
Instructor: Prof. Dr.Ing. Werner HenkelThis course offers a comprehensive exploration of signals and systems which is the key knowledge for almost all electrical engineering tasks. Continuoustime and discretetime concepts/methods are developed in parallel, highlighting their similarities and differences. Introductory treatments of the applications of these basic methods in such areas as filtering, communication, sampling, discretetime processing of continuoustime signals, and feedback, will be discussed.
To this end, all the major linear transforms are introduced, like Fourier series, Fourier transform, Laplace transform, unilateral Laplace transform, Discrete Fourier Transform, diagonalization of a convolutional Toeplitz matrix (eigenvalues/eigenvectors of a Toeplitz matrix), and ztransform. Additionally, Hilbert transform, delay and group delay, stability and minimum phase are discussed. Furthermore, AM and FM modulation is shortly introduced.
Lecture at Jacobs University. [Campusnet link]

The courses uses the following text book:
Alan V. Oppenheim, Alan S. Willsky, and S. Hamid Nawab, Signals and Systems, Pearson, 2nd ed., ISBN 9789332550230
 Energy vs. power, even and odd signals, special functions, such as complex exponentials, cos, sin, Euler’s formula, discretetime exponentials, unti impulse and unit step function (time continuous and timediscrete)
 Continuous and discretetime systems, memory, causality, BIBO stability, time invariance, linearity
 Convolution in continuous and discrete time, deconvolution, causality, linear differential equation for exemplary RL or RC circuit
 Fourier series, real and complex form, response of LTI system inside Fourier series
 Fourier transform
 Properties of the Fourier transform
 Excursion to cascade structure and analog filter design, introducing characteristic impedance for twoports and transmission lines
 Allpass
 Inverse Fourier transform, especially partial fraction expansion.
 Function of homogeneous and particular solutions of a differential equation regarding the network and the source signal, discussion of poles and zeros
 Hilbert transform
 Sampling theorem
 Discretetime Fourier transform, linking to ztransform, convolution as product of polynomials
 Laplace transform and linking to ztransform.
 Convergence fo discretetime Fourier transform, Fourier transform of periodic signals, properties of discretetime Fourier transform
 Excursion to analog modulation, AM, PM, FM (matching timing of Signals and Systems lab)
 Time and freqeuncy characterization of systems, especially delay and group delay
 Laplace transform in detail with region of convergence (RoC), exemplary functions and networks, inverse transform with partial fraction expansion, allpass, minimum phase property, mentioning Heaviside extension (residue theorem), properties of the Laplace transform
 Links between homogeneous solution of a differential equation and the poles of the transfer function, initial and final value theorems
 Unilateral (onesided) Laplace transform, transfer for circuit elements including their initial conditions, i.e., initial charges of a capacitor or initial currents at an inductor
 Introduction to z transform, RoC, transforms of zeros and poles between Laplace and z planes
 Convolution in matrix description, eigenvectors and eigenvalues of a convolutional Toeplitz matrix, diagonalization of a Toeplitz matrix by Fourier matrices
