| Course Unit Code | 450-2036/02 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| MAC37 | Ing. Zdeněk Macháček, Ph.D. |
| Summary |
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The purpose of the course is to provide a common background for BS courses in control and communicastion. It is oriented in digital signal processing and digital filter design.
The course Digital Signals and Systems introduces discrete-time and digital signals and systems. It is a subsequent course to the BS course Foundation of Signals and Systems which is devoted mainly to continuous-time signals and systems.
The course introduces fhe following five major topics: 1. Fundamental concepts (causality, linearity, time-invariance, lumpedness and their applications) 2. Signal analysis (discrete-time Fourier transform, frequency spectrum and its computations) 3. System analysis (LTIL system analysis, the difference equations, z-transform) 4. Stabilities and their implications (filtering, frequency response, model reduction and memory circuits) 5. State variable equations and computer simulations (numerical methods, simulation means). |
| Learning Outcomes of the Course Unit |
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The purpose of the course Digital Signals and Systems is to provide a common background for digital signal processing and digital filter design.
Student will master the analysis of both the discrete-time signal and discrete time LTIL system. The correlation analysis and spectral analysis of signal and system will be discussed. Laboratory work will be made in MATLAB and in MATLAB/Simulink toolbox environment. |
| Course Contents |
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Lectures:
PAM-I modulation. Continuous-Time Impulse Waveform wI(t). Basic Definitions, the Theme of Study. Impulse Signal wI(t) Generation by Sampling a Signal w(t).Autocorrelation Function of Impulse Signal wI(t). Crosscorrelation Function of Impulse Signals wAI(t), wBI(t).
Spectrum of Impulse Signal wI(t).Spectral Density of Impulse Signal wI(t).
Reconstruction of Continuous-Time Signal w(t) by wI(t). Filtering.Theorem of Shannon - Kotelnikov.
Discrete-Time Signal w[k]. Basic Definitions, the Theme of Study. Correlation Function of Discrete-Time Signal w[k]. Cross-correlation Function of Discrete-Time Signals wA[k], wB[k].
Spectrum of Discrete-Time Signal w[k].FFT. Energy Spectrum of Discrete-Time Signal w[k]. Power Spectrum of Discrete-Time Signal w[k].
Spectral Density of Discrete-Time Signal w[k].DTFT. Energy Spectral Density of Discrete-Time Signal w[k]. Power Spectral Density of Discrete-Time Signal w[k].
Discrete-Time System. Basic Definitions, the Theme of Study. LTIL Discrete-Time System. Convolution. Description of LTIL Discrete-Time System H by Difference Equation.
Discrete-Time System Described by Difference Equation.
Analytical Solution in the Time Domain.
Discrete-Time System Described by Difference Equation.
Solution in the Frequency Domain.
Design of Digital Filters and Controllers
The Use of z-Transform. Properties of z-Transform. Description of LTIL System H by Transfer Function H(z).
Stability Analysis of LTIL Discrete-Time System.
State Equation. Derivation of State Equation. Analytical Solution of State Equation.
Laplace Transform and z-Transform of State Equations.
Conclusion.
Computer labs:
Introduction.
Calculation of Spectrum of Impulse Signal wI(t). Calculation of Spectral Density of Impulse Signal wI(t).
PAM-I modulation. Calculation of Charakteristics of Impulse Signal wI(t).
Discrete-Time Signal w[k]. Autocorrelation Function of Disctrete-Time Signal w[k]. Crosscorrelation Function of Discrete-Time Signals wA[k], wB[k].
FFT. Spectrum of Discrete-Time Signal w[k]. Calculation of Spectral Density of Discrete-Time Signal w[k].
Protocol No.1 Specification. Numeric calculation of charakteristics of energy and periodic discret-time signals.
Symbolic Toolbox. Description of LTIL Discrete-Time System H by Difference Equation. z-Transform. Stability Analysis of LTIL Discrete-Time System.
Discrete-Time System Analysis. LTIL Discrete-Time System Responses.
Protocol No.2 Specification. Numeric Analysis of LTIL Discret-Time System. Model of the system, calculation of system response.
Simulation LTIL Discrete-Time System in MATLAB/Simulink.
Numerical Solution of Differential Equation. Analytic Solution of State Equations.
Závěrečný test. Ukončení počítačových laboratoří. |
| Recommended or Required Reading |
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| Required Reading: |
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Chen Chi-Tsong: System and Signal Analysis. Saunders College Publishing, New York 1994.
Nevřiva P.: Signals and system Analysis II.
Soft handout. VŠB TU Ostrava, Ostrava 2005.
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Horák B., Nevřiva P.: Signály a soustavy III. VŠB Ostrava, Ostrava 1998.
Chen Chi-Tsong: System and Signal Analysis. Saunders College Publishing, New York 1994.
Nevřiva P.: Signály a soustavy I a II VŠB Ostrava, Ostrava 1998.
Vejražka F.:Signály a soustavy. ČVUT Praha, Praha 1996.
Nevřiva P.:Signály a soustavy II. Elektronická učebnice. VŠB TU Ostrava, Ostrava 2005.
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| Recommended Reading: |
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Couch L.W.II: Digital and Analog Communications Systems. Macmillan, New York 1989.
E.C. Ifeachor, B.W. Jervis: Digital Signal Processing, A Practical Approach, Addison-Wesley Publishing Company
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Couch L.W.II: Digital and Analog Communications Systems. Macmillan, New York 1989.
Nevřiva P.: Analýza signálů a soustav. BEN Praha, Praha 2000.
E.C. Ifeachor, B.W. Jervis: Digital Signal Processing, A Practical Approach, Addison-Wesley Publishing Company
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| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Experimental work in labs |
| Assesment methods and criteria |
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| Tasks are not Defined |