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

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    Signals and Systems 1

    A tantárgy neve magyarul / Name of the subject in Hungarian: Jelek és rendszerek 1

    Last updated: 2018. május 2.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Signals and Systems 1
    Course ID Semester Assessment Credit Tantárgyfélév
    VIHVAA00 2 3/2/0/v 6  
    3. Course coordinator and department Dr. Horváth Péter, Szélessávú Hírközlés és Villamosságtan Tanszék
    4. Instructors




    Péter Horváth

    assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    Tamás Barbarics

    assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    Szabolcs  Gyimóthy

    assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    József Pávó

    full professor

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    Sándor Bilicz

    assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    5. Required knowledge

    Mathematics: differential and integral calculus, linear algebra and matrix calculus, complex numbers, first order differential equations. The credit of Mathematics A1 is mandatory

    6. Pre-requisites
    TárgyEredmény( "BMETE90AX00" , "jegy" , _ ) >= 2

    ÉS NEM ( TárgyEredmény( "BMEVIHVA109", "jegy" , _ ) >= 2
    VAGY TárgyEredmény("BMEVIHVA109", "FELVETEL", AktualisFelev()) > 0)

    ÉS (Training.Code=("5N-A7") VAGY Training.Code=("5N-A7H") VAGY Training.Code=("5NAA7"))

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rendek grafikus formában itt láthatók.


    7. Objectives, learning outcomes and obtained knowledge

    The objective of the two semester Signals and Systems classes is to introduce the basic concepts of signal and system, and to provide computational methodologies to continuous and discrete time systems. The first semester (Signals and Systems I) presents the time domain and the sinusoidal steady state analysis. The examples refer to continuous systems represented by Kirchoff type electric circuits. The principles to formulate the models and the methods to solve the resulting equations are discussed.

    The students fulfilling the requirements of this class will be able to apply the methodologies of system and network analysis in the time domain and in the frequency domain in case of sinusoidal excitation.

    8. Synopsis

    1-2. classes (1. week)

    Basic concepts: signals, systems and circuits. System properties: linearity, causality and time – invariance. Input – output relationship. Systems represented with electric circuits. Two poles. Kirchhoff type systems.


    3-4. classes (2. week)

    The full set of circuit equations. Series resistors and voltage division. Parallel resistors and current division. The principle of superposition. Node voltage analysis. Mesh current analysis. Source transformations. Maximum power transfer.


    5-6. classes (3. week)

    Coupled two poles: ideal transformer, controlled sources, ideal operational amplifier and gyrator.


    7-8. classes (4. week)

    Two-Port Resistive Networks. Equations of the Two-Port Networks. Reciprocity, symmetry and passivity of the Two-Ports. Equivalent circuits of reciprocal and nonreciprocal Two-Ports. Two-Ports terminated with Two-Poles. Calculation of the input and transfer characteristics.


    9-10. classes (5. week)

    Dynamic circuits. Capacitors, inductors, coupled capacitors and coupled inductors. Circuit equations. Regularity. Initial conditions. State variables. The normal form of the continuous time state equations. Generation of the continuous time state equations from the full set of circuit equations.


    11-13. classes (6-7. week)

    Solution of the continuous time state equations. The natural response and the forced response. First-order circuits. The time constant of first-order circuits. Sequential switching. Second and higher order dynamic systems and circuits. Higher order dynamic circuits with complex or equal eigenvalues. The concept of stability.


    14-16. classes (7-8. week)

    Step function and Dirac delta function. Generalized derivatives. The Step response and Impulse response of dynamic systems. Calculation of linear time invariant dynamic systems response to arbitrary input with convolution. The concept of bounded-input, bounded-output (BIBO) stability.


    17-20. classes (9-10. week)

    Sinusoidal steady state analysis. Phasor notation. The concept of impedances. The methods of circuit analysis with phasors (node voltage and mesh current analysis, source transformations). Resonant circuits, quality factor, Wheatstone-bridge. Coupled inductors (the model of a transformer). Phasor diagrams. AC Steady state power analysis: averaged power, reactive power, complex power, apparent power, power factor. Maximum power transfer.


    21-22. classes (11. week)

    The concept of the Network Function. Logarithmic units and quantities. The Bode- and the Nyquist- diagram. Two-Port Network equations in frequency domain. The scattering parameters of Two-Ports. Interconnection of Two-Ports and equivalent equations.


    23-26. classes (12-13. week)

    Periodic steady state analysis. Fourier series of periodic signals. The trigonometric, the engineering and the complex Fourier series. Calculation of systems response to periodic excitation. Properties of periodic waveforms: definitions and relations to Fourier series. Periodic steady state power analysis. Averaged power calculations based on Fourier series.


    27-28. classes (14. week)

    Summary, auxiliary.

    10. Assessment

    - 3 homeworks

    - 3 small quizzes

    - midterm test

    - exam 

    11. Recaps An unsuccessful midterm exam can be repeated once according to the rules given in the BME TVSz. Homeworks and small quizzes cannot be repeated. Taking a second repeated midterm test is not possible.
    12. Consultations

    As negotiated with the instructor(s). Consultations before the exams are being held on the preceding workday.

    13. References, textbooks and resources

    Dr. Fodor György: Hálózatok és rendszerek. (55064)

    Dr. Fodor György (szerk.): Villamosságtan példatár. (TKV 44555)


    Simonyi Károly: Villamosságtan. Akadémiai Kiadó, 1983

    Dr. Bokor Árpád (szerk.) Hálózatok és rendszerek. Számítógépes gyakorlatok (55042)

    14. Required learning hours and assignment

    Kontakt óra


    Preparation for lectures


    Preparation for the exercises



    Preparation for labs


    Preparation for the midterm


    Independent study of written course material


    Homework preparation


    Exam preparation




    15. Syllabus prepared by




    Dr. Szabolcs Gyimóthy

    Assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    Dr. József Pávó

    Full professor

    Dept. of Broadband Infocommunications and Electromagnetic Theory

    Dr. Péter Horváth

    Assoc. prof.

    Dept. of Broadband Infocommunications and Electromagnetic Theory