5.3 Methods for Analysis and Processing of Discrete Biosignals

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FIR-LP

Sampling points

ideal LP

Fig. 5.45: Frequency-Samples of an ideal low-pass filter for synthesis of a 15th order FIR filter and

associated transfer function

time t / ms

g(t)

Fig. 5.46: Impulse response of an FIR low-pass 15. order according to Figure 5.45.

|G(0)| here corresponds to the magnitude of the frequency response at frequency

f = 0 Hz, |G(1)| to the magnitude of the frequency response at 66.67 Hz, |G(3)| at

133.33 Hz etc.

With these values, the impulse response g(n) of the FIR filter is now calculated

according to Equation 5.115 by inverse discrete Fourier transformation, and we obtain:

g(0) = g(14) = −0.0498159 ;

g(1) = g(13) = 0.0412023 ;

g(2) = g(12) = 0.0666667 ;

g(3) = g(11) = −0.0364879 ;

g(4) = g(10) = −0.1078689 ;

g(5) = g(9) = 0.0340780 ;

g(6) = g(8) = 0.3188924 ;

g(7) = 0.4666667 .

Finally, from the now determined impulse response of the FIR filter, the associated

values of the filter coefficients can be determined, which are, after all, equal to the

values of the impulse response ci = g(i) (cf. Figure 5.46).