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

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    Signals and Systems 2

    A tantárgy neve magyarul / Name of the subject in Hungarian: Jelek és rendszerek 2

    Last updated: 2024. február 19.

    Budapest University of Technology and Economics
    Faculty of Electrical Engineering and Informatics
    Course ID Semester Assessment Credit Tantárgyfélév
    VIHVAB02 3 3/3/0/v 6  
    3. Course coordinator and department dr. Horváth Péter,
    Web page of the course edu.vik.bme.hu
    4. Instructors

    Barbarics Tamás, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék

    Bilicz Sándor, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék

    Gyimóthy Szabolcs, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék

    Horváth Péter, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék

    Pávó József, professor, Szélessávú Hírközlés és Villamosságtan Tanszék

    5. Required knowledge Calculus, basics of linear algebra and matrix algebra, complex numbers, first-order differential equations
    6. Pre-requisites
    Kötelező:
    ((TárgyTeljesítve_Képzésen("BMEVIHVAA03") VAGY
    TárgyTeljesítve_Képzésen("BMEVIHVAA00") ) ÉS


    NEM ( TárgyTeljesítve("BMEVIHVAB01") ) ÉS

    (Kepzes("5N-A7") VAGY
    Kepzes("5N-A7H") VAGY
    Kepzes("5NAA7")) )

    VAGY

    ((Training.Code=("5NAA7")
    VAGY
    Training.Code=("5NAA8"))
    ÉS
    Felevstatusz((Term))="Aktív (Nemzetközi program)")

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

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

    Ajánlott:
    Mandatory: Signals and Systems 1 (VIHVAA00)
    7. Objectives, learning outcomes and obtained knowledge

    This subject is a direct follow-up of Signals and Systems 1. It aims to lay the foundations for analyzing continuous-time systems in the frequency and complex frequency domains. It presents the different means of system characterization and their relationships. Subsequently, discrete-time signals and systems are analyzed in time, frequency, and z-domains. We establish connections between continuous-time and discrete-time signals and systems. We also introduce the basics of distributed-element network modeling.

    8. Synopsis
    Review (1 lecture). Sinusoidal steady-state analysis, complex amplitude, frequency response. Fourier series of periodic continuous-time signals.

    Analysis in the frequency domain (2 lectures). Fourier transform. Properties and theorems of the transform. Inverse transform. Systems analysis; frequency response. Bandwidth of a signal. Bandwidth of a linear, time-invariant system, ideal lowpass filter, tolerance schemes. Distortion-less signal transfer and its requirements.

    Analysis in the complex frequency domain (3 lectures). The Laplace transform. Properties and theorems of the transform; relationship to the Fourier transform. System analysis, transfer function. Pole-zero-map. Network analysis: impedance operator, transient analysis.
     
    Characterization of linear systems (2 lectures). Relationships between the systems functions. Stability analysis. Special systems: memoryless amplifier, integrator, differentiator. Allpass and minimum phase systems, cascade decompositions.
     
    Discrete-time (DT) signals, systems and networks (6 lectures). Basic concepts, elementary signals. DT signal flow graphs. Time-domain analysis: state-space description, asymptotic stability. Difference equation of the system. The solution to difference equations by step-by-step substitution. Impulse response, convolution. DT sinusoidal signals, complex amplitude. DT frequency response. Fourier series of periodic DT signals (DFT). Discrete-time Fourier transform (DTFT). DT complex frequency domain representation, the z transform. System analysis using the z transform. DT transfer function. Characterization of DT linear systems, systems functions. Special DT systems. 

    Sampling and reconstruction. Discrete-time simulation of continuous systems (3 lectures). The sampling theorem, aliasing, undersampling. Signal reconstruction: zero-order hold, first-order hold, ideal lowpass filter. The goals of discrete simulation, perfect simulator. Simulation based on the impulse response and the transfer function, respectively. Error-free simulation for a given input signal.
     
    Distributed networks, wave and scattering parameters (3 lectures). The concept and applications of distributed networks. The telegrapher's equations. Sinusoidal steady state, phasor representation. The Helmholtz equation and its solution. Propagating wave, propagation coefficient, wave impedance, phase velocity. Terminated transmission lines: reflection coefficient, ABCD matrix. Two-ports, wave parameters, and scattering parameters.
     
    The practice sessions consist of solutions to problems. We also demonstrate the capabilities of Matlab/Octave in solving typical problems (solution of systems of linear equations, matrix eigenalues, plotting). 
    9. Method of instruction 3 hours/week lecture and 3 hours/week problem solving exercise
    10. Assessment
    During the semester:
     
    (1) Every student gets assigned a 3-part homework to be solved independently. The parts should be turned in according to the schedule published by the Faculty. Solutions for each part will be rewarded by 0...5 points. Late turn-ins will be awarded by 0 points. (2) There are three small tests throughout the semester, graded to 0...5 points each. Tests not taken can not be repeated, and 0 points will be assigned automatically. (3) One extensive written test is held on the date given in the Faculty schedule, which is graded between 0 and 25 points. (4) Standard university rules apply to the presence requirements during the contact classes. 
     
    The signature is awarded as follows: take the grades of the two better small tests (st1, st2) and the average grade of the two best homework parts (hwa), and the grade of the large test (lt), and add them. GP = (st1 + st2 + hwa + lt). The signature is awarded if and only if GP >= 20 and lt >= 10.
     
    Examinations:
     
    (1) Only students with valid signatures are admitted to the exam. (2) The exam contains a written part and an oral part. The written part is scored between 0...60 points. This score translates to the grade as follows. 0...29 points: 1 (immediate fail); 30...38 points: 2; 39...44 points: 3; 45...50 points: 4; 51...60 points: 5. The oral part is obligatory, and only students who achieve at least 30 points will be admitted. The grade of the written part forms the basis for the final note, which will be corrected according to the performance during the oral exam. Most often, the final grade differs at most by +/- 1 grade, however, in exceptional cases, a larger correction is also possible. The oral exam covers the topics of the entire course.
    11. Recaps
    An unsuccessful midterm test can be re-taken according to the standard university rules. It is not possible to recap the homeworks and the small mid-semester tests.
    12. Consultations
    In-person discussion with the lecturer as advertised on the course page. Consultations are held on the last workday before the exams.
    13. References, textbooks and resources Standard university textbooks on signals and systems.
    14. Required learning hours and assignment
    Kontakt óra84
    Félévközi készülés órákra28
    Felkészülés zárthelyire5
    Házi feladat elkészítése15
    Kijelölt írásos tananyag elsajátítása0
    Vizsgafelkészülés48
    Összesen180
    15. Syllabus prepared by

    Pávó József, professor, Szélessávú Hírközlés és Villamosságtan Tanszék

    Gyimóthy Szabolcs, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék

    Horváth Péter, assoc. prof., Szélessávú Hírközlés és Villamosságtan Tanszék