Biomedical Engineering Reference
In-Depth Information
FIGURE 5-19
Comparison among
the frequency
response of
Butterworth,
Chebyshev, and
elliptical low-pass
filters.
The term Butterworth refers to a type of filter response, not a type of filter. It is
sometimes called the maximally flat approximation, because for a response of order
n
the
first (2
n
−
1) derivatives of the gain with respect to frequency are zero at frequency
=
0.
There is no ripple in the passband, and DC gain is maximally flat.
The term Chebyshev also refers to a type of filter response, not a type of filter. It is
sometimes referred to as an equal-ripple approximation. It features superior attenuation
in the stopband at the expense of ripple in the passband, as shown in Figure 5-19. Generally,
the designer will choose a ripple depth of between 0.1 and 3 dB. Chebyshev filter response,
therefore, is not limited to a single value of response.
Elliptical filters have the best roll-off characteristics even for low-order filters, as
shown in Figure 5-19. This characteristic makes them very useful for antialiasing filters
prior to digitization or to remove clock spurs in direct digital synthesis (DDS) systems. In
these applications, the filter zeros are generally placed at multiples of the clock frequency.
Unfortunately, all of these filter types suffer from group delay problems, as shown in
Figure 5-20. However, very few filters are designed with square waves in mind because
most of the time the signals filtered are sine waves, or close enough that the effect of
harmonics can be ignored. If a waveform with high harmonic content is filtered, such as
a square wave, the harmonics can be delayed with respect to the fundamental frequency,
and distortion will result.
To counteract this problem, filters with a Bessel response are used. This response
features flat group delay in the passband, the characteristic of Bessel filters that makes
them valuable to digital designers.
5.4.2.2 High-Pass Filters
A high-pass filter is a filter that passes high frequencies and attenuates low frequencies, as
illustrated in Figure 5-21. The amplitude response of a high-pass filter is flat from infinity
