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Signals and Systems 1

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

Last updated: 2023. január 12.

Dept. of Broadband Infocommunications and Electromagnetic Theory

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

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

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.

Basic concepts. The concept of signals, systems, networks, and their classification. The system represented by a network. Fundamentals of electrical networks. Properties of two-poles. Kirchhoff's laws. The fundamental system of loops and cuts. Tellegen's theorem. The complete system of network equations.

Analysis of resistive networks. Concept of resistive networks and their analysis; regularity of the network. Analysis methods: superposition principle, method of nodal voltages, method of mesh currents. Coupled two-poles, characteristics, and their treatment in network calculation. Equivalent circuits of two-pole networks: resultant resistance, Thévenin and Norton generators. Maximum power transfer. Linear two-port networks. Reciprocity, symmetry, passivity. Equivalent circuits of two-port networks. Input and transfer characteristics of terminated two-ports.

Analysis of dynamic networks. Concept of dynamic networks and state variables. State-space representation of electrical networks. Initial conditions. Regularity. Sequential switching in first and second order dynamic networks. The natural response and the forced response. Time constant. Step function and Dirac delta function. Step response and impulse response. Generalized derivative. Convolution. Stability concepts (BIBO and asymptotic stability).

Time-harmonic steady state. Concept of time-harmonic steady state and its physical meaning. Phasor representation of sinusoidal signals; operations on phasors. Network equations with phasors. Impedance. Network analysis methods. Phasor diagrams. Transfer ratio and frequency response. Bode plot. Logarithmic scale and unit. Powers in time-harmonic steady state: instantaneous, active, reactive, complex power, power factor. Maximum power transfer.

Nonlinear networks. Resistive nonlinerities. Determination of the operating point. Solvability of nonlinear network equations. Introduction to numerical solution techniques. Linearization around the operating point (small-signal analysis). Dynamic resistance. Small-signal analysis of nonlinear two-ports.

Periodic steady-state. Definition and mean values of periodic signals. Fourier polynomial and Fourier series. Mathematical and engineering real form, complex form of the Fourier series. Convergence properties. System analysis utilizing Fourier series. Calculation of active power, Parseval's theorem.

During the term:

(1) Every participant obtains a 3-part homework assignment on the third week. The homework must be completed without assistance. Turn-in weeks are as indicated on the cover page. The solutions will be graded 0...5 points for each part. Zero points will be awarded for late turn-in or missed turn-in.

(2) Three small written tests are held for 0...5 points each. Missed tests cannot be supplemented.

(3) One midterm test is held, where 0...25 points can be earned.(4) The general university rules apply for course attendance.The participant will be admitted to the exam iff the following achievements are completed:

Sum the point values of the two best small tests (test1, test2), the average value of the two best homework parts (hw) and the midterm points (md): pv = (test1 + test2 + hw + md). The student obtains the signature for admission to the exam if pv is at least 20 AND at least 10 points were obtained for the midterm test.

Exam:(1) Admission the the exam is only possible if the signature has been obtained during the semester.(2) The exam consist of written and oral parts. A maximum of 60 points can be awarded in the written test (pe). The written part is graded as follows: up to 29 points: 1, from 30 points: 2, from 39 points: 3, from 45 points: 4, from 51 points: 5.

Participants who have obtained at least a grade of 2 participate in the oral exam part. The final exam grade is being decided by the examiner, taking into account the grade obtained during the written part (in most cases, a +/- 1 grade correction is customary, however, deviations are possible in some cases). Preliminary exam: N/A

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

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

Recommended:

Simonyi Károly: Villamosságtan. Akadémiai Kiadó, 1983

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