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Explanatory Notes
Instructions
Web page:
https://moodle.fel.cvut.cz/courses/B0M31DSP
Anotation:
The course introduces advanced methods of analysis and processing of digital signals such as correlation, spectral, coherence or cepstral analysis, as well as methods of decomposition into principal and independent components, methods for determining the relationship between random signals and basic classification techniques used in signal analysis. Attention is paid to practical applications of the mentioned techniques, e.g. for noise suppression or compression.
Study targets:
Students will learn to use the above-mentioned advanced signal analysis techniques, interpret the results obtained, and practically use basic classification techniques.
Content:
The lectures cover the theoretical foundations of the above-mentioned techniques. Computer exercises are aimed at acquiring active skills, they follow the lectures thematically and are aimed at acquiring the ability to correctly choose the analysis method and its correct use. The tasks are implemented in the MATLAB programming environment.
Course outlines:
| 1. | | LPC analysis: calculation of AR model parameters, LPC spectrum |
| 2. | | General signal modeling (AR, MA, ARMA) |
| 3. | | Delay measurement using correlation and spectral analysis |
| 4. | | Coherence function, magnitude square coherence (MSC) and its application |
| 5. | | Cepstral analysis and its application |
| 6. | | Spectral and cepstral distance and their application |
| 7. | | Reduction of additive and convolutional noise in the spectral and cepstral domains |
| 8. | | Discrete cosine transform |
| 9. | | Principal component analysis (PCA) as a basis for lossy signal compression |
| 10. | | Basics of classification (k-means, GMM, SVM) |
| 11. | | Use of neural networks in signal processing |
| 12. | | Implementation of discrete wavelet transform by filter bank, quadrature filters |
| 13. | | Principles of blind separation and deconvolution methods of signals |
| 14. | | Reserve |
Exercises outline:
| 1. | | LPC analysis, LPC spectrum |
| 2. | | Signal modeling (AR, MA models of the 1st and 2nd order) |
| 3. | | Delay measurement based on cross-power spectral density |
| 4. | | Properties and applications of the coherence function |
| 5. | | Real and complex cepstrum - definition and basic properties |
| 6. | | Cepstral distance |
| 7. | | Suppression of additive noise in the frequency domain |
| 8. | | Calculation and use of the discrete cosine transform |
| 9. | | Principal component analysis and KLT transform |
| 10. | | Classification based on k-means |
| 11. | | Classification based on GMM |
| 12. | | Noise suppression based on ANN |
| 13. | | Wavelet transform, implementation by a filter bank, noise suppression based on WT |
| 14. | | Reserve |
Literature:
| [1] | | Oppenheim, A. V., Schaffer, R. W. : Discrete-Time Signal Processing. Prentice-Hall, 3rd edition, 2009. |
| [2] | | S. V. Vaseghi: Advanced Digital Signal Processing and Noise Reduction, Wiley, 2009. |
| [3] | | M. Hayes: Statistical digital signal processing and modeling. Wiley, 1999. |
Requirements:
Knowledge of basic techniques of digital signal processing, digital filtering as well as mathematical apparatus for describing continuous and discrete signals and systems is assumed.
Keywords:
digital signal processing, correlation characteristics, spectral representation, coherence function, cepstrum, noise suppression, PCA, ICA, basic classification techniques, k-means, GMM, DNN
Subject is included into these academic programs:
| Page updated 16.6.2026 17:52:00, semester: L/2029-30, Z,L/2027-8, L/2028-9, Z,L/2026-7, Z/2028-9, L/2025-6, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |