Signal Representation

The book focuses on the mathematical description of typical signals in communications engineering, which can alternatively be in the time or frequency domain.

• The spectral transformations which are exclusively applicable to causal signals and systems are not treated in this book
      (for example:  Laplace transform,  Z-transform,  Hilbert transform).
• Here we refer to the book $\text{Linear and Time-Invariant Systems}$ .

The subject matter corresponds to a  $\text{lecture with two semester hours per week (SWS) and one additional SWS exercise}$.

Here is a table of contents based on the  $\text{five main chapters}$  with a total of  $\text{19 individual chapters}$.

Contents

Basic Terms of Communications Engineering

• Principles of Communication
• Signal Classification
• Calculating With Complex Numbers

Periodic Signals

• General Description
• Direct Current Signal - Limit Case of a Periodic Signal
• Harmonic Oscillation
• Fourier Series

Aperiodic Signals - Pulses

• Fourier Transform and Its Inverse
• Special Cases of Pulses
• Fourier Transform Theorems
• The Convolution Theorem and Operation

Band-Pass Signals

• Differences and Similarities of LP and BP Signals
• Analytical Signal and Its Spectral Function
• Equivalent Low-Pass Signal and Its Spectral Function

Time and Frequency-Discrete Signal Representation

• Time Discrete Signal Representation
• Discrete Fourier Transform (DFT)
• Possible Errors When Using DFT
• Spectrum Analysis
• Fast Fourier Transform (FFT)

In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material:

• $\text{Exercises}$
• $\text{Learning videos}$
• $\text{New designed Applets}$  (based on HTML5 and JavaScript, also executable on smartphones)

$\text{Further links:}$

$(1)$    $\text{Recommended reading for the book}$

$(2)$    $\text{General notes about the book}$   (authors,  other participants,  materials as a starting point for the book,  list of sources)