Course detail
Signals and systems analysis
FEKT-BASSAcad. year: 2012/2013
Continuous-time signals and systems. Discrete-time signals and systems. Representation in the time and frequency domains and their relationship. The Z transform and its applications. Continuous-time and discrete-time random signals and power spectral density. Communication signals and systems. Analog and digital modulations in communication systems. Examples of signal and system implementations on microprocessors and digital signal processors. Problems are explained on examples of real signals and systems using the current engineering practice and the Matlab programming is introduced. Measurement and simulation on FFT spectral analyzers and measuring instruments are realized in Labs.
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
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Prerequisites and corequisites
Basic literature
Recommended reading
Classification of course in study plans
- Programme ZRZT-J Bachelor's
branch J-ZRT , 2 year of study, winter semester, compulsory
- Programme EECC Bc. Bachelor's
branch B-MET , 2 year of study, winter semester, compulsory
branch B-TLI , 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
Physiological acoustics, sound masking and its utilization in audio compression algorithms.
Directional and spatial hearing, 3D room simulation using headphones and loudspeakers.
Noise and its measurement, basic measuring instruments for electroacoustic measurement and their application.
Measurement of acoustic power and sound intensity.
Room acoustics, acoustic wave trajectory, room impulse response, acoustic materials.
Electromechanical and electroacoustic analogy.
Types and operation principles of electroacoustic transducers.
Microphones, practical design and measurement of characteristics.
Loudspeakers, acoustic impedance and distortion, mechanical design, horn-loaded loudspeakers.
Loudspeaker systems, types of loudspeaker enclosures, design and construction of loudspeaker enclosures and crossovers.
Surround sound systems principles and formats.
Stereo and multichannel techniques of sound pickup.
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.