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5 Methods for Discrete Processing and Analysis of Biosignals

ECG original

ECG constructed

time t / s

Fig. 5.30: Digital wavelet-transformation and reconstruction of an ECG signal up to the 3rd level:

the calculation was done with the help of the Matlab-functions wavedec() and waverec() using the

wavelet sym4.

In Matlab, this decomposition can be performed using the function wavedec() and the

reconstruction using the function waverec(). Both are available in the (chargeable)

toolbox wavelet from MathWorks. Alternatively, you can use the toolbox wavelet from

Scilab, which is offered as a free software package. As an application example, Fig-

ure 5.30 shows the decomposition of an ECG signal using the wavelet Sym4.

5.3.4 Discrete Linear Time-Invariant Systems and Digital Filters

In the previous chapters, the concept of system has been used repeatedly to describe

methods of signal processing; in the following section, the basics of system theory

will be further explored. Since signals are nowadays usually processed in the discrete,

we will dispense with an introduction of continuous systems and discuss the discrete

systems that are relevant in practice. The following explanations only apply to linear

time-invariant systems (LTI systems), i.e. the principle of linear superposition of sig-