134

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4 Measurement of Biosignals and Analog Signal Processing

Fig. 4.41: RLC-Potency-Filter-Bandstop 2. orders (left) and associated frequency response (calcula-

tion with LTspice, right).

Fig. 4.42: ECG with 50 Hz mains hum before and after filtering with a potency-band block 2nd order.

4.5.1.3 Chebyshev Filter

In a Chebyshev-filter, for the characteristic function K(Ω) a Chebyshev-polynomial

indexChebyshev-polynomial Tn(Ω) weighted by a factor ϵ is used.

K(Ω) = ϵ ⋅Tn(Ω)

(4.44)

is chosen, with

Tn(Ω) = cos(n ⋅arccos(Ω))

for |Ω| < 1 Tn(Ω)= cosh(n ⋅arccosh(Ω))

for |Ω| > 1 .

(4.45)

The value n in turn determines the order of filtering. Examples for Tn(Ω) are:

T1(Ω) = Ω(like power filter) ,

T2(Ω) = −1 + 2 Ω² ,

T3(Ω) = −3 Ω+ 4 Ω³ ,

T4(Ω) = 1 −8 Ω² + 8 Ω⁴ ,

T5(Ω) = 5 Ω−20 Ω³ + 16 Ω⁵ .

(4.46)