Reference Section
•
85
Chapter 5
Butterworth Filter
This is the filter of choice when analyzing signals in the frequency domain,
e.g.
when making power spectra for noise analysis. The Butterworth filter has
a sharp, smooth roll-off in the frequency domain, but introduces an overshoot
and “ringing” appearance to step signals in the time domain.
Choosing the Cutoff Frequency
In practice, there are two important considerations when selecting the filter cutoff
frequency.
Aliasing
If the digitizing interface samples at 2 kHz, for example, any noise in the
sampled signal that has a frequency greater than 1 kHz will appear in the
digitized trace as extra noise in the range 0 to 1 kHz. In other words, higher-
frequency noise (>1 kHz) will appear under the
alias
of lower-frequency noise
(<1 kHz). This error is called aliasing. A fundamental principle of signal
analysis, called the Nyquist Principle, therefore states that, in order to avoid
aliasing, the digitizing frequency (f
d
) should be at least twice the filter cutoff
frequency (f
c
):
f
d
≥
2f
c
The minimum permissible digitizing frequency (exactly twice f
c
) is called the
Nyquist frequency
. In practice, it is better to sample at two or more times the
Nyquist frequency. Thus, f
d
= 5f
c
is commonly used. This means that, if the
MultiClamp 700A filter is set at 5 kHz, your interface should be capable of
digitizing at 25 kHz.
