluid dynamics for wind instruments.
    -Brass instruments.
    -Woodwind instruments.
    -The voice.

    Audio systems

    Semester 1

    -Channel quality: audio specifications: subjective vs objective assessment.
    -Auditory capabilities: masking: just noticeable differences.
    -Stereophony: 2-channel theory: recording techniques: limitations: multi-channel.
    -Sound fields: room acoustics: rooms and the loudspeaker.
    -Audio public address: intelligibility: cluster systems: distributed systems: feedback.
    -Signal conditioning: equalisation: dynamic control.
    -Analogue vs digital systems: sampling: resolution: data density: recording.

    Advanced measurement techniques (single unit)

    Semester 2

    The student will do three of the following six topics.

     Dual channel frequency analysis

    -Impulse response and frequency response functions
    -Correlation and spectra
    -Segment averaging
    -Effects of noise on the computation of the FRF
    -Influence of FFT size on spectral estimates
    -Influence of number of averages on spectral estimates

     Absorption coefficient measurements

    -Absorption coefficient
    -Use of reverberation chamber
    -Use of standing wave tube
    -Diffuse field energy balance
    -One-dimensional standing wave fields
    -Schroeder (backwards) integration

     Active control of sound in a duct

    -Review of active control of sound design procedures
    -Feed-forward active control of tonal disturbances
    -Control algorithms
    -Loudspeaker actuators
    -Microphone sensors
    -Control devices (actuator and sensor amplifiers)
    -Structure- and air-borne flanking paths

     Modal analysis

    -Natural frequencies, modal damping and mode shapes
    -FRFS and modal summation
    -Nyquist plots
    -Circle fitting
    -Stepped sine vibration testing

     The SVD and coherence measurements for acoustic source identification

    -The SVD technique for source identification
    -Coherence as a tool for source identification
    -The Rayleigh criterion as a resolution limit for source identification
    -Near field and far fields
    -The reverberation radius

     Structural vibration at higher frequencies

    -Modes of vibration
    -Frequency average vibration behaviour
    -Point and transfer mobility
    -Modal density
    -Input power, energy and power balance
    -Damping loss factor

    Advanced measurement techniques (double unit)

    Semester 2

    Dual channel frequency analysis

    -Impulse response and frequency response functions
    -Correlation and spectra
    -Segment averaging
    -Effects of noise on the computation of the FRF
    -Influence of FFT size on spectral estimates
    -Influence of number of averages on spectral estimates

     Absorption coefficient measurements

    -Absorption coefficient
    -Use of reverberation chamber
    -Use of standing wave tube
    -Diffuse field energy balance
    -One-dimensional standing wave fields
    -Schroeder (backwards) integration

     Active control of sound in a duct

    -Review of active control of sound design procedures
    -Feed-forward active control of tonal disturbances
    -Control algorithms
    -Loudspeaker actuators
    -Microphone sensors
    -Control devices (actuator and sensor amplifiers)
    -Structure- and air-borne flanking paths

     Modal analysis

    -Natural frequencies, modal damping and mode shapes
    -FRFS and modal summation
    -Nyquist plots
    -Circle fitting
    -Stepped sine vibration testing

     The SVD and coherence measurements for acoustic source identification

    -The SVD technique for source identification
    -Coherence as a tool for source identification
    -The Rayleigh criterion as a resolution limit for source identification
    -Near field and far fields
    -The reverberation radius

     Structural vibration at higher frequencies

    -Modes of vibration
    -Frequency average vibration behaviour
    -Point and transfer mobility
    -Modal density
    -Input power, energy and power balance
    -Damping loss factor

    Analytical & numerical acoustics

    Semester 2

    Multipole Sources

    -The point monopole source
    -The point dipole source; vector dipole strength
    -Longitudinal and lateral quadrupole sources
    -Series expansion techniques

    The Inhomogeneous Wave Equation and its Solution

    -Conservation equations with distributions of volume and force input
    -The Green function. Principle of reciprocity
    -Solution of the inhomogeneous Helmholtz equation
    -The Kirchoff-Helmholtz integral equation
    -Implications for the active control of sound and radiation from arbitrary vibrating bodies

    Introduction to Aeroacoustics

    -Inhomogeneous wave equation with quadrupole source term; Lighthill's acoustic analogy
    -Scaling laws for jet noise and flow/surface interaction noise

