Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

Dr. Tamás Barbarics	associate professor
Zoltán György Horváth	master lecturer

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

The aim of the subject is to familiarize the student with the most important concepts, relationships and mathematical toolkit for the description of signals. The backbone of the curriculum is the analysis of continuous and discrete-time, linear, time-invariant systems, the methods of which are discussed in the time, frequency and complex frequency domains. After the mathematical description, some important methods of digital signal processing, such as sampling, filtering, and restoring signal shapes, will be detailed. At the end of the semester, we present the structure of software radio (Software Defined Radio - SDR) and the basics of programming.

The subject significantly improves modeling and problem-solving skills by presenting models of real engineering problems and solving them. These areas are image processing, sound and image compression, telecommunications, software radio systems, the discussion of which areas deepens the professional subjects of computer science students, such as those learned in Computer Graphics, Communication Networks and other telecommunications and biomedical specializations.

1.lecture

Basic concepts: the concept of signal, system, network; management, control and regulation idea. Classification of signals. discrete and continuous time or value signs. Operations on discrete-time and continuous-time signals. Classification of systems: SISO, MISO, SIMO, MIMO systems; linear and non-linear systems; time invariant and time invariant systems; causal and acausal systems; systems with and without memory; deterministic and stochastic systems.

2. lecture

Networks. Analysis in time domain. The concept of impulse response, stepresponse and relationship. Expressing the response of a linear system. Convolution. (CT and DT systems)

3. lecture

State variable description of the system, solution of the state equation in the time domain (matrix functions) (CT and DT systems). Decomposition of the system response into components, eigenvalues, excitation-response relationship

4. lecture

Description of sinusoidal signals. Steady state of stable systems under harmonic excitation. Determination of transmission coefficient.

5. lecture

Fourier series of periodic signals. Periodic response of linear systems

6. lecture

Spectrum of a general signal, the Fourier transform. Band-limited and time-limited signals. Windowing. Spectrum of the response signal. Undistorted signal transmission, bandwidth condition.

7. lecture

Description of signals in the complex frequency domain, the Laplace transform. Inverse Laplace transform. Transferfunction of CT systems.

8. lecture

Description of signals in the complex frequency domain, the z-transformation. Inverse z-transform. transfer function of DT systems.

9. lecture

Relations between continuous-time and discrete-time signals and systems. simulation, impulse response, transfer function. Shannon's sampling law. Sampling, holding in time and frequency range.

10. lecture

System state variable and signal flow network description, specifying the answer is complex in the frequency range. Bode, Nyquist diagram. Stability. Stability test methods.

11. lecture

Open and closed control circuits. Effect diagram operations, substitution transformations. Value-preserving, follow-up regulations. The role of negative feedback. Characteristics of ideal fundamental elements (proportional, integrating, doubly integrating, differentiating, dead-time element): their impulse response, jump response, Nyquist, Bode diagram. Basics of control systems: closed and open circuit, circuit amplification, model number. Amplification and phase reserve. PID controller.

12. lecture

Filters. FIR, IIR filter structures. Filter design.

13. lecture

Presentation and programming of software radio (SDR) hardware elements. Implementation of simple modulation and demodulation (AM, FM, 4QAM) with software radio.

Lab 1

Impulse response, stepresponse, convolution. Matlab basics. Convolution in one dimension - time domain - reverberation. Two-dimensional convolution as an image processing procedure - averaging, noise filtering, edge enhancement.

Lab 2

State variable description of systems. Calculating the impulse response and jump response of linear state variable systems in the Matlab environment. Determining the response of a linear system.

Lab 3

Identical models of different physical systems – analogies (mechanical, electrical network, economic, biological, biochemical models). Simulation in the Matlab - Simulink environment.

Lab 4

Modeling: physical, black-box system modeling, mixed models. Modeling and simulation. Mathematical models of engineering problems. Structural, operational and impact outline.

Lab 5

Model creation procedures. Steps and tasks of modeling and simulation. Model and its verification.

Lab 6

Modeling and simulation. Mathematical models of engineering problems. Intervening bodies, sensors.

Lab 7

Harmonic excitation. Steady state of the system. Transfer characteristic. Transfer characteristics of simple physics networks. Bode diagram.

Lab 8

 System analysis using periodic excitation signals. Realization of the transfer characteristic and transfer function. FIR, IIR systems, filters in signal processing.

Lab 9

Fourier transformation, testing systems in the frequency domain. FFT algorithm and its application in image and sound compression procedures. Wired and radio communication application examples, amplitude and frequency modulation, frequency and time domain multiple access systems.

Lab 10

Sampling, quantization testing in a Matlab simulation environment. Restore sampled signals.

Lab 11

Examination of a storage system. (Temperature measurement on a heated resistor) Test of a proportional regulator.

Lab 12

PID control of a storage system. (Temperature control for heated resistance)

Lab 13

 Design and simulation of FIR, IIR filters in Matlab environment.

2 lectures and 2 labors pro week

During the lecture period:

The conditions for obtaining an end-of-semester mark are as follows:

· Attendance: regular participation in classes (lecture, lab). The permissible amount of absences is fixed by the rules (30%).

· Midterm Test: during the diligence period, we write a midterm test twice, at the time according to the rules of the Faculty. Each of these has no minimum requirements.

· Homework assignment: each student must solve an individual homework, working independently, related to the knowledge presented in the laboratory session. Accomplishing this at an acceptable level is the requirement of the semester. The homeworks are given out in the 4th week and the solutions must be submitted in the 13th week.

The end-of-semester mark is calculated based on the score of their midterm tests and the homework. A maximum of 2x50 points for the midterm tests, 50 for the large homework, for a total of 150 points. The midterm grade is sufficient if the total score achieved is at least 40%, i.e. 60 points. Additional grades are calculated proportionally between 40-100%.

 During exam period: ---

It is possible to replace midterm test during the replacement week. The two midterm tests can be repaired or replaced together, in which case the new score counts instead of the original scores. There is no second replacement option by default.

 It is possible to submit the homework additionally until the end of the diligence period (last school day, 12:00 p.m.), after which the large homework cannot be submitted. In case of replacement, a special procedure fee is payable.

A.V. Oppenheim, A.S. Willsky and I.T. Young, Signals and Systems, Prentice-Hall, Englewood Cliffs,

New Jersey, 1983

Gy. Fodor, Signals, systems and Networks, Tankönyvkiadó, 1998.