Division Note:

For a Butterworth filter the attenuation is given by:

$$A^2\frac{\mathrm{=\; 1}}{\mathrm{1\; +}{\left(f_{\max }{\mathrm{/\; f}}_0\right)}^{\mathrm{2n}}}{\mathrm{and\; A}}^2\frac{\mathrm{=\; 1}}{\mathrm{1\; +}{\left(f_N{\mathrm{/\; f}}_0\right)}^{\mathrm{2n}}}$$

where:

• n is the filter order

• f_max is the relevant frequency range (30 Hz)

• f_o is the filter cut-off frequency

• f_N is the Nyquist or cut-off frequency.

For a fourth order filter

for A = 0,9995:

• f_o = 2,37 × f_max

for A = 0,0005:

• f_S, = 2 × (6,69 × f_o), where f_S, is the sampling frequency = 2 × f_N.