# Signal theory

The **signal theory** deals with the transmission of signals over different physical media and examined the impact that these media and the environment have on the signals. For this purpose, mainly electrical current is currently used, so that signal theory is mostly viewed as a branch of electrical engineering . Many signal-theoretic concepts also apply when using other information carriers such as light ( optical signal transmission ).

## Signals

For data transmission, the raw data is converted into a form that can be sent via the selected transport medium. This can be done analogously by z. B. the current generated by a microphone is transmitted directly to the amplifier via a cable , or digitally , whereby the data is first sampled and converted into discrete (often binary coded) values, which are then sent across the medium as current surges or voltages of different levels .

Signals can be classified according to different aspects. A distinction is made between *periodic* (repeating at regular intervals) and *non-periodic* signals or *power* signals (with finite electrical power and arithmetically infinite energy) and *energy* signals (with finite energy and without transmitted power). In the case of signals that represent specific data, a distinction is made in practice between RZ and NRZ signals depending on the coding used .

For system analysis, some special signals can be used, some of which cannot be implemented in practice or can only be implemented in a rough approximation, such as the step function or the Dirac function .

## Systems

If signals generated in this way are transmitted over a conductor, this acts with its ohmic resistance , its capacitance and its inductance on the signal, so that it changes through the transmission. In modern miniaturized circuits in particular, signals on neighboring lines can also change the signal due to crosstalk . The mathematical description of these processes is also the subject of signal theory. In doing so, one generally looks at four poles . These are systems with two pairs of connections, an input to which you apply an input signal and an output to which you receive a (usually modified) output signal. A quadrupole can therefore be a simple line or a whole network of different components.

The most important properties of a quadrupole for signal transmission are the transient response and the frequency response . The impulse response , which is the system response to the Dirac impulse , provides information about the frequency response . The step response , i.e. the system response to a step at the input, provides information about the transient response .

According to their properties, one differentiates between the following types of systems:

- In
*linear systems*, the true principle of superposition with,*non-linear systems*do not. - In
*causal systems*, a system reaction can only be determined at the output when an input signal is applied (*non-causal systems*, in which the reaction occurs before the excitation, cannot be implemented, but can only be viewed as a mathematical model). -
*Time-invariant systems*do not change their properties (at least during the period under consideration). If the same input signal is applied repeatedly, the system reaction will always be the same.

In practice, therefore, *linear time-invariant systems* or LTI systems (LTI: linear time invariant) are of particular importance . There is no explicit requirement that the systems should be causal, since all real systems are temporally causal. Most of the standard electronic circuits consisting of resistors, capacitors, coils and transistors represent approximately LTI systems.

## Mathematical tools

- For analysis purposes, signals are usually expressed as functions that describe the signal amplitude as a function of time.
- The properties of lines can be modeled with differential equations .
- Periodic signals can be displayed as the sum of several harmonic signals using the Fourier series display .
- The Fourier transformation enables the analysis of signal spectra .
- The convolution allows the calculation of the output signal of a linear system with a known impulse response for any input signals.

## literature

- Otto Mildenberger:
*Systems and signal theory.*Basics for information technology studies, 3rd revised and expanded edition, Vieweg Verlag, Wiesbaden 1989, ISBN 978-3-528-13039-3 . - Alfred Mertins:
*Signal Theory.*Basics of signal description, 3rd edition, Springer Verlag, Berlin / Heidelberg 2013, ISBN 978-3-8348-1394-7 .

## See also

- Quadrupole theory
- Source coding
- Channel coding
- Line code
- Modulation (technology)
- digital signal processing

## Web links

- Literature on signal theory in the catalog of the German National Library
- Signal Theory (accessed July 26, 2018)
- Acoustics and vibration measurement technology (accessed on July 26, 2018)