    Enclosed Sound Fields

    -The Green function for a rigid walled enclosure
    -Eigenfunctions and eigenvalues
    -Solution to the inhomogeneous Helmholtz equation; Light damping assumption

    -Sound in Ducts

    -Duct modes
    -Cut off frequency, phase speed
    -Green function for an infinite hard walled duct

    Introduction to Acoustic Finite Element Analysis

    -Variational formulation for the wave equation
    -Finite Element discretization and method of computing for 2-dimensional problems
    -Normal modes of irregular-shaped cavities with acoustically hard walls
    -Cavities with one pair of parallel walls, axisymmetric cavities, cavities of general shape
    -Application to practical cavities
    -Use of commercial software

    Analysis of Irregular-Shaped Cavities with Non-Rigid Walls

    -Effect of vibrating surfaces and absorbing materials
    -Practical applications, including duct acoustics, acoustic radiation
    -Use of commercial software

    Introduction to Boundary Element Methods

    -Boundary Integral form of the reduced wave equation
    -Direct collocation method
    -Application to cavity acoustics
    -Application to acoustic radiation; Non-uniqueness problems
    -Use of commercial software

    Indirect Boundary Element Method

    -Formulation in terms of single and double layer potential distributions
    -Non-uniqueness problems

    Human responses to vibration

    Semester 2

    -Principles of the measurement and analysis of human vibration exposure
    -Standards, limits and criteria for whole-body vibration
    -Whole-body vibration, occurrence of hazards
    -Effects of whole-body vibration on activities
    -Discomfort produced by whole-body vibration
    -Vehicle ride
    -Vibration thresholds
    -Building vibration
    -Human response to mechanical shock
    -Hand-transmitted vibration, occurrence of hazards
    -Epidemiology of vibration-induced white finger and other injuries
    -Standards, limits and criteria for hand-arm vibration
    -Hand-tool vibration measurement
    -Motion sickness
    -Ship motion evaluation
    -Preventative measures for whole-body and hand-arm vibration

    Environmental and transportation noise

    Semester 2

    Political and scientific background, key players (UK DEFRA and DfT, EC, WHO, ISO, etc).

    Monetary valuation of noise

    Environmental noise and sustainable development

    Environmental Impact Assessment – the role of public inquiries in the UK

    Human effects – WHO guidelines for community noise

    -speech masking
    -activity interference
    -noise and sleep
    -noise and non-auditory health
    -noise annoyance
    -Noise mapping - demonstration and comparison against physical propagation models

    Current standards and regulations

    -ISO 9613
    -UK Calculation of Road Traffic Noise
    -UK Calculation of Railway Noise
    -Aircaft noise prediction
    -Current legal framework - relevant Acts of Parliament
    -PPG24 - Planning and Noise
    -MPG11 - Minerals sites
    -PPG22 - renewable energy
    -Highways assessment - operation and construction
    -BS 4142
    -BS 5228
    -BS 7445
    -EU noise policy – Environmental Noise Directive

    Noise management in practice – generic procedures

    Additional written notes are provided (but not taught) on relevant acoustical theories and explanations (noise level indicators, measurement procedures, auditory capabilities, etc).

    Structural vibration

    Semester 2


    -Difficulties of applying conventional numerical methods at high frequency.
    -Alternatives available for high frequencies.

    Elastic wave motion in rods and beams

    -Longitudinal, torsional, flexural wave equations.
    -Wave solution, dispersion diagrams.
    -Energy flow in propagating waves, group velocity, damping.

    Forcing, reflection and transmission in beams

    -Receptance of infinite or semi-infinite beam excited by force or moment, input power.
    -Reflection of wave at different types of boundary.
    -Interaction of wave in beam with a discontinuity.

    Prediction of natural frequencies by wave approach

    -Use of phase closure principle for modes in a finite beam.
    -Comparison with exact analysis.
    -Mode count and modal density of 1D systems.

    Waves in plates

    -Bending and in-plane waves.
    -Boundary conditions.
    -Reflection at an edge, phase closure, modal density.
    -Transmission at simple support.

    Modal analysis of continuous structures/I>

    -Free vibration and modes of vibration.
    -Forced vibration, modal decomposition.
    -Experimental modal analysis.

    Modal analysis at high frequencies

    -Difficulties at high frequencies, high frequency approximations.
    -Mean square response, kinetic energy.
    -Frequency average input power and mobility of infinite system.

