7. Objectives, learning outcomes and obtained knowledge
The course is a follow-up of Signals and Systems I. It provides the foundations of analysis methods for continuous time systems in the frequency and complex frequency domains. Furthermore, it presents various system description methods and establishes the connections between these representations.

It also deals with analysis methods of discrete time signals and systems both in time, frequency and z domains. The link between continuous and discrete systems is presented by dealing with discrete approximation of

continuous time systems, and the basics of signal sampling and reconstruction are shown. The last part introduces analysis techniques for continuous time nonlinear circuits and systems.

8. Synopsis
Weeks 1-3: Spectral decomposition of signals. Definition and properties of the Fourier transform. Spectra of rectangular pulses, Dirac pulse, unit step, exponential pulse and periodic signals. System analysis using Fourier transforms: bandwidth of a signal and a system, distortionless transmission. Bode diagrams using asymptotic approximations. Energy spectrum, theorem of Parseval, energy transfer characteristics. Simple examples for signal modulation and demodulation.

Weeks 3-4: Analysis in the complex frequency domain. Laplace transform and its inverse. Theorems of the transform, transforms of some important signals. Inverse transform using partial fraction expansion. Analysis of systems in the complex frequency domain. Transfer function, pole-zero maps.

Week 5: Connection between functions describing systems (impulse response, transfer function, transfer characteristics). Special systems: allpass, minimum phase, amplifier, integrator.

Week 6: Signal flow networks. Signal flow graphs. Feedback systems.

Weeks 6-7: Nonlinear networks and systems. Canonical description. State-space description. Canonical equations. Numerical solution methods. The Euler method. Equilibria. Determination of the operating point. Linearization, small signal equivalents. Stability of the operating point.

Week 8: Discrete time systems. Definition of discrete time signals, systems and networks. Components: scaler, summer, delay element.

Week 9: Analysis of discrete time systems in time domain. State-space description and its solution. Eigenvalues. Asymptotic stability. Solution of difference equations by step-by-step substition and analytic solution methods. Impulse response, convolution theorem, BIBO stability.

Week 10: Periodic steady-state of discrete time systems. Sinusoidal excitation, transfer characteristics. Calculation of the sinusoidal response. Periodic excitation: discrete Fourier series. Calculation of the periodic response.

Weeks 10-11: Analysis of discrete time systems in frequency and z domain. Discrete time Fourier transform and its properties. Definition of the z transform. Transfer functions. Step response, transfer characteristics, transfer function) and their interconnections. Special systems: allpass, minimum phase, FIR and IIR systems.

Week 12: Sampling and reconstruction. Description of sampled signals in time and frequency domains. Connections between the spectra of continuous signals and their sampled counterparts. The sampling theorem. Undersampling. Signal reconstruction using ideal the lowpass filter. Reconstruction using zero order hold. Comparison of the methods.

Week 13: Discrete time simulation. The aim of discrete time simulation. Ideal simulator. Simulation of the impulse response using the convolution theorem. Simulation of the transfer function: bilinear transform, tuning of the parameters.

10. Assessment
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