1. SylabUZ
2. Faculty of Computer Science, Electrical Engineering and Automatics
3. winter term 2024/2025
4. Electrical Engineering - First-cycle Erasmus programme
5. Digital signal processing

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Digital signal processing - course description

Aim of the course

• To familiarize students with basic notions of the digital signal processing.
• To provide basic knowledge about fundamentals of a spectral analysis and digital filtration of discrete signals.
• To give skills in practical implementation of a spectral analysis and filtration of discrete signals.
• To provide knowledge about design of digital filters.

Prerequisites

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• Programming

Scope

Fundamentals of signal theory. Notion of signal. Classifications of signals. Mathematical models of selected signals. Fourier series and Fourier transform for continuous-time signals. Fourier series and Fourier transform properties. An influence of a signal observation in finite time interval on its spectrum.

Analog-to-digital and digital-to-analog conversion. Chain of signal processing during analog-to-digital and digital-to-analog conversion. Sampling, quantization and coding. Quantization error. Spectrum of a sampled signal. Aliasing. Sampling theorem. Anti-aliasing filter. Recovery of an analog signal from samples.

Discrete Fourier transform (DFT). Derivation of amplitude and phase spectrum. Spectral leakage. Windowing. Zero padding. Examples of spectral analysis of discrete-time signals and their interpretation.

Fast Fourier transform (FFT). Butterfly computation schema in radix-2 FFT algorithm. Computational profit. 

Linear and causal time-invariant (LTI) systems. Definitions of a discrete, linear and time-invariant system. Definition of causal system. Convolution. Stability of LTI systems in BIBO sense. Difference equation.

Z-transform. The Z-transform definition. Z-transform properties. The transfer function. Poles and zeros of the transfer function. Pole locus and stability of system.

Digital filters. Finite and infinite impulse response filters. Processing discrete-time signals by digital filters. Basic structures of digital filters. Determination and interpretation of the frequency response of digital filters. Importance of linear phase response in the processing of signal. Group delay.

IIR filter design via bilinear transform. Window-based FIR filter design.

Teaching methods

• Lecture: conventional/traditional lecture with elements of discussion.
• Laboratory: laboratory exercises, work in groups with elements of discussion.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

• Lecture: to receive a final passing grade student has to receive positive grade from written tests conducted at least once a semester.
• Laboratory: to receive a final passing grade student has to receive positive grades in all laboratory exercises provided for in the laboratory syllabus.

Calculation of the final grade = lecture 55% + laboratory 45%

Recommended reading

1. Lyons R.G.: Understanding Digital Signal Processing, Prentice Hall, 2004
2. Mitra S.: Digital Signal Processing: A Computer-Based Approach, McGraw-Hill, 2005
3. Orfanidis S.J.: Introduction to Signal Processing, Prentice Hall, 1999
4. Oppenheim A.V., Schafer R.W., Buck J.R.: Discrete-Time Signal Processing, Prentice Hall, 1999

Further reading

1. Oppenheim A.V., Willsky A.S., Nawab H.: Signals & Systems, Prentice Hall, 1997
2. Owen M.: Practical signal processing, Cambridge University Press, 2007
3. Smith S.W.: Digital Signal Processing: A Practical Guide for Engineers and Scientists, Newnes, 2002

Notes

Modified by dr hab. inż. Radosław Kłosiński, prof. UZ (last modification: 17-04-2024 19:26)