# Subject description - XP31DSP

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XP31DSP Digital signal processing
Roles:S Extent of teaching:2P+2S
Department:13131 Language of teaching:CS
Guarantors:Sovka P. Completion:ZK
Lecturers:Bortel R., Sovka P. Credits:4
Tutors:Bortel R., Sovka P. Semester:Z

Anotation:

This course builds on the basic courses of digital signal processing in master's degree, develops and deepens the knowledge corresponding to the needs of doctoral studies in the area of 1-D signal processing. It covers spectral and cepstral analysis, parametric methods, optimal LTI filters, frequency analysis, methods of analysis of relations between time series.

Study targets:

To deepen the knowledge of basic digital signal processing courses in the master's degree program. To develop and deepen the knowledge corresponding to the needs of doctoral studies in the area of 1-D signal processing. Emphasis is placed on the context and the unified view of different methods.

Content:

Relationships between transformations and their consequences, OLA and OLS signal reconstruction. Recursive filter realization, frequency sampling filters, recursive DFT-Goertzel algorithm. Short-time Fourier transform as a filterbank. Parametric methods: model types, analysis-synthesis, linear prediction and estimation. Spectral and frequency analysis, noise and signal subspace, EVD and SVD. Cepstral analysis, problemas of liftering and signal deconvolution. Notes on adaptive filtering and blind source separation.

Course outlines:

 1 Relationships between Fourier transforms FT, FS, DtFT, DtFS and DFT and consequences 2 Theory behind fast algorithms for DFT, Kronecker matrix multiplication 3 Lagrange interpolation in DSP, frequency sampling filters, Lynn filters, CIC filters 4 Relationship between short-time Fourier transform and filter banks, possibility of resampling 5 Homomorphic systems, theory of cepstral analysis, liftering, spectral envelope 6 Spectral and cepstral distances 7 Spectral factorization, minimum and non-minimum phase systems 8 Signal modelling using linear parametric methods 9 Signal analysis using linear parametric methods 10 MMSE-filters, notes on their performance 11 Karhunen-Loeve transform, singular value decomposition 12 Spectral and frequency estimation, principal components spectrum estimation 13 Reserve

Exercises outline:

 1 Relationships between Fourier transforms - sampling and windowing 2 Types of FFT algorithms, implementation issues 3 Implementing frequency sampling filters, Lynn filters, and CIC filters 4 Implementation of short-time Fourier transform 5 Use of real and complex cepstrum I 6. Use of real and complex cepstrum II 7 Computing spectral and cepstral distances 8 Examples of signal modelling algorithms 9 Effective implementation of parameter estimation algorithms 10 Examples of noise reduction using MMSE-filters 11 Application of Karhunen-Loeve transform 12 Spectral and frequency estimation algorithms 13 Reserve

Literature:

 [1] Madisetti, V.K.: The Digital Signal Processing Handbook, CRC Press, 1998 [2] Lee, T. W.: Independent Component Analysis, Kluwer Academic Publishers, London, 1998 [3] Hayes, M. H.: Statistical Digital Signal Processing and Modeling, John Wiley&sons, New York, 1996

Requirements:

Knowledge required for this course is basic knowledge and concepts covered by basic courses of processing and analysis of 1-D signals in bachelor and master programs.

Webpage:

https://moodle.fel.cvut.cz/courses/XP31DSP

Keywords:

spectral analysis, frequency analysis, filtration, parametric methods, Box-Jenkins methodology

Subject is included into these academic programs:

 Program Branch Role Recommended semester DOKP Common courses S – DOKK Common courses S –

 Page updated 22.1.2021 09:51:56, semester: Z/2020-1, L/2021-2, L/2020-1, Z/2021-2, Send comments about the content to the Administrators of the Academic Programs Proposal and Realization: I. Halaška (K336), J. Novák (K336)