Faculty of Electrical Engineering

Czech Technical University in Prague

CTU in Prague

State doctoral exam topics



Application of boundary value problems for Laplace’s equation, Fourier solution (separation of variables), numerical solution of boundary value problems. Characteristic values and characteristic functions of internal boundary value problem for Helmholtz equation, properties and usage. Solution of equation describing propagation of waves in a space (radiation condition, retarded solution). Solution of parabolic and hyperbolic partial differential equations with mixed boundary value problem (with given initial and boundary conditions).

Sound field theory

Scalar field of sound pressure and vectorial field of particle velocity in gases. Equation of motion, equation of continuity and the first thermodynamic equation for particle of fluid. Linear adiabatic approximation of dynamics of sound field in gases – conditions of linearization. Linear wave equation for sound pressure, particle velocity and velocity potential, sound energy conservation.

Specific impedance for plane spherical and cylindrical wave. Gauss theorem, Green’s theorem, Helmholtz-Huygens integral equation, Rayleigh’s integral.


Analysis of linear systems, method of oriented graphs, synthesis. Filtration of analog signals, algorithms of synthesis of reactant filters, active filters with operating amplifiers. Frequency (loudspeaker) crossovers, synthesis of correction circuits, magnitude and phase correctors, delay circuits. Linear mechanic and acoustics systems with lumped and distributed elements, electromechanic and electroacoustic analogies. Vibrations of diaphragm, bars and plates, their description by equivalent circuits. Approximate solutions of distributed elements systems. Acoustic waveguides, air gaps their description and equivalent circuits. Theory of acoustic transmitters, transmitter of zero and higher orders, spherical and cylindrical. Radiation impedance, directivity function, realization of acoustic transmitters, source sound power. Acoustic antennas, line source, piston source, circular and ring membrane, radiation impedance, directivity function. Theory of acoustic receivers, gradient transducers, wave transducers. Measurement of acoustic transducers, metrology of basic acoustic quantities, calibration methods, metrology of sound pressure. Sound level meters, measurement of sound intensity. General theory of reciprocal electromechanic and electroacoustic transducers with lumped and distributed elements, transducers with magnetic and electric field. Equivalent circuits of electromechanic and electroacoustic transducers. Metrology of mechanical quantities, vibration table, accelerometer, calibration methods, force sensor, impedance head. Artificial ear, head and torso simulator. Applications.

Acoustics and electroacoustics of solid phase

Waves in elastic isotropic medium, general wave equation, scalar and vectorial potential. Waves in free space and hemispace. Reflection and refraction of waves. Reyleigh’s surface wave. Waves in solid state waveguides, Love waves, Lamb waves, Pochhammer frequency equation, waveguides of variable cross-sections in solid state, onedimensional examples, equivalent circuits. Piezo-materials and transducers, elastic, dielectric and piezoelectric properties, tensor description. Types of piezoelectric materials and their applications.


Waves in piezoelectric materials, modes of vibration of piezoelectric bodies. Equivalent circuits of piezoelectric units. Excitation and detection of ultrasonic waves. Surface waves, their excitation and application for signal processing. Propagation of elastic waves in gases and liquids and solids. Acousto-optics, acousto-electronics, and their applications. Magnetoelastic phenomena, propagation of sound in magnetics. Acousto-electric effect in semiconductors. Power ultrasound, its sources and application. Cavitation and its symptoms, ultrasonic cavitation. Methods of measurement of non-electric quantities. Applications of ultrasound in technical diagnostics, ultrasonic testing in industry and medicine.

Signal recording and processing

Basic classification of acoustic signals, deterministic signals periodic, quasiperiodic and transient, stochastic signals non-stationary, stationary ergodic and non-ergodic, pseudorandom signals. Analysis of deterministic and stochastic signals. Linear time invariant systems. Discrete processing of acoustics signals, analysis of digital signals. Fourier analysis and its applications, frequency zoom, cepstral analysis, Z transform, digital filtering. Application of Hilbert transform. Time delay spectrometry. Principles of recording, analog and digital record. Digital signal processing, oversampling bitrate reduction, blind deconvolution, echo removal. R-DAT, S-DAT, WORM, semiconductor memories. Principles of optical record, CD systems, CD-ROM.

Technical acoustics and elastoacoustics

Oscillations of mechanical systems. Vibration of continuum, string, membrane and circular plate. Fundamentals of finite element method, matrix representation of equations of motion, selection of boundary conditions. Modal analysis of mechanical systems, acoustic spaces and elastoacoustsic systems using FEM. Methods of structure born noise control. Methods of air-born noise control.

Environmental acoustics

Environmental laws (laws of the minimum, tolerance, limiting factors, valence). Significant environmental factors: sound, noise, vibrations, infrasound, ultrasound, spectral analysis. The effects of noise on human organism. Vibration measurement and evaluation. Multi-dimensional assessment. Active and passive noise control. Occupational and living related noise pollution, noise limits. Noise prevention. Noise monitoring, noise studies, criteria for assessment, acoustic auditing. Noise maps of land and air transportation.

Physiological acoustics, psychoacoustics and musical acoustics

Human ear, theory of hearing, hearing field, threshold of hearing, loudness, pitch, masking and distortion of hearing sensation, adaptation and fatigue of hearing, binaural and directional hearing, 1st and 2nd order phenomena, sensation of sound color. Psychoacoustics of music signal transmission, methods of subjective testing, objective and subjective measures of music signal, static and dynamic approach, tone and noise, typology of music sounds, analytical procedures and means, sound synthesis methods. Musical instrument as acoustic system, acoustic of chordophone, aerophone, membranophone and idiophone, methodology of measurement and evaluation of musical instruments

Speech acoustics

Speech organ, sources of sound, vocal tract, creation of voice signal. Segmental description of voice signal (description on the level of speech sounds – consonants and vowels). Word stress, stress and rhythm, sentence intonation, segmental and suprasegmental description of speech. Automatic speech recognition, speech synthesis (text-to-speech), main types of synthesizers, Vocal tract models.

Room and building acoustics

Geometrical acoustics: principle and application in sound propagation. Wave acoustics: sound field in enclosed space, modes. Statistical acoustics: assumptions of statistical approach, reverberation time, influence of sound absorption for sound propagation, reverberant distance. Acoustic products: absorption of porous materials on hard wall, vibrating plates, perforated panels, resonance frequency, estimated damping. Laboratory measurements: sound absorption coefficient of liner in reverberation room, acoustic interferometer. Subjective parameter of rooms and corresponding objective criteria. Measurements in situ: reverberation time, impulse response measurements, Schroeder method. Sound systems: required loudness and power, optimal listening, acoustic feedback. Room acoustics modelling: mathematical simulation of sound propagation mechanisms in enclosed space, measurements on models. Building acoustics: transmission loss of simple and multilayer constructions, footfall noise transmission. Criteria of sound insulation in buildings. Measurements and calculation methods.


Responsible person: RNDr. Patrik Mottl, Ph.D.