    Statistical energy analysis

    -Introduction: power and energy, power balance, coupling power proportionality.
    -SEA equations, weak and strong coupling.
    -Energy equations of a simple oscillator, coupled oscillators and multi-modal systems.
    -Wave transmission and coupling loss factors, structural-acoustic coupling.
    -SEA modelling.
    -Problems and pitfalls with SEA.
    -Experimental SEA.

    Finite element vibration analysis

    Semester 2

    Vibration of beams: analytical method

    -Derivation of Euler-Bernoulli wave equation for bending vibration of slender beams.
    -Derivation of Timoshenko wave equation for bending vibration of deep beams.
    -Analytical derivation of natural frequencies and natural modes for bending vibration of slender and deep beams.

    Vibration of beams: Rayleigh-Ritz approximate method

    -The general principle.
    -Spatial given functions and convergence criteria.
    -Matrix formulation and eigenvalue-eigenvector analysis for the calculus of natural frequencies and natural modes.
    -Example: bending vibration of a clamped–simply supported beam.

    Vibration of beams: Finite Element Method (FEM)

    -The methodology.
    -Spatial given functions and convergence criteria.
    -Matrix formulation and eigenvalue-eigenvector analysis for the calculus of natural frequencies and natural modes.
    -Examples: axial and bending vibration of a clamped–simply supported beam.

    FEM for in-plane and out-of-plane vibrations of plates

    -The linear rectangular element.
    -The linear quadrilateral element.
    -Eight nodes elements.
    -Eight nodes elements with curved sides.

    Free vibration

    -Eigenvalue–eigenvector analysis for the calculus of natural frequencies and natural modes.
    -Eigenvalue–eigenvector properties and normalisations.
    -Methods to solve large eigenvalue–eigenvector problems.
    -Reduction of degrees of freedom base on geometrical considerations.
    -Guyan reduction of degrees of freedom approach.

    Forced vibration

    -Modal formulation, modal coordinates.
    -Structural and viscous damping.
    -Steady state response to harmonic excitation.
    -Steady state response to periodic excitation.
    -Response to transient excitation.

    FEM computer packages

    -Commercial computer packages structure.
    -DYNAS survey (DYNamic Analysis of Strucures).
    -FEM–experimental analysis of DYNAS tapered beam.

    Active control of sound & vibration

    Semester 2

    Physics of Active Sound and Vibration Control

    -Use of optimisation techniques in frequency and time domains.
    -Controlled interference of wave fields (one-dimensional examples; sound propagation in a waveguide, flexural wave propagation in beams).
    -Energy interchanges and power flows.
    -Three-dimensional examples in free field sound propagation and two-dimensional flexural wave propagation.
    -Treatment of enclosed sound fields at low and high modal densities.
    Feedforward Control

    -Reference signal techniques for "preview control" (e.g. sound propagation in 1-D waveguide).
    -Digital realisation of transfer functions.
    -Adaptive approaches and multichannel systems.
    -Transfer function approaches and influence of feedback.


    Semester 2

    General Theory (6 lectures)

    Description of electrical, mechanical and electroacoustic systems as two-port networks, coupling, analogies, acoustic networks.

    Loudspeakers (9 lectures)

    Equivalent models for moving coil loudspeakers, and relationship to practical loudspeakers. Loudspeaker performance in terms of frequency response, directivity, and distortion, and their measurement. The influence of an infinite baffle, closed box and tuned cabinets. The horn equation, simple solutions and application.

    Microphones (9 lectures)

    Pressure and pressure gradient principles, diffraction. Diaphragm dynamics and transduction mechanisms, hence complete frequency responses for various microphone types. Methods of calibration. Directivity of first order microphones, diffuse field response.

    Underwater acoustics 2

    Semester 2

    The Sonar Equations

    -Classes of sonar systems: Active/Passive, Monostatic/Bistatic.
    -Definitions of the basic terms within the sonar equations.
    -Signal detection criteria.
    -Derivation of the passive sonar equation
    -Derivation of the active (noise-limited) sonar equations.

    Noise Level Calculations

    -Noise spectral level.
    -The effects of Doppler shifts.

    Transmission Loss

    -Simple models for geometric losses.
    -Transmission loss due to absorption.

    Target Strength Calculations

    -Geometric scattering from a sphere.
    -Rayleigh scattering from a sphere.

    Volume Reverberation

    -The reverberation limit.
    -Calculation of volume reverberation level.
    -The transition between reverberation and noise limited operations.

