Faculty of Electrical Engineering

Czech Technical University in Prague

CTU in Prague

State doctoral exam topics

Electrical Engineering Theory

I. General Basis Courses

  1. Analysis of analog electrical circuits
    • Circuits with lumped and distributed parameters
    • Elementary and general methods of circuit analysis, the nodal voltage and the loop current analysis, generalized nodal voltage analysis, state space.
    • Harmonic steady state.
    • Periodic non-harmonic steady state.
    • Transient analysis, the solution in time and operator domain.
    • Software for circuit analysis (PSPICE, MAPLE).
  2. Signals and Systems Theory
    • Systems for signal discretisation, sampling quantisation and signal reconstruction.
    • Linear time-invariant systems - impulse and step responses.
    • Convolution, stability, causality, stationarity.
    • Transfer function and frequency response.
    • Laplace and Fourier transform, Z-transform - basic properties and relationships.
  3. Electric and magnetic fields
    • Electrostatics, magnetostatics, stationary field of electric current.
    • Quasi-static electromagnetic field.
    • Definition and calculation of the energy of electric and magnetic fields, definition and calculation of the forces in the electric and magnetic fields.
    • Definition and calculation of capacitance and inductance. Basics of numeric solutions of electric and magnetic fields (FD, FEM, FDTD, MoM).
  4. Electromagnetic waves
    • Plane wave in homogeneous isotropic linear medium.
    • Poynting’s theorem.
    • Plane electromagnetic wave on planar boundary between two media. Reflection, refraction, total reflection, polarization reflection.
    • Guided electromagnetic wave (TEM, TM, TE). Metallic and dielectric waveguides, planar transmission lines.
    • Resonators.
    • Radiation of electromagnetic waves, elementary radiators, near-field and far field.
  5. Digital Signal Processing
    • DFT, FFT - properties and applications.
    • Leakage, windowing, linear and cyclic convolution.
    • DCT - characteristics and relationship with DFT.
    • FIR and IIR filters - design methods and properties.
    • Spectral analysis, nonparametric methods (e.g. periodogram, Welch's method), frequency resolution.
    • Time frequency analysis, STFT, wavelet transform, filter banks.
    • Cepstral analysis – properties and application.
    • Discrete Hilbert transform, complex envelope and instantaneous frequency.
    • Principles and use of PCA, ICA.
    • Parametric models (AR, ARMA, MA), Wiener filtering, adaptive filtering (LMS, RLS).
    • Classification methods (k-means, k-NN, LDA, ANN), and statistical evaluation of data.

II. Specialised Courses

  1. The synthesis of analog electrical systems
    • General characteristics of the transfer function: frequency response and group delay, behavior in the time domain.
    • Approximation in the frequency domain, types of filters, frequency transformations, approximations magnitud and group delay characteristics.
    • Realization of analog filters: passive and active analog filters, advanced functional blocks for ASIC.
    • Discrete-time analog systems, filters with switched capacitors and currents: principle of function, hardware implementation, main characteristics, methods of analysis.
    • Numerical methods of synthesis and software optimization of analog systems.
  2. Biomedical applications of digital signals and systems
    • Physiological signals (EEG, EMG, ECG, EOG, PPG) - genesis, parameters, data acquisition and processing.
    • Electrodes for acquisition of bioelectric signals, sensors of non-electrical quantities, biological signal amplifiers, signal artifacts.
    • Diagnostic methods in medicine (ECG, EEG, EMG, pulse oximetry).
    • Imaging methods in medicine (ultrasound, X-ray, CT, MRI, PET, SPECT).
    • The characteristics used in the pathology of voice and speech.
  3. Algorithms and Systems of Speech and Audio Signal Processing
    • Speech production and perception by human (anatomy and physiology, signal production model, perceptual models).
    • Time and spectral characteristics of speech and audio signals, examples of their usage (energy, pitch, formants, DFT and LPC spectrum, AR model, cepstrum, features for speech recognition).
    • Statistical models and methods of artificial intelligence in speech technology and their applications (GMM, HMM, ANN, speech recognition, speaker recognition, language recognition).
    • The phonetic, phonological, and linguistic description of language and its importance in speech technology systems (phonetic sets, statistical language modelling in speech recognition, linguistic analyses and prosody modelling in speech synthesis).
    • Algorithms of voice activity detection and speech enhancement. Waveform and source coding of speech and audio signals.
    • Synthesis of speech and acoustic signals (formant and concatenative speech synthesis, wave-table synthesis, digital audio effects).
  4. Magnetic materials and their characterization
    • Magnetic materials, their characterization, hysteresis loop.
    • Methods of magnetic quantities measurement, dynamic and static magnetization.
    • Circuit models of coils with ferromagnetic cores, modeling of hysteresis.
    • Measurements of magnetic materials properties for closed specimen at DC and AC magnetization.
    • Measurements of magnetic materials properties for open specimen at AC magnetization.
    • Single sheet tester (SST), On-line testers (OLT).
    • Magnetising, and measuring and control systems and algorithms for SST and OLT.
    • Digital processing of measured signals SST and the OLT, the main causes of measurement errors.
  5. Electrodynamics
    • Propagation of electromagnetic wave in non-isotropic media.
    • Electromagnetic field expression by the closed system of waves (plane, cylindrical, spherical).
    • Quasi-optic approximation, Gaussian beam.
    • Electromagnetic field in different inertial reference frames.


