Biomedical Engineering Reference
In-Depth Information
The Chebyshev gives a much steeper roll-off, but passband ripple makes it unsuitable
for audio systems. It is superior for applications in which the passband includes only one
frequency of interest (e.g., the derivation of a sine wave from a square wave, by filtering
out the harmonics).
The Bessel filter gives a constant propagation delay across the input frequency spec-
trum. Therefore, applying a square wave (consisting of a fundamental and many harmon-
ics) to the input of a Bessel filter yields an output square wave with no overshoot (all
the frequencies are delayed by the same amount). Other filters delay the harmonics by
different amounts, resulting in an overshoot on the output waveform.
The elliptical filter is more complicated than the other types, but because it has the
steepest roll-off it is often used in antialiasing filters.
5.4.2.1 Low-Pass Filter
A low-pass filter is a filter that passes low frequencies and attenuates high frequencies,
as shown in Figure 5-18. The amplitude response of a low-pass filter is flat from DC or
near DC to a point where it begins to roll off. A standard reference point for this roll-off is
the point where the amplitude has decreased by 3 dB, to 70.7% of its original amplitude
(volts).
The region from around DC to the point where the amplitude is down 3 dB is defined
as the passband of the filter. The range of frequencies from the 3 dB point to infinity is
defined as the stopband of the filter.
The amplitude of the filter response at ten times the 3 dB frequency is attenuated a
total of 20 dB for a single-pole filter and a total of 40 dB for a two-pole Butterworth filter.
At higher frequencies, the amplitude continues to roll off in a linear fashion, where the
slope of the line is
−
20 dB per decade (10 times frequency) for a single-pole filter and
−
40 dB per decade for a two-pole filter.
FIGURE 5-18
Frequency response
of Butterworth
low-pass filters.