    Directivity Index Calculation

    -Directivity of a uniform line array at the design frequency.
    -Approximation for the directivity of a uniform line array at frequencies away from the design frequency.

    Classes of Acoustic Propagation Models

    -Range dependent vs range independent.
    -2-D and 3-D models.

    Ray Tracing

    -The eikonal and transport equations.
    -Snell’s law as obtained through the eikonal equation.
    -Travel times and distances travelled along rays.
    -Transmission loss along a ray.
    -Focusing factors, shadow zones and caustics.
    -Practical implementation of ray tracing models.

    Method of Images

    -General expression for shallow water, isospeed propagation.
    -Specific solutions for various bottom conditions.

    Method of Normal Modes

    -Model solution of the wave equation, in a sound channel.
    -Truncation of the modal series.
    -Phase and group velocities of modes.
    -Comparison with method of images solution.

    Array Processing

    -Advantages of using an array.
    -General expression for the array gain of a uniform line array.
    -Electronic steering.
    -Array shading.

    Audio Signal Processing

    Semester 2

    -Sound quality and perception
    -Sound recording
    -Analogue and digital processing
    -Single channel effects processing
    -Room, loudspeaker and system identification and equalization
    -Hearing aids
    -Audio compression, synthesis and restoration
    -Speech recognition
    -Multichannel audio processing
    -Virtual sound imaging
    Fundamentals of Aeroacoustics

    Semester 2

    What is aeroacoustics?

    -Review of unsteady fluid flow.
    -Derivation of the acoustic wave equation and its solutions (Green’s functions).
    -The effect of flow on sound sources.
    -Lighthill’s Acoustic Analogy.
    -Application of Lighthill’s Acoustic Analogy to turbulent flows; scaling laws.
    -The effect of boundaries.
    Vibration control

    Semester 2 (one-week module)

    Sources of vibration

    -Types of source mechanisms; rotation, impact, flow, self-excited.
    -Description of vibration generated by these mechanisms; deterministic, random, transient.

    Source identification and transfer path analysis

    -Development of matrix techniques for transfer path analysis in multi-input-multi-output systems.
    -Identification and ranking of independent source contributions using singular value decomposition.
    -Principle component analysis and virtual coherence techniques.
    -Case study: Analysis of vehicle vibration due to multiple sources.

    Mechanical impedance and mobility techniques

    -Impedance and mobility concepts; impedance and mobility of simple elements (mass stiffness and damping, infinite beams and plates).
    -System modelling using impedance and mobility approach; characterisation of sources, transmission paths and receivers.
    -Computation using transfer matrices from impedance and mobility matrices .
    -Measurement of impedance and mobility.
    -Coupling of system components together to predict the overall response.

    Control by isolation

    -Limitations of the simple model.
    -Use of the impedance and mobility approach in the design of isolation systems; engine isolators, aircraft structures and piping systems.

    Control by the addition of vibration neutralisers and tuned mass dampers

    -Control of deterministic vibration using neutralisers.
    -Damping of structures subject to broadband excitation using tuned mass dampers.

    -Control by damping treatments

    -Review of damping mechanisms.
    -Characteristics of damping materials and use of constrained and unconstrained damping treatments.

    Model identification and structural modification

    -Fundamentals of modal analysis.
    -Structural design for reduced vibration including structural modification.

    Biomedical applications of signal processing

    Semester 2 (one-week module)

    Biomedical signals

    -Physiological origin
    -Main characteristics (amplitudes, frequency range, clinically relevant features)
    -Main clinical uses
    -Noise and artefacts
    -Examples taken from ECG, EEG, EMG and blood pressure.

    Biomedical signal acquisition

    -Sources of noise and artefact
    -Basic measures to reduce noise and artefact.

    Biomedical signal analysis

    -Outline of diagnosis, monitoring and prognosis
    -Biomedical signals as random data
    -Intra- and inter-subject variability
    -Specificity, sensitivity and repeatability of diagnostic procedures.

    Application of signal processing techniques to biomedical signals, including

    -coherent averaging
    -digital filtering
    -spectral estimation
    -input-output modelling.

    Signal processing for specific biomedical applications, including

    -estimating evoked potentials
    -detecting QRS complexes in the ECG
    -biophysical and black-box modelling
    -noise reduction.

    Adaptive methods

    Semester 2 (four-day module)

    Introduction to adaptive systems

    -Motivation for adaptive filters.
    -The error surface.
    -Exact least-squares solution.
    -The Wiener filter.

