Digital signal processing

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Circuit Theory

Synopsis:

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.

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.

Syllabus of lectures:

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

Syllabus of tutorials:

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

Study Objective:

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.

Study materials:

[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

Note:

Further information:

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

No time-table has been prepared for this course

The course is a part of the following study plans:

• Doctoral studies, daily studies (compulsory elective course)
• Doctoral studies, combined studies (compulsory elective course)
• Doctoral studies, structured daily studies (compulsory elective course)
• Doctoral studies, structured combined studies (compulsory elective course)