Subject description - BAB31ZZS
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Explanatory Notes
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Web page:
https://moodle.fel.cvut.cz/courses/BAB31ZZS
Anotation:
An introductory course on digital signal processing (DSP). The course introduces the basic digital signals theory with an emphasis on practical applications and analysis of real signals in time. Exercises are built for progressive mastery of the MATLAB programming environment, which provides a friendly and easy-to-use user environment with graphical and audio output. You will apply the acquired knowledge in other courses, projects, theses, and especially in broader engineering and biomedical practice.
Study targets:
Learning basic programming techniques, procedures and principles of real signal and data analysis
Course outlines:
| 1. | | One- and N-dimensional signals, basic division, quantization, sampling, logarithmic measures - decibel [dB] |
| 2. | | Fourier transform I (classes of continuous nad discrete), sampling theorem, aliasing, basic theorems on Fourier transform |
| 3. | | Discrete Fourier Transform - periodization of finite signals, leakage, window weighting, heterodyne mixing, spectrum densification, filtering in spectrum, power spectral density (PSD) |
| 4. | | Analysis of quasi-stationary signals - spectrogram, estimation of PSD by Welch's method |
| 5. | | Correlation (cross-correlation, autocorrelation, cross power spectral density, correlation coefficient) |
| 6. | | Linear time invariant systems (LTI), transfer function, impulse response, convolution and cyclic convolution, convolution algorithm and LTI as a filter (structure) |
| 7. | | Finite impulse response (FIR) filters, normalized frequency, ideal low-pass, low/band/high-pass implementation, filter structure, z-transform and membrane model, basic types of FIR filters |
| 8. | | Infinite impulse response (IIR) filters, filter structure of recursive computation, Butterworth, Chebyshev and elliptic Cauer approximations, stability, phase shift-free filtering, selected types of IIR filters |
| 9. | | Autoregressive modelling (LPC). Change of sampling frequency - resampling |
| 10. | | Nonlinear operations and parameterization: Hilbert transform, signal envelope, nonlinear operations, amplitude and frequency parameterization, stochstic signal parameterization, time segmentation, local maximum detection |
| 11. | | LTI multidimensional system: 2D impulse response, 2D convolution, 2D complex frequency spectrum. Principle of self-clustering algorithms (k-means, EM) for signal classification. Morphological operations (dilation, erosion, closure, opening) on 1D signals. |
| 12. | | Statistical evaluation of stochastic phenomena (agreement rate, outliers, p-value, paired tests, effect size, multiple testing correction) |
Exercises outline:
| 1. | | Introduction to MATLAB. Decibel - calculation and conversion between units |
| 2. | | Signal genesis (mixture of harmonic signals, unit impulse, noise), FFT spectrum |
| 3. | | Sampling theorem, aliasing and its effect on the spectrum. Filtering in the spectrum - removal of 50 Hz interference |
| 4. | | Spectrogram (time segmentation with overlay, window weighting, spectrum densification), effect of window size and overlay on the result. Welch's method of PSD estimation |
| 5. | | Correlation: measurement of delay between signals, relative power spectral density, echo in the signal. Correlation coefficient as a measure of similarity between signals/data |
| 6. | | LTI: system identification, signal convolution and impulse response. Cyclic convolution. Differential equations and filter structure. |
| 7. | | FIR filters: band stop design by prototype filter (sync), comb filter. Determination of transfer characteristics, poles and zeros in z-plane. Signal smoothing by MA-filter for detection of leading and trailing edges. |
| 8. | | IIR filters: low/high/band pass/stop design. Biqvadratic resonator and notch-filter. Cascaded filter ordering and design optimization. |
| 9. | | Resampling: decimation+aliasing filter, interpolation+DAC filter. Filtering of low-frequency components in filter design failure. Autoregressive signal modelling for description of dominant spectral components, model order estimation. |
| 10. | | Detection of local extrema: thresholding, leading/trailing edge detection, non-equidistant time segmentation, determination of local extreme position. |
| 11. | | Parameterization of the signal and its sorting into classes using similarity to the pattern (correlation) or clustering (k-means, EM) - reduction of information complexity |
| 12. | | Confirmatory analysis: data inspection and cleaning, box plots, hypothesis testing, normality testing, two-sample testing, multivariate analysis |
Literature:
| 1. | | McClellan, J.H, Schafer, R.W., Yoder, M.A..: DSP First, A multimedia Approach, Prentice-Hall, Inc., New Jersey, 1998 |
| 2. | | Openheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice-Hall, Inc., New Jersey, 1998 |
| 3. | | Ambardar, A., Borghesani, C.: Mastering DSP Concepts using MATLAB. Prentice-Hall, Inc., New Jersey, 1998 |
Requirements:
Keywords:
digital signal processing, MATLAB
Subject is included into these academic programs:
| Page updated 23.4.2025 17:53:59, semester: Z/2025-6, Z/2026-7, Z,L/2024-5, L/2026-7, L/2025-6, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |