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 LNTwww book  "Linear and Time-Invariant Systems".

Here first a  content overview  on the basis of the  five main chapters  with a total of  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 Low-Pass and Band-Pass Signals
• Analytical Signal and its Spectral Function
• Equivalent Low-Pass Signal and its Spectral Function

Time-Discrete and Frequency-Discrete Signal Representation

• Discrete-Time 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 exercises and multimedia modules on this topic,  which could help to clarify the teaching material:

• $\text{Exercises}$

• $\text{Learning videos}$

• $\text{Applets}$ 

$\text{Further links:}$

$(1)$    $\text{Bibliography for the book}$

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