    The LMS (least mean squares) algorithm

    -Block implementation.
    -Steepest descent.
    -Applications in identification, control, noise cancellation.

    Convergence of the LMS algorithm

    -Principle coordinates.
    -Convergence in the mean.
    -Speed of convergence.
    -Modes of convergence.

    Misadjustment in the LMS algorithm

    -Instantaneous steepest descent.
    -Effect of random weight changes.
    -Stability in the mean square.

    Variants of the LMS algorithm

    -Normalised LMS.
    -Leaky LMS.
    -Sign and smoother LMS.
    -Variable adaptation rate algorithms.

    Finite precision effects

    -Implementation of the LMS.
    -Noise due to output truncation.
    -Noise due to coefficient adaptation.
    -Adaptation "stalling".

    Frequency domain algorithms

    -Exact least-squares solution.
    -Block LMS and frequency domain implementation.
    -Sliding FFT implementation.
    -Sub-band filters.

    Adaptive IIR filters

    -Non-convex error surfaces.
    -Output error approach and Feintuch's algorithm.
    -Equation error approach and Steiglitz-McBride algorithm.

    The RLS (recursive least squares) algorithm

    -Derivation of RLS algorithm.
    -Computation cost and performance of RLS.
    -Other exact least squares algorithms.

    Adaptive nonlinear systems

    -Examples of nonlinear systems.
    -Volterra and NARMAX models.
    -Neural networks.

    Blind deconvolution

    -Application in communications.
    -Bussgang's algorithm.
    -Decision-directed algorithm.

    Adaptive channel equalisation

    -Channel model and properties analytic inversion.
    -Iterative solutions.
    -FIR/IIR structures.

    Adaptive arrays

    -Fixed beamformers.
    -Optimal beamformers.
    -Adaptive beamformers.
    -Generalised sidelobe cancellers.

    Adaptive systems in active control

    -Active control of sound and vibration.
    -Adaptive feedforward control.
    -Applications in aircraft and cars.

    Echo cancellation in mobile telecommunications

    -Need for echo cancellation.
    -Causes of echo and delay in mobile networks.
    -Adaptation algorithms and implementation.
    -Network echo.

    Introduction to random signals

    Semester 2 (one-week module)

    Probability, random variables, moments, time series (continuous and discrete time). Correlation functions and spectral analysis (auto and cross). Estimation methods; bias and variability. Single input, single output linear systems. Frequency response functions. Estimators H1, H2, Hv, H3. Multivariate process. Spectral density matrices, input-output relationships. Partial and multiple coherence, principal component analysis, Singular Value Decomposition. Source identification and ranking. Parametric methods for spectral analysis, AR, ARMA models, maximum entropy spectra, maximum likelihood methods. Detection and classification. Noise suppression, optimal detection. Matched filtering, generalised likelihood methods. Introduction to non-stationary processes (time-frequency methods) and non-Gaussian processes. The course is fully supported by extensive 'hands on' computer based (Matlab) illustrations of the theory using vibro-acoustic examples.

    Sonar & array signal processing

    Semester 2 (one-week module)

    This course aims to provide an overview of the application of DSP techniques to sonar systems. The subjects covered will include beamforming, direction of arrival estimation, adaptive methods, fault detection, pulse design, time-frequency and time-bearing analysis.

    General techniques of array processing are considered with emphasis on sonar applications. Both broad and narrow band implementations will be considered. The problem of optimal source location in a variety of scenarios will be discussed.

    Processing methods for both active and passive sonar will be studied, with theoretical performance limits being derived. The methods for implementation of such schemes will also be presented.

    Project Development

    Semester 2

    In this module preparatory work is carried out for the research project.

    Sessions are held on the use of the library facilities (in semester 1), an introduction to the project, a technical writing workshop and an oral presentations workshop.

    Assessed work consists of a literature survey, the development of a project plan and an oral presentation which is given to the other students.

    Career Opportunities

    Graduates in the field of sound and vibration technology are in great demand. Noise and vibration are becoming increasingly important to manufacturing industry as recent EU directives on machinery, factory and vehicle noise take effect. Graduates work in production and service industries, planning authorities, consultancy organisations, central and local government authorities, health services and environmental control sectors of the community.

    Many of our graduates remain at the ISVR to continue to study for a higher degree. The MSc project provides an ideal training in research methods that can lead into further research for a PhD.

Other programs related to audiology / speech pathology

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