PSPICE software for the analysis and simulation of circuits
MAPLE software for symbolic computation and analysis systems
ASIC Application-Specific Integrated Circuit
DFT/FFT Discrete / Fast Fourier transform
FIR/IIR filters with finite/infinite impulse response
STFT Short-Time Fourier Transform
PCA/ICA Principle / Independent Components Analysis
AR/MA/ARMA Autoregressive / Moving Average / Mixed models
LMS/RLS least mean squares algorithm / recursive least squares algorithm
k-means/k-NN classification method - clustering / k-nearest neighbors algorithm
ANN/ LDA Artificial Neural Network / Linear Discriminant Analysis
GMM, HMM Gaussian Mixture Model / Hidden Markov Models
LPC linear prediction coding  
TEM transversal electromagnetic wave
FD, FEM, FDTD, MoM numerical methods for simulation of physical quantities
EEG/EMG/EKG electroencephalogram / electromyogram / electrocardiogram
EOG/ PPG Electrooculogram / Photopletysmogram
UZV, RTG, CT Ultrasound / X-ray / Computed Tomography
MRI/ PET/ SPECT magnetic resonance imaging / positron emission tomography / single photon emission computed tomography
SST Single Sheet Tester
OLT On-Line Tester

After the agreement with the supervisor determines Subject Board Chairman, three themes, of which at least two of the subjects will be general basis.

Recommended Literature (topics I and II/1-5)

[1] Corne D., Dorigo M., Glover F.: New Ideas in Optimization, McGraw-Hill, UK, 1999 (II/1)

[2] Havlíček, V., Zemánek, I.: Elektrické obvody 2, vyd. 1., Praha: ČVUT, 2008, ISBN: 978-80-01-03971-7 (I/1)

[3] Huang, X., Acero, A., Hon, H. W.: Spoken Language Processing. Prentice Hall, 2001 (II/3)

[4] Irwin, J. D., Nelms, R. M.: Basic engineering circuit analysis, 11th ed., ISBN-13: 978-1118539293 (I/1)

[5] Jackson, J. D.: „Classical Electrodynamics“, 3rd ed., John Wiley & Sons, Inc. New York, 1998, ISBN-13: 978-0471309321 (I/3-4, II/5)

[6] King, M. R., Mody, N. A.: Numerical and Statistical Methods for Bioengineering: Applications in MATLAB (Cambridge Texts in Biomedical Engineering), 1st edition, 2010, ISBN-13: 978-0521871587 (II/2)

[7] Mayer, D.: Aplikovaný elektromagnetizmus, ISBN: 978-80-7232-424-8 (II/4)

[8] McLoughlin, I.: Applied Speech and Audio Processing. Cambridge University Press, 2009 (II/3)

[9] Oppenheim, A. V., Schafer, R. W., Buck, J. R. : Discrete-Time Signal Processing, Prentice Hall, ISBN 978-0137549207 (I/2, 5)

[10] Psutka, J., Müller, L., Matoušek, J., Radová, V.: Mluvíme s počítačem česky. Academia, 2006 (II/3)

[11] Sadiku, M.: Elements of Electromagnetics (Oxford Series in Electrical and Computer Engineering), 6th edition, ISBN-13: 978-0199321384 (I/3-4)

[12] Saltzman, W. M.: Biomedical Engineering: Bridging Medicine and Technology (Cambridge Texts in Biomedical Engineering), 1st edition, 2009, ISBN-13: 978-0521840996 (II/2)

[13] Schaumann R., Ghausi M.S., Laker K. R.: Design of Analog Filters, Passive, Active RC, and Switched Capacitor, Prentice Hall, 1990 (II/1)

[14] Smith, S. W.: The Scientist and Engineer´s Guide to Digital Signal Processing; http://www.dspguide.com/pdfbook.htm,  ISBN-13: 978-0966017632 (I/2, 5)

[15] Spaldin, N.: Magnetic Materials: Fundamentals and Device Applications, Cambridge University Press, c 2003, ISBN-13: 978-0521016582 (I/3-4)

[16] Vaseghi, S. V.: Advanced Diigtal Signal Processing and Noise Reduction. John Wiley & Sons, 2008 (I/5)

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