204

|

5 Methods for Discrete Processing and Analysis of Biosignals

Fig. 5.43: The range of the impulse response of the ideal filter from 0 to 8 ms "cut-out" with the rect-

angular window w(t) according to Figure 5.42 and the samples taken therein ci with i = 0 to N = 8.

ideal low pass

f / Hz

G(f)

Fig. 5.44: Magnitude frequency response of the 8th order FIR filter whose filter coefficients ci have

been calculated according to Equation 5.109 after the values of the impulse response of an ideal

low-pass filter in the time interval from 0 to 8 ms.

As a rule, a considerably higher filter order (e.g. n = 30) is necessary for this. The

favourable behaviour of the FIR filter with regard to the possible constant group delay

and the stability due to the finite impulse response must therefore be bought by a

larger filter order.

Direct Discrete-Time Synthesis Using the Frequency Sampling Method

Instead of the values of the impulse response, the transfer function can also be chosen

for approximation. In the frequency sampling method the desired frequency response

is therefore sampled at regular intervals and can be interpreted as the spectrum of a

periodic signal, which is discrete in the frequency range and only has a value in mul-

tiples of the fundamental frequency (harmonics). Furthermore, in the time domain

the periodic signal is sampled with the sampling interval Ta, whereby the frequency