198

|

5 Methods for Discrete Processing and Analysis of Biosignals

V1

C1

1n

R1

800k

magnitude / dB

phase / °

magnitude

phase

f / Hz

Fig. 5.39: Transfer function G(f)RC = Ua(f)/Ue(f) of a 1st-order RC low-pass filter (calculation with

LTspice).

Fig. 5.40: Transfer function G(f)RC of the 1st order digital low pass generated by the impulse invari-

ance method from the analogue low pass according to Figure 5.39.

a digital low-pass filter with the same cut-off frequency and a sampling frequency of

1 kHz according to the pulse invariance method.

For the corresponding impulse response gan(t) = gRC(t) then follows.

gRC(t) = A1 e^p1t

mit A1 = p1 = −ωg = −1/RC

and thus according to Equation 5.92 for the transfer function of the digital filter to be

realised:

GRC(z) = Ta

A1

1 −e^p1Taz^{−1 = Ta}

A1z

z −e^{p1Ta = 1.26 ⋅z}

z + 0.28 ^.

The Bilinear Transformation Procedure

If one looks at the introductory example according to Figure 5.40, it is noticeable that

at half the sampling frequency of 1 kHz/2 = 500 Hz the signal is only attenuated by