Signal Representation

Brief summary

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)

Exercises and multimedia modules

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

$(1)$    $\text{Exercises}$

$(2)$    $\text{Learning videos}$

$(3)$    $\text{Applets}$ 

Further links

$(4)$    $\text{Bibliography for the book}$

$(5)$    $\text{General notes about the book}$   $($authors,  other participants,  materials as a starting point for the book,  references$)$