Digital Signal Processing
FEKT-MCSIAcad. year: 2018/2019
Definition and classification of 1D and 2D discrete signals and systems. Signal and system examples. Spectral analysis using FFT. Spectrograms and moving spectra. The Hilbert transform. Representation of bandpass signals. Decimation and interpolation. Transversal and polyphase filters. Filter banks with perfect reconstruction. Quadrature mirror filters (QMF). The wavelet transform. Signal analysis with multiple resolution. Stochastic variables and processes, mathematical statistics. Power spectral density (PSD) and its estimation. Non-parametric methods for PSD calculation. Linear prediction analysis. Parametric methods for PSD calculation. Complex and real cepstra. In computer exercises students verify digital signal processing method in the Matlab environment in real time.
Learning outcomes of the course unit
Recommended optional programme components
FLIEGE,N.J.: Multirate Digital Signal Processing. John Wiley, Chichester 1994. ISBN 0 471 93976 5
MADISETTI, V.K., WILLIAMS, D.B.: The Digital Signal Processing Handbook. CRC Press, 1998. ISBN 0-8493-8572-5
MITRA, S.K.: Digital Signal Processing. A Computer-Based Approach. The McGraw-Hill Companies, Inc. New York 1998. ISBN 0-07-042953-7
VÍCH, R., SMÉKAL, Z.: Digital Filters (Číslicové filtry). Academia, Praha 2000. ISBN 80-200-0761-X (In Czech)
SMÉKAL? Z.: Číslicové zpracování signálů, FEKT, VUT v BRně.
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Language of instruction
2. External and internal (state-space) representations. Bounded Input Bounded Output (BIBO) stability, causality. Linear time-invariant 1D discrete system. Connection of partial sections. FIR and IIR systems. Frequency responses, fast convolution. Overlap-save and overlap-add methods. Linear shift-invariant 2D discrete system. The Fourier transform of 2D discrete signals, 2D frequency response.
3. Matrix representation of system equations and their solution. Semi-symbolic computer analysis. Signal flow graphs and Mason’s gain rule. Check of discrete system causality.
4. Definition of a periodic even sequence using an aperiodic sequence, definition of discrete cosine transform from DCT I to DCTIV. Relationship between DCT II and DFT. Definition of the discrete sine transform. Undersampling (decimation) and oversampling (interpolation) of discrete signal in an integer ratio. Description of the time and frequency domains. The transformation of sampling frequency in a rational number ratio. Optimization of the number of multiplier and memory registers of anti-aliasing low pass filter.
5. Zero-pole plot in the z domain, Minimal, maximal and mixed phases. All-pass filter, inverse discrete system. Sampling of bandpas signals. Real signal, analytical signal and complex lowpass signal. The Hilbert transform for continuous-time signals. Quadrature modulator and demodulator. The Hilbert transformer for discrete signals.
6. Analyzing part and synthesizing part of digital filter bank. Calculation of DFT spectrum of discrete signal using uniform-DFT filter banks. Sub-band coding. Quadrature mirror filters (QMF). Perfect signal reconstruction. Transmultiplexers.
7. The Gabor and the short-time Fourier transforms. Time-frequency resolution, The Heisenberg uncertainty principle. Orthogonal systems and their application to spectral analysis. Wavelets and their definition.
8. The continuous-time wavelet transform (CWT), the discrete wavelet transform (DWT). The discrete-time wavelet transform (DTWT). Relationship between DTWT and QMF digital filter banks.
9. Cumulative distribution function and probability density function, general and central moments. Stationary and ergodic continuous- and discrete-time stochastic processes. Estimates, consistent estimate. Random selection from probability distribution, statistics, statistical hypothesis testing, parametric and non-parametric tests, goodness of fit tests.
10. Forward and backward linear prediction. Calculation of linear prediction coefficients. Lattice structure of autoregressive (AR) and autoregressive moving average (ARMA) types and their application. Using linear predictive analysis for speech signal compression.
11. Definition of power spectral density and its properties. Definition of periodogram and its calculation. The Bartlett method of averaging periodograms. The Welch method of averaging modifmodified periodograms. The Blackman and Tukey method of smoothing the periodogram. Performance characteristics of nonparametric power spectral density estimators.
12. AR, MA or ARMA type stochastic processes. Model definition for power spectral density calculation. Relationship between autocorrelation coefficients and model parameters. The Yule-Walker and the Burg methods for AR type model. Selection of the order of type AR model.
13. Complex and real cepstra. Generalized superposition. Homomorphic filtering, definition and its application. Approximation of exponential function by continued fraction expansion.
Specification of controlled education, way of implementation and compensation for absences
Classification of course in study plans
- Programme AUDIO-P Master's
branch P-AUD , 1. year of study, summer semester, 6 credits, compulsory
- Programme EEKR-M1 Master's
branch M1-TIT , 1. year of study, summer semester, 6 credits, compulsory
branch M1-KAM , 1. year of study, summer semester, 6 credits, optional interdisciplinary
branch M1-MEL , 1. year of study, summer semester, 6 credits, optional interdisciplinary
- Programme IBEP-V Master's
- Programme EEKR-CZV lifelong learning
branch ET-CZV , 1. year of study, summer semester, 6 credits, compulsory