2.3 Definition and Classification of Signals

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19

ECG - raw signal

time

x-coordinate / Pixel

y-coordinate / Pixel

MRT picture skull

Fig. 2.9: Example of a time-dependent raw ECG signal U(t) (left) and a two-dimensional MRI image

I(x, y) showing a section through a skull (right)

ical quantity of the (physiological) process via a signal transformation relationship. A

detailed description of this can be found in section 4.3.

2.3.2 Periodic, Quasi-Periodic, Aperiodic and Transient Signals

Periodic processes are frequently encountered in science and technology, whereas

exact-periodic are rarely found in living nature due to large natural fluctuations. In

contrast to very precise oscillators in technology, such as those built into quartz

watches, the periodicity of physiological oscillators is often subject to great inac-

curacies. However, these so-called quasi-periodic processes allow the body to adapt

quickly and effectively to changing external conditions and, unlike exact periodic

processes, remain insensitive to unwanted perturbations. In section 3.2 it is shown to

what extent these physiological fluctuations have an impact in the development of

diseases of the heart, and in subsubsection 6.3.1.1 how they can be used for diagnosis.

A mathematical definition for exactly-periodic processes can be found in the har-

monic functions and the angular frequency ω. Exact-periodic processes are, as we will

see in the next section, always deterministic in nature, i.e. completely predictable, and

exist in analytical form. This is also the reason why every exactly-periodic process can

be expressed by an linear combination of harmonic functions in the form of the Fourier

series.

The most important harmonic functions for the analysis of signals are thus trigo-

nometric functions sine and cosine. In science and technology, harmonic functions

are ubiquitous for describing oscillations and waves. The time dependent sine func-

tion is given by:

y(t) = A sin(ω0t + φ0) = A sin(ω0(t + t0)) ,

(2.11)