Course detail
Signals and Systems Analysis
FEKT-BASSAcad. year: 2016/2017
One-dimensional (1D) and two-dimensional (2D) signals and systems with continuous time and their mathematical models. One-dimensional (1D) and two-dimensional (2D) signals and discrete-time systems and their mathematical models. Examples of real signals. Representation in the time and frequency domains, Fourier representation of signals, mutual respect. Definition and method of calculation of FFT. Transformation Z, unilateral and bilateral transform, direct and inverse transform and its applications to differential equations. Random signals and their description, probability theory, the definition of power spectral density. Communication signals and communication systems definition analog and digital. Analog and digital modulations in communication technology. Methods of implementation of communication systems in microprocessors and digital signal processors. The issue is illustrated by the examples of specific signals and systems, and these examples are presented in Matlab. In the laboratory measurements and run a simulation of signals and systems on spectrum analyzer with FFT and using appropriate measurement products for specific measuring instruments.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Course curriculum
Real signals and their mathematical continuous-time models. Basic signal operations (time scaling, flipping, time shifting translation, time shifting translation and flipping, convolution, correlation). Signal classification, unit impulse, unit step, harmonic signal. Real systems with continuous- and discrete-time. Dynamic system, its input and output, status. Linear time-invariant system. Impulse response. Response of LTI system using convolution, superposition.
2. Periodic signals and their spectrum
Function substitution by functional series. Periodic continuous-time signal, harmonic signal and its representation by phasors. Periodic and harmonic discrete-time signals. Fourier series, spectrum of periodic rectangular pulses, spectrum theorems.
3. Fourier representation of aperiodic continuous-time signals
Definition of the Fourier transform of aperiodic continuous-time signals. Spectra of selected signals. Spectrum theorems. Definition of the inverse Fourier transform. The inverse Fourier transform of rectangular spectral impulse. Relationship between the Fourier series and the Fourier transform.
4. Continuous-time systems
The characteristics of a linear time-invariant (non-parametric) system (frequency response, hodograf). System transfer function, zero-pole plot. Ideal transfer circuit. Frequency filters. Non-linear systems. Superheterodyne.
5. Sampling of continuous-time signals
Ideal sampling of continuous-time signal and its reconstruction. Sampling theorem. Amplitude quantization. A/D and D/A conversions. Aliasing. Sampling of bandpass signals.
6. Discrete-time signals
Discrete time axis. Basic discrete signals. Signal theorems. Discrete linear, periodic and circular convolutions. Using FFT for convolution calculation.
7. Fourier transform of discrete-time signals.
The discrete Fourier series and the discrete Fourier transform. The fast Fourier transform (FFT). Decimation-in-Time (DIT) and Decimation-in-Frequency (DIF) algorithms, FFT algorithm properties.
8. Z transform and its properties
Definition of the Z transform and its properties. The inverse Z transform and its calculation. The relationship between the Z transform and the discrete Fourier transform.
9. Modulation signals in base-band and transition-band
Communication system and its properties, modulation and transmission rates, spectrum of communication channel. Amplitude, frequency, and phase analog modulations and their spectra. Digital modulations.
10. Stochastic variables and processes and their properties
Continuous and discrete time variables. Definition of stochastic processes with continuous- and discrete-time and their representations. Cumulative distribution function, probability density function. Moments (mean, variance, standard deviation, etc.). Stationarity and ergodicity.
11. Power spectral density and its calculation
Power spectral density of continuous- and discrete-time stochastic processes. Periodogram, using FFT for its calculation. White noise. Processing of stochastic signal by linear system. Non-parametric and parametric models.
12. Discrete-time systems
Linear time-invariant discrete system, impulse response. System transfer function, frequency response, zero-pole plot. Systems of the type of IIR and FIR. Connection of LTI systems. Series, parallel and feedback connections of partial sections.
13. Realization of LTI discrete system
Design of LTI discrete system based on analog prototype. Structures of realization. Mason’s gain rule. Implementation of LTI system on microprocessor. Calculation of frequency response based on time responses.
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
SMÉKAL, Z.: Deterministické a náhodné signály pro integrovanou výuku VUT a VŠB-TUO. Elektronické texty, VUT Brno, 2013. ISBN 978-80-2014-4826-1
SMÉKAL, Z.: Signals and Syztems Analysis for joint teaching programme of BUT and VSB-TUO (EN)
Recommended reading
Classification of course in study plans
- Programme EECC Bc. Bachelor's
branch B-TLI , 2 year of study, winter semester, compulsory
branch B-MET , 2 year of study, winter semester, compulsory - Programme AUDIO-J Bachelor's
branch J-AUD , 2 year of study, winter semester, compulsory
- Programme EEKR-CZV lifelong learning
branch EE-FLE , 1 year of study, winter semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
Periodic signals. Fourier series expansion. Properties.
Fourier Transform. Properties of the Fourier transform.
Linear time-invariant systems and their description. Filtering.
Continuous-time random signals.
Sampling and signal recovery. Digital signals.
Discrete-time signals. Discrete Fourier series.
Discrete Fourier transform. FFT.
Random sequences. Pseudorandom sequences. PSD.
Discrete-time systems. Z transform. Examples.
Communication systems. Baseband signals.
Amplitude modulation. Frequency modulation. ASK, FSK, PSK.
I-Q modulations. Multiplexing and multiple-access techniques.
Fundamentals seminar
Teacher / Lecturer
Syllabus
Fourier series expansion. Examples.
Properties of the Fourier transform.
Random signals. Sampling. Quantisation noise.
Discrete Fourier transform.
Amplitude and frequency modulation, keying.
Laboratory exercise
Teacher / Lecturer
Syllabus
Spectral analysis of the periodic signals.
Amplitude and frequency modulation. Analysis of the random signal.
Sampling, aliasing.
Digital signal processing of the own speech.
The frequency response of the discrete-time system.